// fba9dc272a443cf9fdb984676a7732a6a082f4c0
/**
 * @class The built-in Array class.
 * @name Array
 */

/**
 * Creates a new array with the results of calling a provided function on every
 * element in this array. Implemented in Javascript 1.6.
 *
 * @function
 * @name Array.prototype.map
 * @see <a
 * href="https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Array/Map">map</a>
 * documentation.
 * @param {function} f function that produces an element of the new Array from
 * an element of the current one.
 * @param [o] object to use as <tt>this</tt> when executing <tt>f</tt>.
 */
if (!Array.prototype.map) Array.prototype.map = function(f, o) {
  var n = this.length;
  var result = new Array(n);
  for (var i = 0; i < n; i++) {
    if (i in this) {
      result[i] = f.call(o, this[i], i, this);
    }
  }
  return result;
};

/**
 * Creates a new array with all elements that pass the test implemented by the
 * provided function. Implemented in Javascript 1.6.
 *
 * @function
 * @name Array.prototype.filter
 * @see <a
 * href="https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Array/filter">filter</a>
 * documentation.
 * @param {function} f function to test each element of the array.
 * @param [o] object to use as <tt>this</tt> when executing <tt>f</tt>.
 */
if (!Array.prototype.filter) Array.prototype.filter = function(f, o) {
  var n = this.length;
  var result = new Array();
  for (var i = 0; i < n; i++) {
    if (i in this) {
      var v = this[i];
      if (f.call(o, v, i, this)) result.push(v);
    }
  }
  return result;
};

/**
 * Executes a provided function once per array element. Implemented in
 * Javascript 1.6.
 *
 * @function
 * @name Array.prototype.forEach
 * @see <a
 * href="https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Array/ForEach">forEach</a>
 * documentation.
 * @param {function} f function to execute for each element.
 * @param [o] object to use as <tt>this</tt> when executing <tt>f</tt>.
 */
if (!Array.prototype.forEach) Array.prototype.forEach = function(f, o) {
  var n = this.length >>> 0;
  for (var i = 0; i < n; i++) {
    if (i in this) f.call(o, this[i], i, this);
  }
};

/**
 * Apply a function against an accumulator and each value of the array (from
 * left-to-right) as to reduce it to a single value. Implemented in Javascript
 * 1.8.
 *
 * @function
 * @name Array.prototype.reduce
 * @see <a
 * href="https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Array/Reduce">reduce</a>
 * documentation.
 * @param {function} f function to execute on each value in the array.
 * @param [v] object to use as the first argument to the first call of
 * <tt>t</tt>.
 */
if (!Array.prototype.reduce) Array.prototype.reduce = function(f, v) {
  var len = this.length;
  if (!len && (arguments.length == 1)) {
    throw new Error("reduce: empty array, no initial value");
  }

  var i = 0;
  if (arguments.length < 2) {
    while (true) {
      if (i in this) {
        v = this[i++];
        break;
      }
      if (++i >= len) {
        throw new Error("reduce: no values, no initial value");
      }
    }
  }

  for (; i < len; i++) {
    if (i in this) {
      v = f(v, this[i], i, this);
    }
  }
  return v;
};
/**
 * The top-level Protovis namespace. All public methods and fields should be
 * registered on this object. Note that core Protovis source is surrounded by an
 * anonymous function, so any other declared globals will not be visible outside
 * of core methods. This also allows multiple versions of Protovis to coexist,
 * since each version will see their own <tt>pv</tt> namespace.
 *
 * @namespace The top-level Protovis namespace, <tt>pv</tt>.
 */
var pv = {};

/**
 * Protovis major and minor version numbers.
 *
 * @namespace Protovis major and minor version numbers.
 */
pv.version = {
  /**
   * The major version number.
   *
   * @type number
   * @constant
   */
  major: 3,

  /**
   * The minor version number.
   *
   * @type number
   * @constant
   */
  minor: 2
};

/**
 * Returns the passed-in argument, <tt>x</tt>; the identity function. This method
 * is provided for convenience since it is used as the default behavior for a
 * number of property functions.
 *
 * @param x a value.
 * @returns the value <tt>x</tt>.
 */
pv.identity = function(x) { return x; };

/**
 * Returns <tt>this.index</tt>. This method is provided for convenience for use
 * with scales. For example, to color bars by their index, say:
 *
 * <pre>.fillStyle(pv.Colors.category10().by(pv.index))</pre>
 *
 * This method is equivalent to <tt>function() this.index</tt>, but more
 * succinct. Note that the <tt>index</tt> property is also supported for
 * accessor functions with {@link pv.max}, {@link pv.min} and other array
 * utility methods.
 *
 * @see pv.Scale
 * @see pv.Mark#index
 */
pv.index = function() { return this.index; };

/**
 * Returns <tt>this.childIndex</tt>. This method is provided for convenience for
 * use with scales. For example, to color bars by their child index, say:
 *
 * <pre>.fillStyle(pv.Colors.category10().by(pv.child))</pre>
 *
 * This method is equivalent to <tt>function() this.childIndex</tt>, but more
 * succinct.
 *
 * @see pv.Scale
 * @see pv.Mark#childIndex
 */
pv.child = function() { return this.childIndex; };

/**
 * Returns <tt>this.parent.index</tt>. This method is provided for convenience
 * for use with scales. This method is provided for convenience for use with
 * scales. For example, to color bars by their parent index, say:
 *
 * <pre>.fillStyle(pv.Colors.category10().by(pv.parent))</pre>
 *
 * Tthis method is equivalent to <tt>function() this.parent.index</tt>, but more
 * succinct.
 *
 * @see pv.Scale
 * @see pv.Mark#index
 */
pv.parent = function() { return this.parent.index; };

/**
 * Stores the current event. This field is only set within event handlers.
 *
 * @type Event
 * @name pv.event
 */
/**
 * @private Returns a prototype object suitable for extending the given class
 * <tt>f</tt>. Rather than constructing a new instance of <tt>f</tt> to serve as
 * the prototype (which unnecessarily runs the constructor on the created
 * prototype object, potentially polluting it), an anonymous function is
 * generated internally that shares the same prototype:
 *
 * <pre>function g() {}
 * g.prototype = f.prototype;
 * return new g();</pre>
 *
 * For more details, see Douglas Crockford's essay on prototypal inheritance.
 *
 * @param {function} f a constructor.
 * @returns a suitable prototype object.
 * @see Douglas Crockford's essay on <a
 * href="http://javascript.crockford.com/prototypal.html">prototypal
 * inheritance</a>.
 */
pv.extend = function(f) {
  function g() {}
  g.prototype = f.prototype || f;
  return new g();
};

try {
  eval("pv.parse = function(x) x;"); // native support
} catch (e) {

/**
 * @private Parses a Protovis specification, which may use JavaScript 1.8
 * function expresses, replacing those function expressions with proper
 * functions such that the code can be run by a JavaScript 1.6 interpreter. This
 * hack only supports function expressions (using clumsy regular expressions, no
 * less), and not other JavaScript 1.8 features such as let expressions.
 *
 * @param {string} s a Protovis specification (i.e., a string of JavaScript 1.8
 * source code).
 * @returns {string} a conformant JavaScript 1.6 source code.
 */
  pv.parse = function(js) { // hacky regex support
    var re = new RegExp("function\\s*(\\b\\w+)?\\s*\\([^)]*\\)\\s*", "mg"), m, d, i = 0, s = "";
    while (m = re.exec(js)) {
      var j = m.index + m[0].length;
      if (js.charAt(j) != '{') {
        s += js.substring(i, j) + "{return ";
        i = j;
        for (var p = 0; p >= 0 && j < js.length; j++) {
          var c = js.charAt(j);
          switch (c) {
            case '"': case '\'': {
              while (++j < js.length && (d = js.charAt(j)) != c) {
                if (d == '\\') j++;
              }
              break;
            }
            case '[': case '(': p++; break;
            case ']': case ')': p--; break;
            case ';':
            case ',': if (p == 0) p--; break;
          }
        }
        s += pv.parse(js.substring(i, --j)) + ";}";
        i = j;
      }
      re.lastIndex = j;
    }
    s += js.substring(i);
    return s;
  };
}

/**
 * @private Computes the value of the specified CSS property <tt>p</tt> on the
 * specified element <tt>e</tt>.
 *
 * @param {string} p the name of the CSS property.
 * @param e the element on which to compute the CSS property.
 */
pv.css = function(e, p) {
  return window.getComputedStyle
      ? window.getComputedStyle(e, null).getPropertyValue(p)
      : e.currentStyle[p];
};

/**
 * @private Reports the specified error to the JavaScript console. Mozilla only
 * allows logging to the console for privileged code; if the console is
 * unavailable, the alert dialog box is used instead.
 *
 * @param e the exception that triggered the error.
 */
pv.error = function(e) {
  (typeof console == "undefined") ? alert(e) : console.error(e);
};

/**
 * @private Registers the specified listener for events of the specified type on
 * the specified target. For standards-compliant browsers, this method uses
 * <tt>addEventListener</tt>; for Internet Explorer, <tt>attachEvent</tt>.
 *
 * @param target a DOM element.
 * @param {string} type the type of event, such as "click".
 * @param {function} the event handler callback.
 */
pv.listen = function(target, type, listener) {
  listener = pv.listener(listener);
  return target.addEventListener
      ? target.addEventListener(type, listener, false)
      : target.attachEvent("on" + type, listener);
};

/**
 * @private Returns a wrapper for the specified listener function such that the
 * {@link pv.event} is set for the duration of the listener's invocation. The
 * wrapper is cached on the returned function, such that duplicate registrations
 * of the wrapped event handler are ignored.
 *
 * @param {function} f an event handler.
 * @returns {function} the wrapped event handler.
 */
pv.listener = function(f) {
  return f.$listener || (f.$listener = function(e) {
      try {
        pv.event = e;
        return f.call(this, e);
      } finally {
        delete pv.event;
      }
    });
};

/**
 * @private Returns true iff <i>a</i> is an ancestor of <i>e</i>. This is useful
 * for ignoring mouseout and mouseover events that are contained within the
 * target element.
 */
pv.ancestor = function(a, e) {
  while (e) {
    if (e == a) return true;
    e = e.parentNode;
  }
  return false;
};

/** @private Returns a locally-unique positive id. */
pv.id = function() {
  var id = 1; return function() { return id++; };
}();

/** @private Returns a function wrapping the specified constant. */
pv.functor = function(v) {
  return typeof v == "function" ? v : function() { return v; };
};
/*
 * Parses the Protovis specifications on load, allowing the use of JavaScript
 * 1.8 function expressions on browsers that only support JavaScript 1.6.
 *
 * @see pv.parse
 */
pv.listen(window, "load", function() {
   /*
    * Note: in Firefox any variables declared here are visible to the eval'd
    * script below. Even worse, any global variables declared by the script
    * could overwrite local variables here (such as the index, `i`)!  To protect
    * against this, all variables are explicitly scoped on a pv.$ object.
    */
    pv.$ = {i:0, x:document.getElementsByTagName("script")};
    for (; pv.$.i < pv.$.x.length; pv.$.i++) {
      pv.$.s = pv.$.x[pv.$.i];
      if (pv.$.s.type == "text/javascript+protovis") {
        try {
          window.eval(pv.parse(pv.$.s.text));
        } catch (e) {
          pv.error(e);
        }
      }
    }
    delete pv.$;
  });
/**
 * Abstract; see an implementing class.
 *
 * @class Represents an abstract text formatter and parser. A <i>format</i> is a
 * function that converts an object of a given type, such as a <tt>Date</tt>, to
 * a human-readable string representation. The format may also have a
 * {@link #parse} method for converting a string representation back to the
 * given object type.
 *
 * <p>Because formats are themselves functions, they can be used directly as
 * mark properties. For example, if the data associated with a label are dates,
 * a date format can be used as label text:
 *
 * <pre>    .text(pv.Format.date("%m/%d/%y"))</pre>
 *
 * And as with scales, if the format is used in multiple places, it can be
 * convenient to declare it as a global variable and then reference it from the
 * appropriate property functions. For example, if the data has a <tt>date</tt>
 * attribute, and <tt>format</tt> references a given date format:
 *
 * <pre>    .text(function(d) format(d.date))</pre>
 *
 * Similarly, to parse a string into a date:
 *
 * <pre>var date = format.parse("4/30/2010");</pre>
 *
 * Not all format implementations support parsing. See the implementing class
 * for details.
 *
 * @see pv.Format.date
 * @see pv.Format.number
 * @see pv.Format.time
 */
pv.Format = {};

/**
 * Formats the specified object, returning the string representation.
 *
 * @function
 * @name pv.Format.prototype.format
 * @param {object} x the object to format.
 * @returns {string} the formatted string.
 */

/**
 * Parses the specified string, returning the object representation.
 *
 * @function
 * @name pv.Format.prototype.parse
 * @param {string} x the string to parse.
 * @returns {object} the parsed object.
 */

/**
 * @private Given a string that may be used as part of a regular expression,
 * this methods returns an appropriately quoted version of the specified string,
 * with any special characters escaped.
 *
 * @param {string} s a string to quote.
 * @returns {string} the quoted string.
 */
pv.Format.re = function(s) {
  return s.replace(/[\\\^\$\*\+\?\[\]\(\)\.\{\}]/g, "\\$&");
};

/**
 * @private Optionally pads the specified string <i>s</i> so that it is at least
 * <i>n</i> characters long, using the padding character <i>c</i>.
 *
 * @param {string} c the padding character.
 * @param {number} n the minimum string length.
 * @param {string} s the string to pad.
 * @returns {string} the padded string.
 */
pv.Format.pad = function(c, n, s) {
  var m = n - String(s).length;
  return (m < 1) ? s : new Array(m + 1).join(c) + s;
};
/**
 * Constructs a new date format with the specified string pattern.
 *
 * @class The format string is in the same format expected by the
 * <tt>strftime</tt> function in C. The following conversion specifications are
 * supported:<ul>
 *
 * <li>%a - abbreviated weekday name.</li>
 * <li>%A - full weekday name.</li>
 * <li>%b - abbreviated month names.</li>
 * <li>%B - full month names.</li>
 * <li>%c - locale's appropriate date and time.</li>
 * <li>%C - century number.</li>
 * <li>%d - day of month [01,31] (zero padded).</li>
 * <li>%D - same as %m/%d/%y.</li>
 * <li>%e - day of month [ 1,31] (space padded).</li>
 * <li>%h - same as %b.</li>
 * <li>%H - hour (24-hour clock) [00,23] (zero padded).</li>
 * <li>%I - hour (12-hour clock) [01,12] (zero padded).</li>
 * <li>%m - month number [01,12] (zero padded).</li>
 * <li>%M - minute [0,59] (zero padded).</li>
 * <li>%n - newline character.</li>
 * <li>%p - locale's equivalent of a.m. or p.m.</li>
 * <li>%r - same as %I:%M:%S %p.</li>
 * <li>%R - same as %H:%M.</li>
 * <li>%S - second [00,61] (zero padded).</li>
 * <li>%t - tab character.</li>
 * <li>%T - same as %H:%M:%S.</li>
 * <li>%x - same as %m/%d/%y.</li>
 * <li>%X - same as %I:%M:%S %p.</li>
 * <li>%y - year with century [00,99] (zero padded).</li>
 * <li>%Y - year including century.</li>
 * <li>%% - %.</li>
 *
 * </ul>The following conversion specifications are currently <i>unsupported</i>
 * for formatting:<ul>
 *
 * <li>%j - day number [1,366].</li>
 * <li>%u - weekday number [1,7].</li>
 * <li>%U - week number [00,53].</li>
 * <li>%V - week number [01,53].</li>
 * <li>%w - weekday number [0,6].</li>
 * <li>%W - week number [00,53].</li>
 * <li>%Z - timezone name or abbreviation.</li>
 *
 * </ul>In addition, the following conversion specifications are currently
 * <i>unsupported</i> for parsing:<ul>
 *
 * <li>%a - day of week, either abbreviated or full name.</li>
 * <li>%A - same as %a.</li>
 * <li>%c - locale's appropriate date and time.</li>
 * <li>%C - century number.</li>
 * <li>%D - same as %m/%d/%y.</li>
 * <li>%I - hour (12-hour clock) [1,12].</li>
 * <li>%n - any white space.</li>
 * <li>%p - locale's equivalent of a.m. or p.m.</li>
 * <li>%r - same as %I:%M:%S %p.</li>
 * <li>%R - same as %H:%M.</li>
 * <li>%t - same as %n.</li>
 * <li>%T - same as %H:%M:%S.</li>
 * <li>%x - locale's equivalent to %m/%d/%y.</li>
 * <li>%X - locale's equivalent to %I:%M:%S %p.</li>
 *
 * </ul>
 *
 * @see <a
 * href="http://www.opengroup.org/onlinepubs/007908799/xsh/strftime.html">strftime</a>
 * documentation.
 * @see <a
 * href="http://www.opengroup.org/onlinepubs/007908799/xsh/strptime.html">strptime</a>
 * documentation.
 * @extends pv.Format
 * @param {string} pattern the format pattern.
 */
pv.Format.date = function(pattern) {
  var pad = pv.Format.pad;

  /** @private */
  function format(d) {
    return pattern.replace(/%[a-zA-Z0-9]/g, function(s) {
        switch (s) {
          case '%a': return [
              "Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"
            ][d.getDay()];
          case '%A': return [
              "Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday",
              "Saturday"
            ][d.getDay()];
          case '%h':
          case '%b': return [
              "Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep",
              "Oct", "Nov", "Dec"
            ][d.getMonth()];
          case '%B': return [
              "January", "February", "March", "April", "May", "June", "July",
              "August", "September", "October", "November", "December"
            ][d.getMonth()];
          case '%c': return d.toLocaleString();
          case '%C': return pad("0", 2, Math.floor(d.getFullYear() / 100) % 100);
          case '%d': return pad("0", 2, d.getDate());
          case '%x':
          case '%D': return pad("0", 2, d.getMonth() + 1)
                    + "/" + pad("0", 2, d.getDate())
                    + "/" + pad("0", 2, d.getFullYear() % 100);
          case '%e': return pad(" ", 2, d.getDate());
          case '%H': return pad("0", 2, d.getHours());
          case '%I': {
            var h = d.getHours() % 12;
            return h ? pad("0", 2, h) : 12;
          }
          // TODO %j: day of year as a decimal number [001,366]
          case '%m': return pad("0", 2, d.getMonth() + 1);
          case '%M': return pad("0", 2, d.getMinutes());
          case '%n': return "\n";
          case '%p': return d.getHours() < 12 ? "AM" : "PM";
          case '%T':
          case '%X':
          case '%r': {
            var h = d.getHours() % 12;
            return (h ? pad("0", 2, h) : 12)
                    + ":" + pad("0", 2, d.getMinutes())
                    + ":" + pad("0", 2, d.getSeconds())
                    + " " + (d.getHours() < 12 ? "AM" : "PM");
          }
          case '%R': return pad("0", 2, d.getHours()) + ":" + pad("0", 2, d.getMinutes());
          case '%S': return pad("0", 2, d.getSeconds());
          case '%Q': return pad("0", 3, d.getMilliseconds());
          case '%t': return "\t";
          case '%u': {
            var w = d.getDay();
            return w ? w : 1;
          }
          // TODO %U: week number (sunday first day) [00,53]
          // TODO %V: week number (monday first day) [01,53] ... with weirdness
          case '%w': return d.getDay();
          // TODO %W: week number (monday first day) [00,53] ... with weirdness
          case '%y': return pad("0", 2, d.getFullYear() % 100);
          case '%Y': return d.getFullYear();
          // TODO %Z: timezone name or abbreviation
          case '%%': return "%";
        }
        return s;
      });
  }

  /**
   * Converts a date to a string using the associated formatting pattern.
   *
   * @function
   * @name pv.Format.date.prototype.format
   * @param {Date} date a date to format.
   * @returns {string} the formatted date as a string.
   */
  format.format = format;

  /**
   * Parses a date from a string using the associated formatting pattern.
   *
   * @function
   * @name pv.Format.date.prototype.parse
   * @param {string} s the string to parse as a date.
   * @returns {Date} the parsed date.
   */
  format.parse = function(s) {
    var year = 1970, month = 0, date = 1, hour = 0, minute = 0, second = 0;
    var fields = [function() {}];

    /* Register callbacks for each field in the format pattern. */
    var re = pv.Format.re(pattern).replace(/%[a-zA-Z0-9]/g, function(s) {
        switch (s) {
          // TODO %a: day of week, either abbreviated or full name
          // TODO %A: same as %a
          case '%b': {
            fields.push(function(x) { month = {
                  Jan: 0, Feb: 1, Mar: 2, Apr: 3, May: 4, Jun: 5, Jul: 6, Aug: 7,
                  Sep: 8, Oct: 9, Nov: 10, Dec: 11
                }[x]; });
            return "([A-Za-z]+)";
          }
          case '%h':
          case '%B': {
            fields.push(function(x) { month = {
                  January: 0, February: 1, March: 2, April: 3, May: 4, June: 5,
                  July: 6, August: 7, September: 8, October: 9, November: 10,
                  December: 11
                }[x]; });
            return "([A-Za-z]+)";
          }
          // TODO %c: locale's appropriate date and time
          // TODO %C: century number[0,99]
          case '%e':
          case '%d': {
            fields.push(function(x) { date = x; });
            return "([0-9]+)";
          }
          // TODO %D: same as %m/%d/%y
          case '%I':
          case '%H': {
            fields.push(function(x) { hour = x; });
            return "([0-9]+)";
          }
          // TODO %j: day number [1,366]
          case '%m': {
            fields.push(function(x) { month = x - 1; });
            return "([0-9]+)";
          }
          case '%M': {
            fields.push(function(x) { minute = x; });
            return "([0-9]+)";
          }
          // TODO %n: any white space
          // TODO %p: locale's equivalent of a.m. or p.m.
          case '%p': { // TODO this is a hack
            fields.push(function(x) {
              if (hour == 12) {
                if (x == "am") hour = 0;
              } else if (x == "pm") {
                hour = Number(hour) + 12;
              }
            });
            return "(am|pm)";
          }
          // TODO %r: %I:%M:%S %p
          // TODO %R: %H:%M
          case '%S': {
            fields.push(function(x) { second = x; });
            return "([0-9]+)";
          }
          // TODO %t: any white space
          // TODO %T: %H:%M:%S
          // TODO %U: week number [00,53]
          // TODO %w: weekday [0,6]
          // TODO %W: week number [00, 53]
          // TODO %x: locale date (%m/%d/%y)
          // TODO %X: locale time (%I:%M:%S %p)
          case '%y': {
            fields.push(function(x) {
                x = Number(x);
                year = x + (((0 <= x) && (x < 69)) ? 2000
                    : (((x >= 69) && (x < 100) ? 1900 : 0)));
              });
            return "([0-9]+)";
          }
          case '%Y': {
            fields.push(function(x) { year = x; });
            return "([0-9]+)";
          }
          case '%%': {
            fields.push(function() {});
            return "%";
          }
        }
        return s;
      });

    var match = s.match(re);
    if (match) match.forEach(function(m, i) { fields[i](m); });
    return new Date(year, month, date, hour, minute, second);
  };

  return format;
};
/**
 * Returns a time format of the given type, either "short" or "long".
 *
 * @class Represents a time format, converting between a <tt>number</tt>
 * representing a duration in milliseconds, and a <tt>string</tt>. Two types of
 * time formats are supported: "short" and "long". The <i>short</i> format type
 * returns a string such as "3.3 days" or "12.1 minutes", while the <i>long</i>
 * format returns "13:04:12" or similar.
 *
 * @extends pv.Format
 * @param {string} type the type; "short" or "long".
 */
pv.Format.time = function(type) {
  var pad = pv.Format.pad;

  /*
   * MILLISECONDS = 1
   * SECONDS = 1e3
   * MINUTES = 6e4
   * HOURS = 36e5
   * DAYS = 864e5
   * WEEKS = 6048e5
   * MONTHS = 2592e6
   * YEARS = 31536e6
   */

  /** @private */
  function format(t) {
    t = Number(t); // force conversion from Date
    switch (type) {
      case "short": {
        if (t >= 31536e6) {
          return (t / 31536e6).toFixed(1) + " years";
        } else if (t >= 6048e5) {
          return (t / 6048e5).toFixed(1) + " weeks";
        } else if (t >= 864e5) {
          return (t / 864e5).toFixed(1) + " days";
        } else if (t >= 36e5) {
          return (t / 36e5).toFixed(1) + " hours";
        } else if (t >= 6e4) {
          return (t / 6e4).toFixed(1) + " minutes";
        }
        return (t / 1e3).toFixed(1) + " seconds";
      }
      case "long": {
        var a = [],
            s = ((t % 6e4) / 1e3) >> 0,
            m = ((t % 36e5) / 6e4) >> 0;
        a.push(pad("0", 2, s));
        if (t >= 36e5) {
          var h = ((t % 864e5) / 36e5) >> 0;
          a.push(pad("0", 2, m));
          if (t >= 864e5) {
            a.push(pad("0", 2, h));
            a.push(Math.floor(t / 864e5).toFixed());
          } else {
            a.push(h.toFixed());
          }
        } else {
          a.push(m.toFixed());
        }
        return a.reverse().join(":");
      }
    }
  }

  /**
   * Formats the specified time, returning the string representation.
   *
   * @function
   * @name pv.Format.time.prototype.format
   * @param {number} t the duration in milliseconds. May also be a <tt>Date</tt>.
   * @returns {string} the formatted string.
   */
  format.format = format;

  /**
   * Parses the specified string, returning the time in milliseconds.
   *
   * @function
   * @name pv.Format.time.prototype.parse
   * @param {string} s a formatted string.
   * @returns {number} the parsed duration in milliseconds.
   */
  format.parse = function(s) {
    switch (type) {
      case "short": {
        var re = /([0-9,.]+)\s*([a-z]+)/g, a, t = 0;
        while (a = re.exec(s)) {
          var f = parseFloat(a[0].replace(",", "")), u = 0;
          switch (a[2].toLowerCase()) {
            case "year": case "years": u = 31536e6; break;
            case "week": case "weeks": u = 6048e5; break;
            case "day": case "days": u = 864e5; break;
            case "hour": case "hours": u = 36e5; break;
            case "minute": case "minutes": u = 6e4; break;
            case "second": case "seconds": u = 1e3; break;
          }
          t += f * u;
        }
        return t;
      }
      case "long": {
        var a = s.replace(",", "").split(":").reverse(), t = 0;
        if (a.length) t += parseFloat(a[0]) * 1e3;
        if (a.length > 1) t += parseFloat(a[1]) * 6e4;
        if (a.length > 2) t += parseFloat(a[2]) * 36e5;
        if (a.length > 3) t += parseFloat(a[3]) * 864e5;
        return t;
      }
    }
  }

  return format;
};
/**
 * Returns a default number format.
 *
 * @class Represents a number format, converting between a <tt>number</tt> and a
 * <tt>string</tt>. This class allows numbers to be formatted with variable
 * precision (both for the integral and fractional part of the number), optional
 * thousands grouping, and optional padding. The thousands (",") and decimal
 * (".") separator can be customized.
 *
 * @returns {pv.Format.number} a number format.
 */
pv.Format.number = function() {
  var mini = 0, // default minimum integer digits
      maxi = Infinity, // default maximum integer digits
      mins = 0, // mini, including group separators
      minf = 0, // default minimum fraction digits
      maxf = 0, // default maximum fraction digits
      maxk = 1, // 10^maxf
      padi = "0", // default integer pad
      padf = "0", // default fraction pad
      padg = true, // whether group separator affects integer padding
      decimal = ".", // default decimal separator
      group = ","; // default group separator

  /** @private */
  function format(x) {
    /* Round the fractional part, and split on decimal separator. */
    if (Infinity > maxf) x = Math.round(x * maxk) / maxk;
    var s = String(Math.abs(x)).split(".");

    /* Pad, truncate and group the integral part. */
    var i = s[0], n = (x < 0) ? "-" : "";
    if (i.length > maxi) i = i.substring(i.length - maxi);
    if (padg && (i.length < mini)) i = n + new Array(mini - i.length + 1).join(padi) + i;
    if (i.length > 3) i = i.replace(/\B(?=(?:\d{3})+(?!\d))/g, group);
    if (!padg && (i.length < mins)) i = new Array(mins - i.length + 1).join(padi) + n + i;
    s[0] = i;

    /* Pad the fractional part. */
    var f = s[1] || "";
    if (f.length < minf) s[1] = f + new Array(minf - f.length + 1).join(padf);

    return s.join(decimal);
  }

  /**
   * @function
   * @name pv.Format.number.prototype.format
   * @param {number} x
   * @returns {string}
   */
  format.format = format;

  /**
   * Parses the specified string as a number. Before parsing, leading and
   * trailing padding is removed. Group separators are also removed, and the
   * decimal separator is replaced with the standard point ("."). The integer
   * part is truncated per the maximum integer digits, and the fraction part is
   * rounded per the maximum fraction digits.
   *
   * @function
   * @name pv.Format.number.prototype.parse
   * @param {string} x the string to parse.
   * @returns {number} the parsed number.
   */
  format.parse = function(x) {
    var re = pv.Format.re;

    /* Remove leading and trailing padding. Split on the decimal separator. */
    var s = String(x)
        .replace(new RegExp("^(" + re(padi) + ")*"), "")
        .replace(new RegExp("(" + re(padf) + ")*$"), "")
        .split(decimal);

    /* Remove grouping and truncate the integral part. */
    var i = s[0].replace(new RegExp(re(group), "g"), "");
    if (i.length > maxi) i = i.substring(i.length - maxi);

    /* Round the fractional part. */
    var f = s[1] ? Number("0." + s[1]) : 0;
    if (Infinity > maxf) f = Math.round(f * maxk) / maxk;

    return Math.round(i) + f;
  };

  /**
   * Sets or gets the minimum and maximum number of integer digits. This
   * controls the number of decimal digits to display before the decimal
   * separator for the integral part of the number. If the number of digits is
   * smaller than the minimum, the digits are padded; if the number of digits is
   * larger, the digits are truncated, showing only the lower-order digits. The
   * default range is [0, Infinity].
   *
   * <p>If only one argument is specified to this method, this value is used as
   * both the minimum and maximum number. If no arguments are specified, a
   * two-element array is returned containing the minimum and the maximum.
   *
   * @function
   * @name pv.Format.number.prototype.integerDigits
   * @param {number} [min] the minimum integer digits.
   * @param {number} [max] the maximum integer digits.
   * @returns {pv.Format.number} <tt>this</tt>, or the current integer digits.
   */
  format.integerDigits = function(min, max) {
    if (arguments.length) {
      mini = Number(min);
      maxi = (arguments.length > 1) ? Number(max) : mini;
      mins = mini + Math.floor(mini / 3) * group.length;
      return this;
    }
    return [mini, maxi];
  };

  /**
   * Sets or gets the minimum and maximum number of fraction digits. The
   * controls the number of decimal digits to display after the decimal
   * separator for the fractional part of the number. If the number of digits is
   * smaller than the minimum, the digits are padded; if the number of digits is
   * larger, the fractional part is rounded, showing only the higher-order
   * digits. The default range is [0, 0].
   *
   * <p>If only one argument is specified to this method, this value is used as
   * both the minimum and maximum number. If no arguments are specified, a
   * two-element array is returned containing the minimum and the maximum.
   *
   * @function
   * @name pv.Format.number.prototype.fractionDigits
   * @param {number} [min] the minimum fraction digits.
   * @param {number} [max] the maximum fraction digits.
   * @returns {pv.Format.number} <tt>this</tt>, or the current fraction digits.
   */
  format.fractionDigits = function(min, max) {
    if (arguments.length) {
      minf = Number(min);
      maxf = (arguments.length > 1) ? Number(max) : minf;
      maxk = Math.pow(10, maxf);
      return this;
    }
    return [minf, maxf];
  };

  /**
   * Sets or gets the character used to pad the integer part. The integer pad is
   * used when the number of integer digits is smaller than the minimum. The
   * default pad character is "0" (zero).
   *
   * @param {string} [x] the new pad character.
   * @returns {pv.Format.number} <tt>this</tt> or the current pad character.
   */
  format.integerPad = function(x) {
    if (arguments.length) {
      padi = String(x);
      padg = /\d/.test(padi);
      return this;
    }
    return padi;
  };

  /**
   * Sets or gets the character used to pad the fration part. The fraction pad
   * is used when the number of fraction digits is smaller than the minimum. The
   * default pad character is "0" (zero).
   *
   * @param {string} [x] the new pad character.
   * @returns {pv.Format.number} <tt>this</tt> or the current pad character.
   */
  format.fractionPad = function(x) {
    if (arguments.length) {
      padf = String(x);
      return this;
    }
    return padf;
  };

  /**
   * Sets or gets the character used as the decimal point, separating the
   * integer and fraction parts of the number. The default decimal point is ".".
   *
   * @param {string} [x] the new decimal separator.
   * @returns {pv.Format.number} <tt>this</tt> or the current decimal separator.
   */
  format.decimal = function(x) {
    if (arguments.length) {
      decimal = String(x);
      return this;
    }
    return decimal;
  };

  /**
   * Sets or gets the character used as the group separator, grouping integer
   * digits by thousands. The default decimal point is ",". Grouping can be
   * disabled by using "" for the separator.
   *
   * @param {string} [x] the new group separator.
   * @returns {pv.Format.number} <tt>this</tt> or the current group separator.
   */
  format.group = function(x) {
    if (arguments.length) {
      group = x ? String(x) : "";
      mins = mini + Math.floor(mini / 3) * group.length;
      return this;
    }
    return group;
  };

  return format;
};
/**
 * @private A private variant of Array.prototype.map that supports the index
 * property.
 */
pv.map = function(array, f) {
  var o = {};
  return f
      ? array.map(function(d, i) { o.index = i; return f.call(o, d); })
      : array.slice();
};

/**
 * Concatenates the specified array with itself <i>n</i> times. For example,
 * <tt>pv.repeat([1, 2])</tt> returns [1, 2, 1, 2].
 *
 * @param {array} a an array.
 * @param {number} [n] the number of times to repeat; defaults to two.
 * @returns {array} an array that repeats the specified array.
 */
pv.repeat = function(array, n) {
  if (arguments.length == 1) n = 2;
  return pv.blend(pv.range(n).map(function() { return array; }));
};

/**
 * Given two arrays <tt>a</tt> and <tt>b</tt>, <style
 * type="text/css">sub{line-height:0}</style> returns an array of all possible
 * pairs of elements [a<sub>i</sub>, b<sub>j</sub>]. The outer loop is on array
 * <i>a</i>, while the inner loop is on <i>b</i>, such that the order of
 * returned elements is [a<sub>0</sub>, b<sub>0</sub>], [a<sub>0</sub>,
 * b<sub>1</sub>], ... [a<sub>0</sub>, b<sub>m</sub>], [a<sub>1</sub>,
 * b<sub>0</sub>], [a<sub>1</sub>, b<sub>1</sub>], ... [a<sub>1</sub>,
 * b<sub>m</sub>], ... [a<sub>n</sub>, b<sub>m</sub>]. If either array is empty,
 * an empty array is returned.
 *
 * @param {array} a an array.
 * @param {array} b an array.
 * @returns {array} an array of pairs of elements in <tt>a</tt> and <tt>b</tt>.
 */
pv.cross = function(a, b) {
  var array = [];
  for (var i = 0, n = a.length, m = b.length; i < n; i++) {
    for (var j = 0, x = a[i]; j < m; j++) {
      array.push([x, b[j]]);
    }
  }
  return array;
};

/**
 * Given the specified array of arrays, concatenates the arrays into a single
 * array. If the individual arrays are explicitly known, an alternative to blend
 * is to use JavaScript's <tt>concat</tt> method directly. These two equivalent
 * expressions:<ul>
 *
 * <li><tt>pv.blend([[1, 2, 3], ["a", "b", "c"]])</tt>
 * <li><tt>[1, 2, 3].concat(["a", "b", "c"])</tt>
 *
 * </ul>return [1, 2, 3, "a", "b", "c"].
 *
 * @param {array[]} arrays an array of arrays.
 * @returns {array} an array containing all the elements of each array in
 * <tt>arrays</tt>.
 */
pv.blend = function(arrays) {
  return Array.prototype.concat.apply([], arrays);
};

/**
 * Given the specified array of arrays, <style
 * type="text/css">sub{line-height:0}</style> transposes each element
 * array<sub>ij</sub> with array<sub>ji</sub>. If the array has dimensions
 * <i>n</i>&times;<i>m</i>, it will have dimensions <i>m</i>&times;<i>n</i>
 * after this method returns. This method transposes the elements of the array
 * in place, mutating the array, and returning a reference to the array.
 *
 * @param {array[]} arrays an array of arrays.
 * @returns {array[]} the passed-in array, after transposing the elements.
 */
pv.transpose = function(arrays) {
  var n = arrays.length, m = pv.max(arrays, function(d) { return d.length; });

  if (m > n) {
    arrays.length = m;
    for (var i = n; i < m; i++) {
      arrays[i] = new Array(n);
    }
    for (var i = 0; i < n; i++) {
      for (var j = i + 1; j < m; j++) {
        var t = arrays[i][j];
        arrays[i][j] = arrays[j][i];
        arrays[j][i] = t;
      }
    }
  } else {
    for (var i = 0; i < m; i++) {
      arrays[i].length = n;
    }
    for (var i = 0; i < n; i++) {
      for (var j = 0; j < i; j++) {
        var t = arrays[i][j];
        arrays[i][j] = arrays[j][i];
        arrays[j][i] = t;
      }
    }
  }

  arrays.length = m;
  for (var i = 0; i < m; i++) {
    arrays[i].length = n;
  }

  return arrays;
};

/**
 * Returns a normalized copy of the specified array, such that the sum of the
 * returned elements sum to one. If the specified array is not an array of
 * numbers, an optional accessor function <tt>f</tt> can be specified to map the
 * elements to numbers. For example, if <tt>array</tt> is an array of objects,
 * and each object has a numeric property "foo", the expression
 *
 * <pre>pv.normalize(array, function(d) d.foo)</pre>
 *
 * returns a normalized array on the "foo" property. If an accessor function is
 * not specified, the identity function is used. Accessor functions can refer to
 * <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number[]} an array of numbers that sums to one.
 */
pv.normalize = function(array, f) {
  var norm = pv.map(array, f), sum = pv.sum(norm);
  for (var i = 0; i < norm.length; i++) norm[i] /= sum;
  return norm;
};

/**
 * Returns a permutation of the specified array, using the specified array of
 * indexes. The returned array contains the corresponding element in
 * <tt>array</tt> for each index in <tt>indexes</tt>, in order. For example,
 *
 * <pre>pv.permute(["a", "b", "c"], [1, 2, 0])</pre>
 *
 * returns <tt>["b", "c", "a"]</tt>. It is acceptable for the array of indexes
 * to be a different length from the array of elements, and for indexes to be
 * duplicated or omitted. The optional accessor function <tt>f</tt> can be used
 * to perform a simultaneous mapping of the array elements. Accessor functions
 * can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array.
 * @param {number[]} indexes an array of indexes into <tt>array</tt>.
 * @param {function} [f] an optional accessor function.
 * @returns {array} an array of elements from <tt>array</tt>; a permutation.
 */
pv.permute = function(array, indexes, f) {
  if (!f) f = pv.identity;
  var p = new Array(indexes.length), o = {};
  indexes.forEach(function(j, i) { o.index = j; p[i] = f.call(o, array[j]); });
  return p;
};

/**
 * Returns a map from key to index for the specified <tt>keys</tt> array. For
 * example,
 *
 * <pre>pv.numerate(["a", "b", "c"])</pre>
 *
 * returns <tt>{a: 0, b: 1, c: 2}</tt>. Note that since JavaScript maps only
 * support string keys, <tt>keys</tt> must contain strings, or other values that
 * naturally map to distinct string values. Alternatively, an optional accessor
 * function <tt>f</tt> can be specified to compute the string key for the given
 * element. Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} keys an array, usually of string keys.
 * @param {function} [f] an optional key function.
 * @returns a map from key to index.
 */
pv.numerate = function(keys, f) {
  if (!f) f = pv.identity;
  var map = {}, o = {};
  keys.forEach(function(x, i) { o.index = i; map[f.call(o, x)] = i; });
  return map;
};

/**
 * Returns the unique elements in the specified array, in the order they appear.
 * Note that since JavaScript maps only support string keys, <tt>array</tt> must
 * contain strings, or other values that naturally map to distinct string
 * values. Alternatively, an optional accessor function <tt>f</tt> can be
 * specified to compute the string key for the given element. Accessor functions
 * can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array, usually of string keys.
 * @param {function} [f] an optional key function.
 * @returns {array} the unique values.
 */
pv.uniq = function(array, f) {
  if (!f) f = pv.identity;
  var map = {}, keys = [], o = {}, y;
  array.forEach(function(x, i) {
    o.index = i;
    y = f.call(o, x);
    if (!(y in map)) map[y] = keys.push(y);
  });
  return keys;
};

/**
 * The comparator function for natural order. This can be used in conjunction with
 * the built-in array <tt>sort</tt> method to sort elements by their natural
 * order, ascending. Note that if no comparator function is specified to the
 * built-in <tt>sort</tt> method, the default order is lexicographic, <i>not</i>
 * natural!
 *
 * @see <a
 * href="http://developer.mozilla.org/en/Core_JavaScript_1.5_Reference/Global_Objects/Array/sort">Array.sort</a>.
 * @param a an element to compare.
 * @param b an element to compare.
 * @returns {number} negative if a &lt; b; positive if a &gt; b; otherwise 0.
 */
pv.naturalOrder = function(a, b) {
  return (a < b) ? -1 : ((a > b) ? 1 : 0);
};

/**
 * The comparator function for reverse natural order. This can be used in
 * conjunction with the built-in array <tt>sort</tt> method to sort elements by
 * their natural order, descending. Note that if no comparator function is
 * specified to the built-in <tt>sort</tt> method, the default order is
 * lexicographic, <i>not</i> natural!
 *
 * @see #naturalOrder
 * @param a an element to compare.
 * @param b an element to compare.
 * @returns {number} negative if a &lt; b; positive if a &gt; b; otherwise 0.
 */
pv.reverseOrder = function(b, a) {
  return (a < b) ? -1 : ((a > b) ? 1 : 0);
};

/**
 * Searches the specified array of numbers for the specified value using the
 * binary search algorithm. The array must be sorted (as by the <tt>sort</tt>
 * method) prior to making this call. If it is not sorted, the results are
 * undefined. If the array contains multiple elements with the specified value,
 * there is no guarantee which one will be found.
 *
 * <p>The <i>insertion point</i> is defined as the point at which the value
 * would be inserted into the array: the index of the first element greater than
 * the value, or <tt>array.length</tt>, if all elements in the array are less
 * than the specified value. Note that this guarantees that the return value
 * will be nonnegative if and only if the value is found.
 *
 * @param {number[]} array the array to be searched.
 * @param {number} value the value to be searched for.
 * @returns the index of the search value, if it is contained in the array;
 * otherwise, (-(<i>insertion point</i>) - 1).
 * @param {function} [f] an optional key function.
 */
pv.search = function(array, value, f) {
  if (!f) f = pv.identity;
  var low = 0, high = array.length - 1;
  while (low <= high) {
    var mid = (low + high) >> 1, midValue = f(array[mid]);
    if (midValue < value) low = mid + 1;
    else if (midValue > value) high = mid - 1;
    else return mid;
  }
  return -low - 1;
};

pv.search.index = function(array, value, f) {
  var i = pv.search(array, value, f);
  return (i < 0) ? (-i - 1) : i;
};
/**
 * Returns an array of numbers, starting at <tt>start</tt>, incrementing by
 * <tt>step</tt>, until <tt>stop</tt> is reached. The stop value is
 * exclusive. If only a single argument is specified, this value is interpeted
 * as the <i>stop</i> value, with the <i>start</i> value as zero. If only two
 * arguments are specified, the step value is implied to be one.
 *
 * <p>The method is modeled after the built-in <tt>range</tt> method from
 * Python. See the Python documentation for more details.
 *
 * @see <a href="http://docs.python.org/library/functions.html#range">Python range</a>
 * @param {number} [start] the start value.
 * @param {number} stop the stop value.
 * @param {number} [step] the step value.
 * @returns {number[]} an array of numbers.
 */
pv.range = function(start, stop, step) {
  if (arguments.length == 1) {
    stop = start;
    start = 0;
  }
  if (step == undefined) step = 1;
  if ((stop - start) / step == Infinity) throw new Error("range must be finite");
  var array = [], i = 0, j;
  if (step < 0) {
    while ((j = start + step * i++) > stop) {
      array.push(j);
    }
  } else {
    while ((j = start + step * i++) < stop) {
      array.push(j);
    }
  }
  return array;
};

/**
 * Returns a random number in the range [<tt>start</tt>, <tt>stop</tt>) that is
 * a multiple of <tt>step</tt>. More specifically, the returned number is of the
 * form <tt>start</tt> + <i>n</i> * <tt>step</tt>, where <i>n</i> is a
 * nonnegative integer. If <tt>step</tt> is not specified, it defaults to 1,
 * returning a random integer if <tt>start</tt> is also an integer.
 *
 * @param {number} [start] the start value value.
 * @param {number} stop the stop value.
 * @param {number} [step] the step value.
 * @returns {number} a random number between <i>start</i> and <i>stop</i>.
 */
pv.random = function(start, stop, step) {
  if (arguments.length == 1) {
    stop = start;
    start = 0;
  }
  if (step == undefined) step = 1;
  return step
      ? (Math.floor(Math.random() * (stop - start) / step) * step + start)
      : (Math.random() * (stop - start) + start);
};

/**
 * Returns the sum of the specified array. If the specified array is not an
 * array of numbers, an optional accessor function <tt>f</tt> can be specified
 * to map the elements to numbers. See {@link #normalize} for an example.
 * Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the sum of the specified array.
 */
pv.sum = function(array, f) {
  var o = {};
  return array.reduce(f
      ? function(p, d, i) { o.index = i; return p + f.call(o, d); }
      : function(p, d) { return p + d; }, 0);
};

/**
 * Returns the maximum value of the specified array. If the specified array is
 * not an array of numbers, an optional accessor function <tt>f</tt> can be
 * specified to map the elements to numbers. See {@link #normalize} for an
 * example. Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the maximum value of the specified array.
 */
pv.max = function(array, f) {
  if (f == pv.index) return array.length - 1;
  return Math.max.apply(null, f ? pv.map(array, f) : array);
};

/**
 * Returns the index of the maximum value of the specified array. If the
 * specified array is not an array of numbers, an optional accessor function
 * <tt>f</tt> can be specified to map the elements to numbers. See
 * {@link #normalize} for an example. Accessor functions can refer to
 * <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the index of the maximum value of the specified array.
 */
pv.max.index = function(array, f) {
  if (!array.length) return -1;
  if (f == pv.index) return array.length - 1;
  if (!f) f = pv.identity;
  var maxi = 0, maxx = -Infinity, o = {};
  for (var i = 0; i < array.length; i++) {
    o.index = i;
    var x = f.call(o, array[i]);
    if (x > maxx) {
      maxx = x;
      maxi = i;
    }
  }
  return maxi;
}

/**
 * Returns the minimum value of the specified array of numbers. If the specified
 * array is not an array of numbers, an optional accessor function <tt>f</tt>
 * can be specified to map the elements to numbers. See {@link #normalize} for
 * an example. Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the minimum value of the specified array.
 */
pv.min = function(array, f) {
  if (f == pv.index) return 0;
  return Math.min.apply(null, f ? pv.map(array, f) : array);
};

/**
 * Returns the index of the minimum value of the specified array. If the
 * specified array is not an array of numbers, an optional accessor function
 * <tt>f</tt> can be specified to map the elements to numbers. See
 * {@link #normalize} for an example. Accessor functions can refer to
 * <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the index of the minimum value of the specified array.
 */
pv.min.index = function(array, f) {
  if (!array.length) return -1;
  if (f == pv.index) return 0;
  if (!f) f = pv.identity;
  var mini = 0, minx = Infinity, o = {};
  for (var i = 0; i < array.length; i++) {
    o.index = i;
    var x = f.call(o, array[i]);
    if (x < minx) {
      minx = x;
      mini = i;
    }
  }
  return mini;
}

/**
 * Returns the arithmetic mean, or average, of the specified array. If the
 * specified array is not an array of numbers, an optional accessor function
 * <tt>f</tt> can be specified to map the elements to numbers. See
 * {@link #normalize} for an example. Accessor functions can refer to
 * <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the mean of the specified array.
 */
pv.mean = function(array, f) {
  return pv.sum(array, f) / array.length;
};

/**
 * Returns the median of the specified array. If the specified array is not an
 * array of numbers, an optional accessor function <tt>f</tt> can be specified
 * to map the elements to numbers. See {@link #normalize} for an example.
 * Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the median of the specified array.
 */
pv.median = function(array, f) {
  if (f == pv.index) return (array.length - 1) / 2;
  array = pv.map(array, f).sort(pv.naturalOrder);
  if (array.length % 2) return array[Math.floor(array.length / 2)];
  var i = array.length / 2;
  return (array[i - 1] + array[i]) / 2;
};

/**
 * Returns the unweighted variance of the specified array. If the specified
 * array is not an array of numbers, an optional accessor function <tt>f</tt>
 * can be specified to map the elements to numbers. See {@link #normalize} for
 * an example. Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the variance of the specified array.
 */
pv.variance = function(array, f) {
  if (array.length < 1) return NaN;
  if (array.length == 1) return 0;
  var mean = pv.mean(array, f), sum = 0, o = {};
  if (!f) f = pv.identity;
  for (var i = 0; i < array.length; i++) {
    o.index = i;
    var d = f.call(o, array[i]) - mean;
    sum += d * d;
  }
  return sum;
};

/**
 * Returns an unbiased estimation of the standard deviation of a population,
 * given the specified random sample. If the specified array is not an array of
 * numbers, an optional accessor function <tt>f</tt> can be specified to map the
 * elements to numbers. See {@link #normalize} for an example. Accessor
 * functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the standard deviation of the specified array.
 */
pv.deviation = function(array, f) {
  return Math.sqrt(pv.variance(array, f) / (array.length - 1));
};

/**
 * Returns the logarithm with a given base value.
 *
 * @param {number} x the number for which to compute the logarithm.
 * @param {number} b the base of the logarithm.
 * @returns {number} the logarithm value.
 */
pv.log = function(x, b) {
  return Math.log(x) / Math.log(b);
};

/**
 * Computes a zero-symmetric logarithm. Computes the logarithm of the absolute
 * value of the input, and determines the sign of the output according to the
 * sign of the input value.
 *
 * @param {number} x the number for which to compute the logarithm.
 * @param {number} b the base of the logarithm.
 * @returns {number} the symmetric log value.
 */
pv.logSymmetric = function(x, b) {
  return (x == 0) ? 0 : ((x < 0) ? -pv.log(-x, b) : pv.log(x, b));
};

/**
 * Computes a zero-symmetric logarithm, with adjustment to values between zero
 * and the logarithm base. This adjustment introduces distortion for values less
 * than the base number, but enables simultaneous plotting of log-transformed
 * data involving both positive and negative numbers.
 *
 * @param {number} x the number for which to compute the logarithm.
 * @param {number} b the base of the logarithm.
 * @returns {number} the adjusted, symmetric log value.
 */
pv.logAdjusted = function(x, b) {
  if (!isFinite(x)) return x;
  var negative = x < 0;
  if (x < b) x += (b - x) / b;
  return negative ? -pv.log(x, b) : pv.log(x, b);
};

/**
 * Rounds an input value down according to its logarithm. The method takes the
 * floor of the logarithm of the value and then uses the resulting value as an
 * exponent for the base value.
 *
 * @param {number} x the number for which to compute the logarithm floor.
 * @param {number} b the base of the logarithm.
 * @returns {number} the rounded-by-logarithm value.
 */
pv.logFloor = function(x, b) {
  return (x > 0)
      ? Math.pow(b, Math.floor(pv.log(x, b)))
      : -Math.pow(b, -Math.floor(-pv.log(-x, b)));
};

/**
 * Rounds an input value up according to its logarithm. The method takes the
 * ceiling of the logarithm of the value and then uses the resulting value as an
 * exponent for the base value.
 *
 * @param {number} x the number for which to compute the logarithm ceiling.
 * @param {number} b the base of the logarithm.
 * @returns {number} the rounded-by-logarithm value.
 */
pv.logCeil = function(x, b) {
  return (x > 0)
      ? Math.pow(b, Math.ceil(pv.log(x, b)))
      : -Math.pow(b, -Math.ceil(-pv.log(-x, b)));
};

(function() {
  var radians = Math.PI / 180,
      degrees = 180 / Math.PI;

  /** Returns the number of radians corresponding to the specified degrees. */
  pv.radians = function(degrees) { return radians * degrees; };

  /** Returns the number of degrees corresponding to the specified radians. */
  pv.degrees = function(radians) { return degrees * radians; };
})();
/**
 * Returns all of the property names (keys) of the specified object (a map). The
 * order of the returned array is not defined.
 *
 * @param map an object.
 * @returns {string[]} an array of strings corresponding to the keys.
 * @see #entries
 */
pv.keys = function(map) {
  var array = [];
  for (var key in map) {
    array.push(key);
  }
  return array;
};

/**
 * Returns all of the entries (key-value pairs) of the specified object (a
 * map). The order of the returned array is not defined. Each key-value pair is
 * represented as an object with <tt>key</tt> and <tt>value</tt> attributes,
 * e.g., <tt>{key: "foo", value: 42}</tt>.
 *
 * @param map an object.
 * @returns {array} an array of key-value pairs corresponding to the keys.
 */
pv.entries = function(map) {
  var array = [];
  for (var key in map) {
    array.push({ key: key, value: map[key] });
  }
  return array;
};

/**
 * Returns all of the values (attribute values) of the specified object (a
 * map). The order of the returned array is not defined.
 *
 * @param map an object.
 * @returns {array} an array of objects corresponding to the values.
 * @see #entries
 */
pv.values = function(map) {
  var array = [];
  for (var key in map) {
    array.push(map[key]);
  }
  return array;
};

/**
 * Returns a map constructed from the specified <tt>keys</tt>, using the
 * function <tt>f</tt> to compute the value for each key. The single argument to
 * the value function is the key. The callback is invoked only for indexes of
 * the array which have assigned values; it is not invoked for indexes which
 * have been deleted or which have never been assigned values.
 *
 * <p>For example, this expression creates a map from strings to string length:
 *
 * <pre>pv.dict(["one", "three", "seventeen"], function(s) s.length)</pre>
 *
 * The returned value is <tt>{one: 3, three: 5, seventeen: 9}</tt>. Accessor
 * functions can refer to <tt>this.index</tt>.
 *
 * @param {array} keys an array.
 * @param {function} f a value function.
 * @returns a map from keys to values.
 */
pv.dict = function(keys, f) {
  var m = {}, o = {};
  for (var i = 0; i < keys.length; i++) {
    if (i in keys) {
      var k = keys[i];
      o.index = i;
      m[k] = f.call(o, k);
    }
  }
  return m;
};
/**
 * Returns a {@link pv.Dom} operator for the given map. This is a convenience
 * factory method, equivalent to <tt>new pv.Dom(map)</tt>. To apply the operator
 * and retrieve the root node, call {@link pv.Dom#root}; to retrieve all nodes
 * flattened, use {@link pv.Dom#nodes}.
 *
 * @see pv.Dom
 * @param map a map from which to construct a DOM.
 * @returns {pv.Dom} a DOM operator for the specified map.
 */
pv.dom = function(map) {
  return new pv.Dom(map);
};

/**
 * Constructs a DOM operator for the specified map. This constructor should not
 * be invoked directly; use {@link pv.dom} instead.
 *
 * @class Represets a DOM operator for the specified map. This allows easy
 * transformation of a hierarchical JavaScript object (such as a JSON map) to a
 * W3C Document Object Model hierarchy. For more information on which attributes
 * and methods from the specification are supported, see {@link pv.Dom.Node}.
 *
 * <p>Leaves in the map are determined using an associated <i>leaf</i> function;
 * see {@link #leaf}. By default, leaves are any value whose type is not
 * "object", such as numbers or strings.
 *
 * @param map a map from which to construct a DOM.
 */
pv.Dom = function(map) {
  this.$map = map;
};

/** @private The default leaf function. */
pv.Dom.prototype.$leaf = function(n) {
  return typeof n != "object";
};

/**
 * Sets or gets the leaf function for this DOM operator. The leaf function
 * identifies which values in the map are leaves, and which are internal nodes.
 * By default, objects are considered internal nodes, and primitives (such as
 * numbers and strings) are considered leaves.
 *
 * @param {function} f the new leaf function.
 * @returns the current leaf function, or <tt>this</tt>.
 */
pv.Dom.prototype.leaf = function(f) {
  if (arguments.length) {
    this.$leaf = f;
    return this;
  }
  return this.$leaf;
};

/**
 * Applies the DOM operator, returning the root node.
 *
 * @returns {pv.Dom.Node} the root node.
 * @param {string} [nodeName] optional node name for the root.
 */
pv.Dom.prototype.root = function(nodeName) {
  var leaf = this.$leaf, root = recurse(this.$map);

  /** @private */
  function recurse(map) {
    var n = new pv.Dom.Node();
    for (var k in map) {
      var v = map[k];
      n.appendChild(leaf(v) ? new pv.Dom.Node(v) : recurse(v)).nodeName = k;
    }
    return n;
  }

  root.nodeName = nodeName;
  return root;
};

/**
 * Applies the DOM operator, returning the array of all nodes in preorder
 * traversal.
 *
 * @returns {array} the array of nodes in preorder traversal.
 */
pv.Dom.prototype.nodes = function() {
  return this.root().nodes();
};

/**
 * Constructs a DOM node for the specified value. Instances of this class are
 * not typically created directly; instead they are generated from a JavaScript
 * map using the {@link pv.Dom} operator.
 *
 * @class Represents a <tt>Node</tt> in the W3C Document Object Model.
 */
pv.Dom.Node = function(value) {
  this.nodeValue = value;
  this.childNodes = [];
};

/**
 * The node name. When generated from a map, the node name corresponds to the
 * key at the given level in the map. Note that the root node has no associated
 * key, and thus has an undefined node name (and no <tt>parentNode</tt>).
 *
 * @type string
 * @field pv.Dom.Node.prototype.nodeName
 */

/**
 * The node value. When generated from a map, node value corresponds to the leaf
 * value for leaf nodes, and is undefined for internal nodes.
 *
 * @field pv.Dom.Node.prototype.nodeValue
 */

/**
 * The array of child nodes. This array is empty for leaf nodes. An easy way to
 * check if child nodes exist is to query <tt>firstChild</tt>.
 *
 * @type array
 * @field pv.Dom.Node.prototype.childNodes
 */

/**
 * The parent node, which is null for root nodes.
 *
 * @type pv.Dom.Node
 */
pv.Dom.Node.prototype.parentNode = null;

/**
 * The first child, which is null for leaf nodes.
 *
 * @type pv.Dom.Node
 */
pv.Dom.Node.prototype.firstChild = null;

/**
 * The last child, which is null for leaf nodes.
 *
 * @type pv.Dom.Node
 */
pv.Dom.Node.prototype.lastChild = null;

/**
 * The previous sibling node, which is null for the first child.
 *
 * @type pv.Dom.Node
 */
pv.Dom.Node.prototype.previousSibling = null;

/**
 * The next sibling node, which is null for the last child.
 *
 * @type pv.Dom.Node
 */
pv.Dom.Node.prototype.nextSibling = null;

/**
 * Removes the specified child node from this node.
 *
 * @throws Error if the specified child is not a child of this node.
 * @returns {pv.Dom.Node} the removed child.
 */
pv.Dom.Node.prototype.removeChild = function(n) {
  var i = this.childNodes.indexOf(n);
  if (i == -1) throw new Error("child not found");
  this.childNodes.splice(i, 1);
  if (n.previousSibling) n.previousSibling.nextSibling = n.nextSibling;
  else this.firstChild = n.nextSibling;
  if (n.nextSibling) n.nextSibling.previousSibling = n.previousSibling;
  else this.lastChild = n.previousSibling;
  delete n.nextSibling;
  delete n.previousSibling;
  delete n.parentNode;
  return n;
};

/**
 * Appends the specified child node to this node. If the specified child is
 * already part of the DOM, the child is first removed before being added to
 * this node.
 *
 * @returns {pv.Dom.Node} the appended child.
 */
pv.Dom.Node.prototype.appendChild = function(n) {
  if (n.parentNode) n.parentNode.removeChild(n);
  n.parentNode = this;
  n.previousSibling = this.lastChild;
  if (this.lastChild) this.lastChild.nextSibling = n;
  else this.firstChild = n;
  this.lastChild = n;
  this.childNodes.push(n);
  return n;
};

/**
 * Inserts the specified child <i>n</i> before the given reference child
 * <i>r</i> of this node. If <i>r</i> is null, this method is equivalent to
 * {@link #appendChild}. If <i>n</i> is already part of the DOM, it is first
 * removed before being inserted.
 *
 * @throws Error if <i>r</i> is non-null and not a child of this node.
 * @returns {pv.Dom.Node} the inserted child.
 */
pv.Dom.Node.prototype.insertBefore = function(n, r) {
  if (!r) return this.appendChild(n);
  var i = this.childNodes.indexOf(r);
  if (i == -1) throw new Error("child not found");
  if (n.parentNode) n.parentNode.removeChild(n);
  n.parentNode = this;
  n.nextSibling = r;
  n.previousSibling = r.previousSibling;
  if (r.previousSibling) {
    r.previousSibling.nextSibling = n;
  } else {
    if (r == this.lastChild) this.lastChild = n;
    this.firstChild = n;
  }
  this.childNodes.splice(i, 0, n);
  return n;
};

/**
 * Replaces the specified child <i>r</i> of this node with the node <i>n</i>. If
 * <i>n</i> is already part of the DOM, it is first removed before being added.
 *
 * @throws Error if <i>r</i> is not a child of this node.
 */
pv.Dom.Node.prototype.replaceChild = function(n, r) {
  var i = this.childNodes.indexOf(r);
  if (i == -1) throw new Error("child not found");
  if (n.parentNode) n.parentNode.removeChild(n);
  n.parentNode = this;
  n.nextSibling = r.nextSibling;
  n.previousSibling = r.previousSibling;
  if (r.previousSibling) r.previousSibling.nextSibling = n;
  else this.firstChild = n;
  if (r.nextSibling) r.nextSibling.previousSibling = n;
  else this.lastChild = n;
  this.childNodes[i] = n;
  return r;
};

/**
 * Visits each node in the tree in preorder traversal, applying the specified
 * function <i>f</i>. The arguments to the function are:<ol>
 *
 * <li>The current node.
 * <li>The current depth, starting at 0 for the root node.</ol>
 *
 * @param {function} f a function to apply to each node.
 */
pv.Dom.Node.prototype.visitBefore = function(f) {
  function visit(n, i) {
    f(n, i);
    for (var c = n.firstChild; c; c = c.nextSibling) {
      visit(c, i + 1);
    }
  }
  visit(this, 0);
};

/**
 * Visits each node in the tree in postorder traversal, applying the specified
 * function <i>f</i>. The arguments to the function are:<ol>
 *
 * <li>The current node.
 * <li>The current depth, starting at 0 for the root node.</ol>
 *
 * @param {function} f a function to apply to each node.
 */
pv.Dom.Node.prototype.visitAfter = function(f) {
  function visit(n, i) {
    for (var c = n.firstChild; c; c = c.nextSibling) {
      visit(c, i + 1);
    }
    f(n, i);
  }
  visit(this, 0);
};

/**
 * Sorts child nodes of this node, and all descendent nodes recursively, using
 * the specified comparator function <tt>f</tt>. The comparator function is
 * passed two nodes to compare.
 *
 * <p>Note: during the sort operation, the comparator function should not rely
 * on the tree being well-formed; the values of <tt>previousSibling</tt> and
 * <tt>nextSibling</tt> for the nodes being compared are not defined during the
 * sort operation.
 *
 * @param {function} f a comparator function.
 * @returns this.
 */
pv.Dom.Node.prototype.sort = function(f) {
  if (this.firstChild) {
    this.childNodes.sort(f);
    var p = this.firstChild = this.childNodes[0], c;
    delete p.previousSibling;
    for (var i = 1; i < this.childNodes.length; i++) {
      p.sort(f);
      c = this.childNodes[i];
      c.previousSibling = p;
      p = p.nextSibling = c;
    }
    this.lastChild = p;
    delete p.nextSibling;
    p.sort(f);
  }
  return this;
};

/**
 * Reverses all sibling nodes.
 *
 * @returns this.
 */
pv.Dom.Node.prototype.reverse = function() {
  var childNodes = [];
  this.visitAfter(function(n) {
      while (n.lastChild) childNodes.push(n.removeChild(n.lastChild));
      for (var c; c = childNodes.pop();) n.insertBefore(c, n.firstChild);
    });
  return this;
};

/** Returns all descendants of this node in preorder traversal. */
pv.Dom.Node.prototype.nodes = function() {
  var array = [];

  /** @private */
  function flatten(node) {
    array.push(node);
    node.childNodes.forEach(flatten);
  }

  flatten(this, array);
  return array;
};

/**
 * Toggles the child nodes of this node. If this node is not yet toggled, this
 * method removes all child nodes and appends them to a new <tt>toggled</tt>
 * array attribute on this node. Otherwise, if this node is toggled, this method
 * re-adds all toggled child nodes and deletes the <tt>toggled</tt> attribute.
 *
 * <p>This method has no effect if the node has no child nodes.
 *
 * @param {boolean} [recursive] whether the toggle should apply to descendants.
 */
pv.Dom.Node.prototype.toggle = function(recursive) {
  if (recursive) return this.toggled
      ? this.visitBefore(function(n) { if (n.toggled) n.toggle(); })
      : this.visitAfter(function(n) { if (!n.toggled) n.toggle(); });
  var n = this;
  if (n.toggled) {
    for (var c; c = n.toggled.pop();) n.appendChild(c);
    delete n.toggled;
  } else if (n.lastChild) {
    n.toggled = [];
    while (n.lastChild) n.toggled.push(n.removeChild(n.lastChild));
  }
};

/**
 * Given a flat array of values, returns a simple DOM with each value wrapped by
 * a node that is a child of the root node.
 *
 * @param {array} values.
 * @returns {array} nodes.
 */
pv.nodes = function(values) {
  var root = new pv.Dom.Node();
  for (var i = 0; i < values.length; i++) {
    root.appendChild(new pv.Dom.Node(values[i]));
  }
  return root.nodes();
};
/**
 * Returns a {@link pv.Tree} operator for the specified array. This is a
 * convenience factory method, equivalent to <tt>new pv.Tree(array)</tt>.
 *
 * @see pv.Tree
 * @param {array} array an array from which to construct a tree.
 * @returns {pv.Tree} a tree operator for the specified array.
 */
pv.tree = function(array) {
  return new pv.Tree(array);
};

/**
 * Constructs a tree operator for the specified array. This constructor should
 * not be invoked directly; use {@link pv.tree} instead.
 *
 * @class Represents a tree operator for the specified array. The tree operator
 * allows a hierarchical map to be constructed from an array; it is similar to
 * the {@link pv.Nest} operator, except the hierarchy is derived dynamically
 * from the array elements.
 *
 * <p>For example, given an array of size information for ActionScript classes:
 *
 * <pre>{ name: "flare.flex.FlareVis", size: 4116 },
 * { name: "flare.physics.DragForce", size: 1082 },
 * { name: "flare.physics.GravityForce", size: 1336 }, ...</pre>
 *
 * To facilitate visualization, it may be useful to nest the elements by their
 * package hierarchy:
 *
 * <pre>var tree = pv.tree(classes)
 *     .keys(function(d) d.name.split("."))
 *     .map();</pre>
 *
 * The resulting tree is:
 *
 * <pre>{ flare: {
 *     flex: {
 *       FlareVis: {
 *         name: "flare.flex.FlareVis",
 *         size: 4116 } },
 *     physics: {
 *       DragForce: {
 *         name: "flare.physics.DragForce",
 *         size: 1082 },
 *       GravityForce: {
 *         name: "flare.physics.GravityForce",
 *         size: 1336 } },
 *     ... } }</pre>
 *
 * By specifying a value function,
 *
 * <pre>var tree = pv.tree(classes)
 *     .keys(function(d) d.name.split("."))
 *     .value(function(d) d.size)
 *     .map();</pre>
 *
 * we can further eliminate redundant data:
 *
 * <pre>{ flare: {
 *     flex: {
 *       FlareVis: 4116 },
 *     physics: {
 *       DragForce: 1082,
 *       GravityForce: 1336 },
 *   ... } }</pre>
 *
 * For visualizations with large data sets, performance improvements may be seen
 * by storing the data in a tree format, and then flattening it into an array at
 * runtime with {@link pv.Flatten}.
 *
 * @param {array} array an array from which to construct a tree.
 */
pv.Tree = function(array) {
  this.array = array;
};

/**
 * Assigns a <i>keys</i> function to this operator; required. The keys function
 * returns an array of <tt>string</tt>s for each element in the associated
 * array; these keys determine how the elements are nested in the tree. The
 * returned keys should be unique for each element in the array; otherwise, the
 * behavior of this operator is undefined.
 *
 * @param {function} k the keys function.
 * @returns {pv.Tree} this.
 */
pv.Tree.prototype.keys = function(k) {
  this.k = k;
  return this;
};

/**
 * Assigns a <i>value</i> function to this operator; optional. The value
 * function specifies an optional transformation of the element in the array
 * before it is inserted into the map. If no value function is specified, it is
 * equivalent to using the identity function.
 *
 * @param {function} k the value function.
 * @returns {pv.Tree} this.
 */
pv.Tree.prototype.value = function(v) {
  this.v = v;
  return this;
};

/**
 * Returns a hierarchical map of values. The hierarchy is determined by the keys
 * function; the values in the map are determined by the value function.
 *
 * @returns a hierarchical map of values.
 */
pv.Tree.prototype.map = function() {
  var map = {}, o = {};
  for (var i = 0; i < this.array.length; i++) {
    o.index = i;
    var value = this.array[i], keys = this.k.call(o, value), node = map;
    for (var j = 0; j < keys.length - 1; j++) {
      node = node[keys[j]] || (node[keys[j]] = {});
    }
    node[keys[j]] = this.v ? this.v.call(o, value) : value;
  }
  return map;
};
/**
 * Returns a {@link pv.Nest} operator for the specified array. This is a
 * convenience factory method, equivalent to <tt>new pv.Nest(array)</tt>.
 *
 * @see pv.Nest
 * @param {array} array an array of elements to nest.
 * @returns {pv.Nest} a nest operator for the specified array.
 */
pv.nest = function(array) {
  return new pv.Nest(array);
};

/**
 * Constructs a nest operator for the specified array. This constructor should
 * not be invoked directly; use {@link pv.nest} instead.
 *
 * @class Represents a {@link Nest} operator for the specified array. Nesting
 * allows elements in an array to be grouped into a hierarchical tree
 * structure. The levels in the tree are specified by <i>key</i> functions. The
 * leaf nodes of the tree can be sorted by value, while the internal nodes can
 * be sorted by key. Finally, the tree can be returned either has a
 * multidimensional array via {@link #entries}, or as a hierarchical map via
 * {@link #map}. The {@link #rollup} routine similarly returns a map, collapsing
 * the elements in each leaf node using a summary function.
 *
 * <p>For example, consider the following tabular data structure of Barley
 * yields, from various sites in Minnesota during 1931-2:
 *
 * <pre>{ yield: 27.00, variety: "Manchuria", year: 1931, site: "University Farm" },
 * { yield: 48.87, variety: "Manchuria", year: 1931, site: "Waseca" },
 * { yield: 27.43, variety: "Manchuria", year: 1931, site: "Morris" }, ...</pre>
 *
 * To facilitate visualization, it may be useful to nest the elements first by
 * year, and then by variety, as follows:
 *
 * <pre>var nest = pv.nest(yields)
 *     .key(function(d) d.year)
 *     .key(function(d) d.variety)
 *     .entries();</pre>
 *
 * This returns a nested array. Each element of the outer array is a key-values
 * pair, listing the values for each distinct key:
 *
 * <pre>{ key: 1931, values: [
 *   { key: "Manchuria", values: [
 *       { yield: 27.00, variety: "Manchuria", year: 1931, site: "University Farm" },
 *       { yield: 48.87, variety: "Manchuria", year: 1931, site: "Waseca" },
 *       { yield: 27.43, variety: "Manchuria", year: 1931, site: "Morris" },
 *       ...
 *     ] },
 *   { key: "Glabron", values: [
 *       { yield: 43.07, variety: "Glabron", year: 1931, site: "University Farm" },
 *       { yield: 55.20, variety: "Glabron", year: 1931, site: "Waseca" },
 *       ...
 *     ] },
 *   ] },
 * { key: 1932, values: ... }</pre>
 *
 * Further details, including sorting and rollup, is provided below on the
 * corresponding methods.
 *
 * @param {array} array an array of elements to nest.
 */
pv.Nest = function(array) {
  this.array = array;
  this.keys = [];
};

/**
 * Nests using the specified key function. Multiple keys may be added to the
 * nest; the array elements will be nested in the order keys are specified.
 *
 * @param {function} key a key function; must return a string or suitable map
 * key.
 * @returns {pv.Nest} this.
 */
pv.Nest.prototype.key = function(key) {
  this.keys.push(key);
  return this;
};

/**
 * Sorts the previously-added keys. The natural sort order is used by default
 * (see {@link pv.naturalOrder}); if an alternative order is desired,
 * <tt>order</tt> should be a comparator function. If this method is not called
 * (i.e., keys are <i>unsorted</i>), keys will appear in the order they appear
 * in the underlying elements array. For example,
 *
 * <pre>pv.nest(yields)
 *     .key(function(d) d.year)
 *     .key(function(d) d.variety)
 *     .sortKeys()
 *     .entries()</pre>
 *
 * groups yield data by year, then variety, and sorts the variety groups
 * lexicographically (since the variety attribute is a string).
 *
 * <p>Key sort order is only used in conjunction with {@link #entries}, which
 * returns an array of key-values pairs. If the nest is used to construct a
 * {@link #map} instead, keys are unsorted.
 *
 * @param {function} [order] an optional comparator function.
 * @returns {pv.Nest} this.
 */
pv.Nest.prototype.sortKeys = function(order) {
  this.keys[this.keys.length - 1].order = order || pv.naturalOrder;
  return this;
};

/**
 * Sorts the leaf values. The natural sort order is used by default (see
 * {@link pv.naturalOrder}); if an alternative order is desired, <tt>order</tt>
 * should be a comparator function. If this method is not called (i.e., values
 * are <i>unsorted</i>), values will appear in the order they appear in the
 * underlying elements array. For example,
 *
 * <pre>pv.nest(yields)
 *     .key(function(d) d.year)
 *     .key(function(d) d.variety)
 *     .sortValues(function(a, b) a.yield - b.yield)
 *     .entries()</pre>
 *
 * groups yield data by year, then variety, and sorts the values for each
 * variety group by yield.
 *
 * <p>Value sort order, unlike keys, applies to both {@link #entries} and
 * {@link #map}. It has no effect on {@link #rollup}.
 *
 * @param {function} [order] an optional comparator function.
 * @returns {pv.Nest} this.
 */
pv.Nest.prototype.sortValues = function(order) {
  this.order = order || pv.naturalOrder;
  return this;
};

/**
 * Returns a hierarchical map of values. Each key adds one level to the
 * hierarchy. With only a single key, the returned map will have a key for each
 * distinct value of the key function; the correspond value with be an array of
 * elements with that key value. If a second key is added, this will be a nested
 * map. For example:
 *
 * <pre>pv.nest(yields)
 *     .key(function(d) d.variety)
 *     .key(function(d) d.site)
 *     .map()</pre>
 *
 * returns a map <tt>m</tt> such that <tt>m[variety][site]</tt> is an array, a subset of
 * <tt>yields</tt>, with each element having the given variety and site.
 *
 * @returns a hierarchical map of values.
 */
pv.Nest.prototype.map = function() {
  var map = {}, values = [];

  /* Build the map. */
  for (var i, j = 0; j < this.array.length; j++) {
    var x = this.array[j];
    var m = map;
    for (i = 0; i < this.keys.length - 1; i++) {
      var k = this.keys[i](x);
      if (!m[k]) m[k] = {};
      m = m[k];
    }
    k = this.keys[i](x);
    if (!m[k]) {
      var a = [];
      values.push(a);
      m[k] = a;
    }
    m[k].push(x);
  }

  /* Sort each leaf array. */
  if (this.order) {
    for (var i = 0; i < values.length; i++) {
      values[i].sort(this.order);
    }
  }

  return map;
};

/**
 * Returns a hierarchical nested array. This method is similar to
 * {@link pv.entries}, but works recursively on the entire hierarchy. Rather
 * than returning a map like {@link #map}, this method returns a nested
 * array. Each element of the array has a <tt>key</tt> and <tt>values</tt>
 * field. For leaf nodes, the <tt>values</tt> array will be a subset of the
 * underlying elements array; for non-leaf nodes, the <tt>values</tt> array will
 * contain more key-values pairs.
 *
 * <p>For an example usage, see the {@link Nest} constructor.
 *
 * @returns a hierarchical nested array.
 */
pv.Nest.prototype.entries = function() {

  /** Recursively extracts the entries for the given map. */
  function entries(map) {
    var array = [];
    for (var k in map) {
      var v = map[k];
      array.push({ key: k, values: (v instanceof Array) ? v : entries(v) });
    };
    return array;
  }

  /** Recursively sorts the values for the given key-values array. */
  function sort(array, i) {
    var o = this.keys[i].order;
    if (o) array.sort(function(a, b) { return o(a.key, b.key); });
    if (++i < this.keys.length) {
      for (var j = 0; j < array.length; j++) {
        sort.call(this, array[j].values, i);
      }
    }
    return array;
  }

  return sort.call(this, entries(this.map()), 0);
};

/**
 * Returns a rollup map. The behavior of this method is the same as
 * {@link #map}, except that the leaf values are replaced with the return value
 * of the specified rollup function <tt>f</tt>. For example,
 *
 * <pre>pv.nest(yields)
 *      .key(function(d) d.site)
 *      .rollup(function(v) pv.median(v, function(d) d.yield))</pre>
 *
 * first groups yield data by site, and then returns a map from site to median
 * yield for the given site.
 *
 * @see #map
 * @param {function} f a rollup function.
 * @returns a hierarchical map, with the leaf values computed by <tt>f</tt>.
 */
pv.Nest.prototype.rollup = function(f) {

  /** Recursively descends to the leaf nodes (arrays) and does rollup. */
  function rollup(map) {
    for (var key in map) {
      var value = map[key];
      if (value instanceof Array) {
        map[key] = f(value);
      } else {
        rollup(value);
      }
    }
    return map;
  }

  return rollup(this.map());
};
/**
 * Returns a {@link pv.Flatten} operator for the specified map. This is a
 * convenience factory method, equivalent to <tt>new pv.Flatten(map)</tt>.
 *
 * @see pv.Flatten
 * @param map a map to flatten.
 * @returns {pv.Flatten} a flatten operator for the specified map.
 */
pv.flatten = function(map) {
  return new pv.Flatten(map);
};

/**
 * Constructs a flatten operator for the specified map. This constructor should
 * not be invoked directly; use {@link pv.flatten} instead.
 *
 * @class Represents a flatten operator for the specified array. Flattening
 * allows hierarchical maps to be flattened into an array. The levels in the
 * input tree are specified by <i>key</i> functions.
 *
 * <p>For example, consider the following hierarchical data structure of Barley
 * yields, from various sites in Minnesota during 1931-2:
 *
 * <pre>{ 1931: {
 *     Manchuria: {
 *       "University Farm": 27.00,
 *       "Waseca": 48.87,
 *       "Morris": 27.43,
 *       ... },
 *     Glabron: {
 *       "University Farm": 43.07,
 *       "Waseca": 55.20,
 *       ... } },
 *   1932: {
 *     ... } }</pre>
 *
 * To facilitate visualization, it may be useful to flatten the tree into a
 * tabular array:
 *
 * <pre>var array = pv.flatten(yields)
 *     .key("year")
 *     .key("variety")
 *     .key("site")
 *     .key("yield")
 *     .array();</pre>
 *
 * This returns an array of object elements. Each element in the array has
 * attributes corresponding to this flatten operator's keys:
 *
 * <pre>{ site: "University Farm", variety: "Manchuria", year: 1931, yield: 27 },
 * { site: "Waseca", variety: "Manchuria", year: 1931, yield: 48.87 },
 * { site: "Morris", variety: "Manchuria", year: 1931, yield: 27.43 },
 * { site: "University Farm", variety: "Glabron", year: 1931, yield: 43.07 },
 * { site: "Waseca", variety: "Glabron", year: 1931, yield: 55.2 }, ...</pre>
 *
 * <p>The flatten operator is roughly the inverse of the {@link pv.Nest} and
 * {@link pv.Tree} operators.
 *
 * @param map a map to flatten.
 */
pv.Flatten = function(map) {
  this.map = map;
  this.keys = [];
};

/**
 * Flattens using the specified key function. Multiple keys may be added to the
 * flatten; the tiers of the underlying tree must correspond to the specified
 * keys, in order. The order of the returned array is undefined; however, you
 * can easily sort it.
 *
 * @param {string} key the key name.
 * @param {function} [f] an optional value map function.
 * @returns {pv.Nest} this.
 */
pv.Flatten.prototype.key = function(key, f) {
  this.keys.push({name: key, value: f});
  delete this.$leaf;
  return this;
};

/**
 * Flattens using the specified leaf function. This is an alternative to
 * specifying an explicit set of keys; the tiers of the underlying tree will be
 * determined dynamically by recursing on the values, and the resulting keys
 * will be stored in the entries <tt>keys</tt> attribute. The leaf function must
 * return true for leaves, and false for internal nodes.
 *
 * @param {function} f a leaf function.
 * @returns {pv.Nest} this.
 */
pv.Flatten.prototype.leaf = function(f) {
  this.keys.length = 0;
  this.$leaf = f;
  return this;
};

/**
 * Returns the flattened array. Each entry in the array is an object; each
 * object has attributes corresponding to this flatten operator's keys.
 *
 * @returns an array of elements from the flattened map.
 */
pv.Flatten.prototype.array = function() {
  var entries = [], stack = [], keys = this.keys, leaf = this.$leaf;

  /* Recursively visit using the leaf function. */
  if (leaf) {
    function recurse(value, i) {
      if (leaf(value)) {
        entries.push({keys: stack.slice(), value: value});
      } else {
        for (var key in value) {
          stack.push(key);
          recurse(value[key], i + 1);
          stack.pop();
        }
      }
    }
    recurse(this.map, 0);
    return entries;
  }

  /* Recursively visits the specified value. */
  function visit(value, i) {
    if (i < keys.length - 1) {
      for (var key in value) {
        stack.push(key);
        visit(value[key], i + 1);
        stack.pop();
      }
    } else {
      entries.push(stack.concat(value));
    }
  }

  visit(this.map, 0);
  return entries.map(function(stack) {
      var m = {};
      for (var i = 0; i < keys.length; i++) {
        var k = keys[i], v = stack[i];
        m[k.name] = k.value ? k.value.call(null, v) : v;
      }
      return m;
    });
};
/**
 * Returns a {@link pv.Vector} for the specified <i>x</i> and <i>y</i>
 * coordinate. This is a convenience factory method, equivalent to <tt>new
 * pv.Vector(x, y)</tt>.
 *
 * @see pv.Vector
 * @param {number} x the <i>x</i> coordinate.
 * @param {number} y the <i>y</i> coordinate.
 * @returns {pv.Vector} a vector for the specified coordinates.
 */
pv.vector = function(x, y) {
  return new pv.Vector(x, y);
};

/**
 * Constructs a {@link pv.Vector} for the specified <i>x</i> and <i>y</i>
 * coordinate. This constructor should not be invoked directly; use
 * {@link pv.vector} instead.
 *
 * @class Represents a two-dimensional vector; a 2-tuple <i>&#x27e8;x,
 * y&#x27e9;</i>. The intent of this class is to simplify vector math. Note that
 * in performance-sensitive cases it may be more efficient to represent 2D
 * vectors as simple objects with <tt>x</tt> and <tt>y</tt> attributes, rather
 * than using instances of this class.
 *
 * @param {number} x the <i>x</i> coordinate.
 * @param {number} y the <i>y</i> coordinate.
 */
pv.Vector = function(x, y) {
  this.x = x;
  this.y = y;
};

/**
 * Returns a vector perpendicular to this vector: <i>&#x27e8;-y, x&#x27e9;</i>.
 *
 * @returns {pv.Vector} a perpendicular vector.
 */
pv.Vector.prototype.perp = function() {
  return new pv.Vector(-this.y, this.x);
};

/**
 * Returns a normalized copy of this vector: a vector with the same direction,
 * but unit length. If this vector has zero length this method returns a copy of
 * this vector.
 *
 * @returns {pv.Vector} a unit vector.
 */
pv.Vector.prototype.norm = function() {
  var l = this.length();
  return this.times(l ? (1 / l) : 1);
};

/**
 * Returns the magnitude of this vector, defined as <i>sqrt(x * x + y * y)</i>.
 *
 * @returns {number} a length.
 */
pv.Vector.prototype.length = function() {
  return Math.sqrt(this.x * this.x + this.y * this.y);
};

/**
 * Returns a scaled copy of this vector: <i>&#x27e8;x * k, y * k&#x27e9;</i>.
 * To perform the equivalent divide operation, use <i>1 / k</i>.
 *
 * @param {number} k the scale factor.
 * @returns {pv.Vector} a scaled vector.
 */
pv.Vector.prototype.times = function(k) {
  return new pv.Vector(this.x * k, this.y * k);
};

/**
 * Returns this vector plus the vector <i>v</i>: <i>&#x27e8;x + v.x, y +
 * v.y&#x27e9;</i>. If only one argument is specified, it is interpreted as the
 * vector <i>v</i>.
 *
 * @param {number} x the <i>x</i> coordinate to add.
 * @param {number} y the <i>y</i> coordinate to add.
 * @returns {pv.Vector} a new vector.
 */
pv.Vector.prototype.plus = function(x, y) {
  return (arguments.length == 1)
      ? new pv.Vector(this.x + x.x, this.y + x.y)
      : new pv.Vector(this.x + x, this.y + y);
};

/**
 * Returns this vector minus the vector <i>v</i>: <i>&#x27e8;x - v.x, y -
 * v.y&#x27e9;</i>. If only one argument is specified, it is interpreted as the
 * vector <i>v</i>.
 *
 * @param {number} x the <i>x</i> coordinate to subtract.
 * @param {number} y the <i>y</i> coordinate to subtract.
 * @returns {pv.Vector} a new vector.
 */
pv.Vector.prototype.minus = function(x, y) {
  return (arguments.length == 1)
      ? new pv.Vector(this.x - x.x, this.y - x.y)
      : new pv.Vector(this.x - x, this.y - y);
};

/**
 * Returns the dot product of this vector and the vector <i>v</i>: <i>x * v.x +
 * y * v.y</i>. If only one argument is specified, it is interpreted as the
 * vector <i>v</i>.
 *
 * @param {number} x the <i>x</i> coordinate to dot.
 * @param {number} y the <i>y</i> coordinate to dot.
 * @returns {number} a dot product.
 */
pv.Vector.prototype.dot = function(x, y) {
  return (arguments.length == 1)
      ? this.x * x.x + this.y * x.y
      : this.x * x + this.y * y;
};
/**
 * Returns a new identity transform.
 *
 * @class Represents a transformation matrix. The transformation matrix is
 * limited to expressing translate and uniform scale transforms only; shearing,
 * rotation, general affine, and other transforms are not supported.
 *
 * <p>The methods on this class treat the transform as immutable, returning a
 * copy of the transformation matrix with the specified transform applied. Note,
 * alternatively, that the matrix fields can be get and set directly.
 */
pv.Transform = function() {};
pv.Transform.prototype = {k: 1, x: 0, y: 0};

/**
 * The scale magnitude; defaults to 1.
 *
 * @type number
 * @name pv.Transform.prototype.k
 */

/**
 * The x-offset; defaults to 0.
 *
 * @type number
 * @name pv.Transform.prototype.x
 */

/**
 * The y-offset; defaults to 0.
 *
 * @type number
 * @name pv.Transform.prototype.y
 */

/**
 * @private The identity transform.
 *
 * @type pv.Transform
 */
pv.Transform.identity = new pv.Transform();

// k 0 x   1 0 a   k 0 ka+x
// 0 k y * 0 1 b = 0 k kb+y
// 0 0 1   0 0 1   0 0 1

/**
 * Returns a translated copy of this transformation matrix.
 *
 * @param {number} x the x-offset.
 * @param {number} y the y-offset.
 * @returns {pv.Transform} the translated transformation matrix.
 */
pv.Transform.prototype.translate = function(x, y) {
  var v = new pv.Transform();
  v.k = this.k;
  v.x = this.k * x + this.x;
  v.y = this.k * y + this.y;
  return v;
};

// k 0 x   d 0 0   kd  0 x
// 0 k y * 0 d 0 =  0 kd y
// 0 0 1   0 0 1    0  0 1

/**
 * Returns a scaled copy of this transformation matrix.
 *
 * @param {number} k
 * @returns {pv.Transform} the scaled transformation matrix.
 */
pv.Transform.prototype.scale = function(k) {
  var v = new pv.Transform();
  v.k = this.k * k;
  v.x = this.x;
  v.y = this.y;
  return v;
};

/**
 * Returns the inverse of this transformation matrix.
 *
 * @returns {pv.Transform} the inverted transformation matrix.
 */
pv.Transform.prototype.invert = function() {
  var v = new pv.Transform(), k = 1 / this.k;
  v.k = k;
  v.x = -this.x * k;
  v.y = -this.y * k;
  return v;
};

// k 0 x   d 0 a   kd  0 ka+x
// 0 k y * 0 d b =  0 kd kb+y
// 0 0 1   0 0 1    0  0    1

/**
 * Returns this matrix post-multiplied by the specified matrix <i>m</i>.
 *
 * @param {pv.Transform} m
 * @returns {pv.Transform} the post-multiplied transformation matrix.
 */
pv.Transform.prototype.times = function(m) {
  var v = new pv.Transform();
  v.k = this.k * m.k;
  v.x = this.k * m.x + this.x;
  v.y = this.k * m.y + this.y;
  return v;
};
/**
 * Abstract; see the various scale implementations.
 *
 * @class Represents a scale; a function that performs a transformation from
 * data domain to visual range. For quantitative and quantile scales, the domain
 * is expressed as numbers; for ordinal scales, the domain is expressed as
 * strings (or equivalently objects with unique string representations). The
 * "visual range" may correspond to pixel space, colors, font sizes, and the
 * like.
 *
 * <p>Note that scales are functions, and thus can be used as properties
 * directly, assuming that the data associated with a mark is a number. While
 * this is convenient for single-use scales, frequently it is desirable to
 * define scales globally:
 *
 * <pre>var y = pv.Scale.linear(0, 100).range(0, 640);</pre>
 *
 * The <tt>y</tt> scale can now be equivalently referenced within a property:
 *
 * <pre>    .height(function(d) y(d))</pre>
 *
 * Alternatively, if the data are not simple numbers, the appropriate value can
 * be passed to the <tt>y</tt> scale (e.g., <tt>d.foo</tt>). The {@link #by}
 * method similarly allows the data to be mapped to a numeric value before
 * performing the linear transformation.
 *
 * @see pv.Scale.quantitative
 * @see pv.Scale.quantile
 * @see pv.Scale.ordinal
 * @extends function
 */
pv.Scale = function() {};

/**
 * @private Returns a function that interpolators from the start value to the
 * end value, given a parameter <i>t</i> in [0, 1].
 *
 * @param start the start value.
 * @param end the end value.
 */
pv.Scale.interpolator = function(start, end) {
  if (typeof start == "number") {
    return function(t) {
      return t * (end - start) + start;
    };
  }

  /* For now, assume color. */
  start = pv.color(start).rgb();
  end = pv.color(end).rgb();
  return function(t) {
    var a = start.a * (1 - t) + end.a * t;
    if (a < 1e-5) a = 0; // avoid scientific notation
    return (start.a == 0) ? pv.rgb(end.r, end.g, end.b, a)
        : ((end.a == 0) ? pv.rgb(start.r, start.g, start.b, a)
        : pv.rgb(
            Math.round(start.r * (1 - t) + end.r * t),
            Math.round(start.g * (1 - t) + end.g * t),
            Math.round(start.b * (1 - t) + end.b * t), a));
  };
};

/**
 * Returns a view of this scale by the specified accessor function <tt>f</tt>.
 * Given a scale <tt>y</tt>, <tt>y.by(function(d) d.foo)</tt> is equivalent to
 * <tt>function(d) y(d.foo)</tt>.
 *
 * <p>This method is provided for convenience, such that scales can be
 * succinctly defined inline. For example, given an array of data elements that
 * have a <tt>score</tt> attribute with the domain [0, 1], the height property
 * could be specified as:
 *
 * <pre>    .height(pv.Scale.linear().range(0, 480).by(function(d) d.score))</pre>
 *
 * This is equivalent to:
 *
 * <pre>    .height(function(d) d.score * 480)</pre>
 *
 * This method should be used judiciously; it is typically more clear to invoke
 * the scale directly, passing in the value to be scaled.
 *
 * @function
 * @name pv.Scale.prototype.by
 * @param {function} f an accessor function.
 * @returns {pv.Scale} a view of this scale by the specified accessor function.
 */
/**
 * Returns a default quantitative, linear, scale for the specified domain. The
 * arguments to this constructor are optional, and equivalent to calling
 * {@link #domain}. The default domain and range are [0,1].
 *
 * <p>This constructor is typically not used directly; see one of the
 * quantitative scale implementations instead.
 *
 * @class Represents an abstract quantitative scale; a function that performs a
 * numeric transformation. This class is typically not used directly; see one of
 * the quantitative scale implementations (linear, log, root, etc.)
 * instead. <style type="text/css">sub{line-height:0}</style> A quantitative
 * scale represents a 1-dimensional transformation from a numeric domain of
 * input data [<i>d<sub>0</sub></i>, <i>d<sub>1</sub></i>] to a numeric range of
 * pixels [<i>r<sub>0</sub></i>, <i>r<sub>1</sub></i>]. In addition to
 * readability, scales offer several useful features:
 *
 * <p>1. The range can be expressed in colors, rather than pixels. For example:
 *
 * <pre>    .fillStyle(pv.Scale.linear(0, 100).range("red", "green"))</pre>
 *
 * will fill the marks "red" on an input value of 0, "green" on an input value
 * of 100, and some color in-between for intermediate values.
 *
 * <p>2. The domain and range can be subdivided for a non-uniform
 * transformation. For example, you may want a diverging color scale that is
 * increasingly red for negative values, and increasingly green for positive
 * values:
 *
 * <pre>    .fillStyle(pv.Scale.linear(-1, 0, 1).range("red", "white", "green"))</pre>
 *
 * The domain can be specified as a series of <i>n</i> monotonically-increasing
 * values; the range must also be specified as <i>n</i> values, resulting in
 * <i>n - 1</i> contiguous linear scales.
 *
 * <p>3. Quantitative scales can be inverted for interaction. The
 * {@link #invert} method takes a value in the output range, and returns the
 * corresponding value in the input domain. This is frequently used to convert
 * the mouse location (see {@link pv.Mark#mouse}) to a value in the input
 * domain. Note that inversion is only supported for numeric ranges, and not
 * colors.
 *
 * <p>4. A scale can be queried for reasonable "tick" values. The {@link #ticks}
 * method provides a convenient way to get a series of evenly-spaced rounded
 * values in the input domain. Frequently these are used in conjunction with
 * {@link pv.Rule} to display tick marks or grid lines.
 *
 * <p>5. A scale can be "niced" to extend the domain to suitable rounded
 * numbers. If the minimum and maximum of the domain are messy because they are
 * derived from data, you can use {@link #nice} to round these values down and
 * up to even numbers.
 *
 * @param {number...} domain... optional domain values.
 * @see pv.Scale.linear
 * @see pv.Scale.log
 * @see pv.Scale.root
 * @extends pv.Scale
 */
pv.Scale.quantitative = function() {
  var d = [0, 1], // default domain
      l = [0, 1], // default transformed domain
      r = [0, 1], // default range
      i = [pv.identity], // default interpolators
      type = Number, // default type
      n = false, // whether the domain is negative
      f = pv.identity, // default forward transform
      g = pv.identity, // default inverse transform
      tickFormat = String; // default tick formatting function

  /** @private */
  function newDate(x) {
    return new Date(x);
  }

  /** @private */
  function scale(x) {
    var j = pv.search(d, x);
    if (j < 0) j = -j - 2;
    j = Math.max(0, Math.min(i.length - 1, j));
    return i[j]((f(x) - l[j]) / (l[j + 1] - l[j]));
  }

  /** @private */
  scale.transform = function(forward, inverse) {
    /** @ignore */ f = function(x) { return n ? -forward(-x) : forward(x); };
    /** @ignore */ g = function(y) { return n ? -inverse(-y) : inverse(y); };
    l = d.map(f);
    return this;
  };

  /**
   * Sets or gets the input domain. This method can be invoked several ways:
   *
   * <p>1. <tt>domain(min, ..., max)</tt>
   *
   * <p>Specifying the domain as a series of numbers is the most explicit and
   * recommended approach. Most commonly, two numbers are specified: the minimum
   * and maximum value. However, for a diverging scale, or other subdivided
   * non-uniform scales, multiple values can be specified. Values can be derived
   * from data using {@link pv.min} and {@link pv.max}. For example:
   *
   * <pre>    .domain(0, pv.max(array))</pre>
   *
   * An alternative method for deriving minimum and maximum values from data
   * follows.
   *
   * <p>2. <tt>domain(array, minf, maxf)</tt>
   *
   * <p>When both the minimum and maximum value are derived from data, the
   * arguments to the <tt>domain</tt> method can be specified as the array of
   * data, followed by zero, one or two accessor functions. For example, if the
   * array of data is just an array of numbers:
   *
   * <pre>    .domain(array)</pre>
   *
   * On the other hand, if the array elements are objects representing stock
   * values per day, and the domain should consider the stock's daily low and
   * daily high:
   *
   * <pre>    .domain(array, function(d) d.low, function(d) d.high)</pre>
   *
   * The first method of setting the domain is preferred because it is more
   * explicit; setting the domain using this second method should be used only
   * if brevity is required.
   *
   * <p>3. <tt>domain()</tt>
   *
   * <p>Invoking the <tt>domain</tt> method with no arguments returns the
   * current domain as an array of numbers.
   *
   * @function
   * @name pv.Scale.quantitative.prototype.domain
   * @param {number...} domain... domain values.
   * @returns {pv.Scale.quantitative} <tt>this</tt>, or the current domain.
   */
  scale.domain = function(array, min, max) {
    if (arguments.length) {
      var o; // the object we use to infer the domain type
      if (array instanceof Array) {
        if (arguments.length < 2) min = pv.identity;
        if (arguments.length < 3) max = min;
        o = array.length && min(array[0]);
        d = array.length ? [pv.min(array, min), pv.max(array, max)] : [];
      } else {
        o = array;
        d = Array.prototype.slice.call(arguments).map(Number);
      }
      if (!d.length) d = [-Infinity, Infinity];
      else if (d.length == 1) d = [d[0], d[0]];
      n = (d[0] || d[d.length - 1]) < 0;
      l = d.map(f);
      type = (o instanceof Date) ? newDate : Number;
      return this;
    }
    return d.map(type);
  };

  /**
   * Sets or gets the output range. This method can be invoked several ways:
   *
   * <p>1. <tt>range(min, ..., max)</tt>
   *
   * <p>The range may be specified as a series of numbers or colors. Most
   * commonly, two numbers are specified: the minimum and maximum pixel values.
   * For a color scale, values may be specified as {@link pv.Color}s or
   * equivalent strings. For a diverging scale, or other subdivided non-uniform
   * scales, multiple values can be specified. For example:
   *
   * <pre>    .range("red", "white", "green")</pre>
   *
   * <p>Currently, only numbers and colors are supported as range values. The
   * number of range values must exactly match the number of domain values, or
   * the behavior of the scale is undefined.
   *
   * <p>2. <tt>range()</tt>
   *
   * <p>Invoking the <tt>range</tt> method with no arguments returns the current
   * range as an array of numbers or colors.
   *
   * @function
   * @name pv.Scale.quantitative.prototype.range
   * @param {...} range... range values.
   * @returns {pv.Scale.quantitative} <tt>this</tt>, or the current range.
   */
  scale.range = function() {
    if (arguments.length) {
      r = Array.prototype.slice.call(arguments);
      if (!r.length) r = [-Infinity, Infinity];
      else if (r.length == 1) r = [r[0], r[0]];
      i = [];
      for (var j = 0; j < r.length - 1; j++) {
        i.push(pv.Scale.interpolator(r[j], r[j + 1]));
      }
      return this;
    }
    return r;
  };

  /**
   * Inverts the specified value in the output range, returning the
   * corresponding value in the input domain. This is frequently used to convert
   * the mouse location (see {@link pv.Mark#mouse}) to a value in the input
   * domain. Inversion is only supported for numeric ranges, and not colors.
   *
   * <p>Note that this method does not do any rounding or bounds checking. If
   * the input domain is discrete (e.g., an array index), the returned value
   * should be rounded. If the specified <tt>y</tt> value is outside the range,
   * the returned value may be equivalently outside the input domain.
   *
   * @function
   * @name pv.Scale.quantitative.prototype.invert
   * @param {number} y a value in the output range (a pixel location).
   * @returns {number} a value in the input domain.
   */
  scale.invert = function(y) {
    var j = pv.search(r, y);
    if (j < 0) j = -j - 2;
    j = Math.max(0, Math.min(i.length - 1, j));
    return type(g(l[j] + (y - r[j]) / (r[j + 1] - r[j]) * (l[j + 1] - l[j])));
  };

  /**
   * Returns an array of evenly-spaced, suitably-rounded values in the input
   * domain. This method attempts to return between 5 and 10 tick values. These
   * values are frequently used in conjunction with {@link pv.Rule} to display
   * tick marks or grid lines.
   *
   * @function
   * @name pv.Scale.quantitative.prototype.ticks
   * @param {number} [m] optional number of desired ticks.
   * @returns {number[]} an array input domain values to use as ticks.
   */
  scale.ticks = function(m) {
    var start = d[0],
        end = d[d.length - 1],
        reverse = end < start,
        min = reverse ? end : start,
        max = reverse ? start : end,
        span = max - min;

    /* Special case: empty, invalid or infinite span. */
    if (!span || !isFinite(span)) {
      if (type == newDate) tickFormat = pv.Format.date("%x");
      return [type(min)];
    }

    /* Special case: dates. */
    if (type == newDate) {
      /* Floor the date d given the precision p. */
      function floor(d, p) {
        switch (p) {
          case 31536e6: d.setMonth(0);
          case 2592e6: d.setDate(1);
          case 6048e5: if (p == 6048e5) d.setDate(d.getDate() - d.getDay());
          case 864e5: d.setHours(0);
          case 36e5: d.setMinutes(0);
          case 6e4: d.setSeconds(0);
          case 1e3: d.setMilliseconds(0);
        }
      }

      var precision, format, increment, step = 1;
      if (span >= 3 * 31536e6) {
        precision = 31536e6;
        format = "%Y";
        /** @ignore */ increment = function(d) { d.setFullYear(d.getFullYear() + step); };
      } else if (span >= 3 * 2592e6) {
        precision = 2592e6;
        format = "%m/%Y";
        /** @ignore */ increment = function(d) { d.setMonth(d.getMonth() + step); };
      } else if (span >= 3 * 6048e5) {
        precision = 6048e5;
        format = "%m/%d";
        /** @ignore */ increment = function(d) { d.setDate(d.getDate() + 7 * step); };
      } else if (span >= 3 * 864e5) {
        precision = 864e5;
        format = "%m/%d";
        /** @ignore */ increment = function(d) { d.setDate(d.getDate() + step); };
      } else if (span >= 3 * 36e5) {
        precision = 36e5;
        format = "%I:%M %p";
        /** @ignore */ increment = function(d) { d.setHours(d.getHours() + step); };
      } else if (span >= 3 * 6e4) {
        precision = 6e4;
        format = "%I:%M %p";
        /** @ignore */ increment = function(d) { d.setMinutes(d.getMinutes() + step); };
      } else if (span >= 3 * 1e3) {
        precision = 1e3;
        format = "%I:%M:%S";
        /** @ignore */ increment = function(d) { d.setSeconds(d.getSeconds() + step); };
      } else {
        precision = 1;
        format = "%S.%Qs";
        /** @ignore */ increment = function(d) { d.setTime(d.getTime() + step); };
      }
      tickFormat = pv.Format.date(format);

      var date = new Date(min), dates = [];
      floor(date, precision);

      /* If we'd generate too many ticks, skip some!. */
      var n = span / precision;
      if (n > 10) {
        switch (precision) {
          case 36e5: {
            step = (n > 20) ? 6 : 3;
            date.setHours(Math.floor(date.getHours() / step) * step);
            break;
          }
          case 2592e6: {
            step = 3; // seasons
            date.setMonth(Math.floor(date.getMonth() / step) * step);
            break;
          }
          case 6e4: {
            step = (n > 30) ? 15 : ((n > 15) ? 10 : 5);
            date.setMinutes(Math.floor(date.getMinutes() / step) * step);
            break;
          }
          case 1e3: {
            step = (n > 90) ? 15 : ((n > 60) ? 10 : 5);
            date.setSeconds(Math.floor(date.getSeconds() / step) * step);
            break;
          }
          case 1: {
            step = (n > 1000) ? 250 : ((n > 200) ? 100 : ((n > 100) ? 50 : ((n > 50) ? 25 : 5)));
            date.setMilliseconds(Math.floor(date.getMilliseconds() / step) * step);
            break;
          }
          default: {
            step = pv.logCeil(n / 15, 10);
            if (n / step < 2) step /= 5;
            else if (n / step < 5) step /= 2;
            date.setFullYear(Math.floor(date.getFullYear() / step) * step);
            break;
          }
        }
      }

      while (true) {
        increment(date);
        if (date > max) break;
        dates.push(new Date(date));
      }
      return reverse ? dates.reverse() : dates;
    }

    /* Normal case: numbers. */
    if (!arguments.length) m = 10;
    var step = pv.logFloor(span / m, 10),
        err = m / (span / step);
    if (err <= .15) step *= 10;
    else if (err <= .35) step *= 5;
    else if (err <= .75) step *= 2;
    var start = Math.ceil(min / step) * step,
        end = Math.floor(max / step) * step;
    tickFormat = pv.Format.number()
        .fractionDigits(Math.max(0, -Math.floor(pv.log(step, 10) + .01)));
    var ticks = pv.range(start, end + step, step);
    return reverse ? ticks.reverse() : ticks;
  };

  /**
   * Formats the specified tick value using the appropriate precision, based on
   * the step interval between tick marks. If {@link #ticks} has not been called,
   * the argument is converted to a string, but no formatting is applied.
   *
   * @function
   * @name pv.Scale.quantitative.prototype.tickFormat
   * @param {number} t a tick value.
   * @returns {string} a formatted tick value.
   */
  scale.tickFormat = function (t) { return tickFormat(t); };

  /**
   * "Nices" this scale, extending the bounds of the input domain to
   * evenly-rounded values. Nicing is useful if the domain is computed
   * dynamically from data, and may be irregular. For example, given a domain of
   * [0.20147987687960267, 0.996679553296417], a call to <tt>nice()</tt> might
   * extend the domain to [0.2, 1].
   *
   * <p>This method must be invoked each time after setting the domain.
   *
   * @function
   * @name pv.Scale.quantitative.prototype.nice
   * @returns {pv.Scale.quantitative} <tt>this</tt>.
   */
  scale.nice = function() {
    if (d.length != 2) return this; // TODO support non-uniform domains
    var start = d[0],
        end = d[d.length - 1],
        reverse = end < start,
        min = reverse ? end : start,
        max = reverse ? start : end,
        span = max - min;

    /* Special case: empty, invalid or infinite span. */
    if (!span || !isFinite(span)) return this;

    var step = Math.pow(10, Math.round(Math.log(span) / Math.log(10)) - 1);
    d = [Math.floor(min / step) * step, Math.ceil(max / step) * step];
    if (reverse) d.reverse();
    l = d.map(f);
    return this;
  };

  /**
   * Returns a view of this scale by the specified accessor function <tt>f</tt>.
   * Given a scale <tt>y</tt>, <tt>y.by(function(d) d.foo)</tt> is equivalent to
   * <tt>function(d) y(d.foo)</tt>.
   *
   * <p>This method is provided for convenience, such that scales can be
   * succinctly defined inline. For example, given an array of data elements
   * that have a <tt>score</tt> attribute with the domain [0, 1], the height
   * property could be specified as:
   *
   * <pre>    .height(pv.Scale.linear().range(0, 480).by(function(d) d.score))</pre>
   *
   * This is equivalent to:
   *
   * <pre>    .height(function(d) d.score * 480)</pre>
   *
   * This method should be used judiciously; it is typically more clear to
   * invoke the scale directly, passing in the value to be scaled.
   *
   * @function
   * @name pv.Scale.quantitative.prototype.by
   * @param {function} f an accessor function.
   * @returns {pv.Scale.quantitative} a view of this scale by the specified
   * accessor function.
   */
  scale.by = function(f) {
    function by() { return scale(f.apply(this, arguments)); }
    for (var method in scale) by[method] = scale[method];
    return by;
  };

  scale.domain.apply(scale, arguments);
  return scale;
};
/**
 * Returns a linear scale for the specified domain. The arguments to this
 * constructor are optional, and equivalent to calling {@link #domain}.
 * The default domain and range are [0,1].
 *
 * @class Represents a linear scale; a function that performs a linear
 * transformation. <style type="text/css">sub{line-height:0}</style> Most
 * commonly, a linear scale represents a 1-dimensional linear transformation
 * from a numeric domain of input data [<i>d<sub>0</sub></i>,
 * <i>d<sub>1</sub></i>] to a numeric range of pixels [<i>r<sub>0</sub></i>,
 * <i>r<sub>1</sub></i>]. The equation for such a scale is:
 *
 * <blockquote><i>f(x) = (x - d<sub>0</sub>) / (d<sub>1</sub> - d<sub>0</sub>) *
 * (r<sub>1</sub> - r<sub>0</sub>) + r<sub>0</sub></i></blockquote>
 *
 * For example, a linear scale from the domain [0, 100] to range [0, 640]:
 *
 * <blockquote><i>f(x) = (x - 0) / (100 - 0) * (640 - 0) + 0</i><br>
 * <i>f(x) = x / 100 * 640</i><br>
 * <i>f(x) = x * 6.4</i><br>
 * </blockquote>
 *
 * Thus, saying
 *
 * <pre>    .height(function(d) d * 6.4)</pre>
 *
 * is identical to
 *
 * <pre>    .height(pv.Scale.linear(0, 100).range(0, 640))</pre>
 *
 * Note that the scale is itself a function, and thus can be used as a property
 * directly, assuming that the data associated with a mark is a number. While
 * this is convenient for single-use scales, frequently it is desirable to
 * define scales globally:
 *
 * <pre>var y = pv.Scale.linear(0, 100).range(0, 640);</pre>
 *
 * The <tt>y</tt> scale can now be equivalently referenced within a property:
 *
 * <pre>    .height(function(d) y(d))</pre>
 *
 * Alternatively, if the data are not simple numbers, the appropriate value can
 * be passed to the <tt>y</tt> scale (e.g., <tt>d.foo</tt>). The {@link #by}
 * method similarly allows the data to be mapped to a numeric value before
 * performing the linear transformation.
 *
 * @param {number...} domain... optional domain values.
 * @extends pv.Scale.quantitative
 */
pv.Scale.linear = function() {
  var scale = pv.Scale.quantitative();
  scale.domain.apply(scale, arguments);
  return scale;
};
/**
 * Returns a log scale for the specified domain. The arguments to this
 * constructor are optional, and equivalent to calling {@link #domain}.
 * The default domain is [1,10] and the default range is [0,1].
 *
 * @class Represents a log scale. <style
 * type="text/css">sub{line-height:0}</style> Most commonly, a log scale
 * represents a 1-dimensional log transformation from a numeric domain of input
 * data [<i>d<sub>0</sub></i>, <i>d<sub>1</sub></i>] to a numeric range of
 * pixels [<i>r<sub>0</sub></i>, <i>r<sub>1</sub></i>]. The equation for such a
 * scale is:
 *
 * <blockquote><i>f(x) = (log(x) - log(d<sub>0</sub>)) / (log(d<sub>1</sub>) -
 * log(d<sub>0</sub>)) * (r<sub>1</sub> - r<sub>0</sub>) +
 * r<sub>0</sub></i></blockquote>
 *
 * where <i>log(x)</i> represents the zero-symmetric logarthim of <i>x</i> using
 * the scale's associated base (default: 10, see {@link pv.logSymmetric}). For
 * example, a log scale from the domain [1, 100] to range [0, 640]:
 *
 * <blockquote><i>f(x) = (log(x) - log(1)) / (log(100) - log(1)) * (640 - 0) + 0</i><br>
 * <i>f(x) = log(x) / 2 * 640</i><br>
 * <i>f(x) = log(x) * 320</i><br>
 * </blockquote>
 *
 * Thus, saying
 *
 * <pre>    .height(function(d) Math.log(d) * 138.974)</pre>
 *
 * is equivalent to
 *
 * <pre>    .height(pv.Scale.log(1, 100).range(0, 640))</pre>
 *
 * Note that the scale is itself a function, and thus can be used as a property
 * directly, assuming that the data associated with a mark is a number. While
 * this is convenient for single-use scales, frequently it is desirable to
 * define scales globally:
 *
 * <pre>var y = pv.Scale.log(1, 100).range(0, 640);</pre>
 *
 * The <tt>y</tt> scale can now be equivalently referenced within a property:
 *
 * <pre>    .height(function(d) y(d))</pre>
 *
 * Alternatively, if the data are not simple numbers, the appropriate value can
 * be passed to the <tt>y</tt> scale (e.g., <tt>d.foo</tt>). The {@link #by}
 * method similarly allows the data to be mapped to a numeric value before
 * performing the log transformation.
 *
 * @param {number...} domain... optional domain values.
 * @extends pv.Scale.quantitative
 */
pv.Scale.log = function() {
  var scale = pv.Scale.quantitative(1, 10),
      b, // logarithm base
      p, // cached Math.log(b)
      /** @ignore */ log = function(x) { return Math.log(x) / p; },
      /** @ignore */ pow = function(y) { return Math.pow(b, y); };

  /**
   * Returns an array of evenly-spaced, suitably-rounded values in the input
   * domain. These values are frequently used in conjunction with
   * {@link pv.Rule} to display tick marks or grid lines.
   *
   * @function
   * @name pv.Scale.log.prototype.ticks
   * @returns {number[]} an array input domain values to use as ticks.
   */
  scale.ticks = function() {
    // TODO support non-uniform domains
    var d = scale.domain(),
        n = d[0] < 0,
        i = Math.floor(n ? -log(-d[0]) : log(d[0])),
        j = Math.ceil(n ? -log(-d[1]) : log(d[1])),
        ticks = [];
    if (n) {
      ticks.push(-pow(-i));
      for (; i++ < j;) for (var k = b - 1; k > 0; k--) ticks.push(-pow(-i) * k);
    } else {
      for (; i < j; i++) for (var k = 1; k < b; k++) ticks.push(pow(i) * k);
      ticks.push(pow(i));
    }
    for (i = 0; ticks[i] < d[0]; i++); // strip small values
    for (j = ticks.length; ticks[j - 1] > d[1]; j--); // strip big values
    return ticks.slice(i, j);
  };

  /**
   * Formats the specified tick value using the appropriate precision, assuming
   * base 10.
   *
   * @function
   * @name pv.Scale.log.prototype.tickFormat
   * @param {number} t a tick value.
   * @returns {string} a formatted tick value.
   */
  scale.tickFormat = function(t) {
    return t.toPrecision(1);
  };

  /**
   * "Nices" this scale, extending the bounds of the input domain to
   * evenly-rounded values. This method uses {@link pv.logFloor} and
   * {@link pv.logCeil}. Nicing is useful if the domain is computed dynamically
   * from data, and may be irregular. For example, given a domain of
   * [0.20147987687960267, 0.996679553296417], a call to <tt>nice()</tt> might
   * extend the domain to [0.1, 1].
   *
   * <p>This method must be invoked each time after setting the domain (and
   * base).
   *
   * @function
   * @name pv.Scale.log.prototype.nice
   * @returns {pv.Scale.log} <tt>this</tt>.
   */
  scale.nice = function() {
    // TODO support non-uniform domains
    var d = scale.domain();
    return scale.domain(pv.logFloor(d[0], b), pv.logCeil(d[1], b));
  };

  /**
   * Sets or gets the logarithm base. Defaults to 10.
   *
   * @function
   * @name pv.Scale.log.prototype.base
   * @param {number} [v] the new base.
   * @returns {pv.Scale.log} <tt>this</tt>, or the current base.
   */
  scale.base = function(v) {
    if (arguments.length) {
      b = Number(v);
      p = Math.log(b);
      scale.transform(log, pow); // update transformed domain
      return this;
    }
    return b;
  };

  scale.domain.apply(scale, arguments);
  return scale.base(10);
};
/**
 * Returns a root scale for the specified domain. The arguments to this
 * constructor are optional, and equivalent to calling {@link #domain}.
 * The default domain and range are [0,1].
 *
 * @class Represents a root scale; a function that performs a power
 * transformation. <style type="text/css">sub{line-height:0}</style> Most
 * commonly, a root scale represents a 1-dimensional root transformation from a
 * numeric domain of input data [<i>d<sub>0</sub></i>, <i>d<sub>1</sub></i>] to
 * a numeric range of pixels [<i>r<sub>0</sub></i>, <i>r<sub>1</sub></i>].
 *
 * <p>Note that the scale is itself a function, and thus can be used as a
 * property directly, assuming that the data associated with a mark is a
 * number. While this is convenient for single-use scales, frequently it is
 * desirable to define scales globally:
 *
 * <pre>var y = pv.Scale.root(0, 100).range(0, 640);</pre>
 *
 * The <tt>y</tt> scale can now be equivalently referenced within a property:
 *
 * <pre>    .height(function(d) y(d))</pre>
 *
 * Alternatively, if the data are not simple numbers, the appropriate value can
 * be passed to the <tt>y</tt> scale (e.g., <tt>d.foo</tt>). The {@link #by}
 * method similarly allows the data to be mapped to a numeric value before
 * performing the root transformation.
 *
 * @param {number...} domain... optional domain values.
 * @extends pv.Scale.quantitative
 */
pv.Scale.root = function() {
  var scale = pv.Scale.quantitative();

  /**
   * Sets or gets the exponent; defaults to 2.
   *
   * @function
   * @name pv.Scale.root.prototype.power
   * @param {number} [v] the new exponent.
   * @returns {pv.Scale.root} <tt>this</tt>, or the current base.
   */
  scale.power = function(v) {
    if (arguments.length) {
      var b = Number(v), p = 1 / b;
      scale.transform(
        function(x) { return Math.pow(x, p); },
        function(y) { return Math.pow(y, b); });
      return this;
    }
    return b;
  };

  scale.domain.apply(scale, arguments);
  return scale.power(2);
};
/**
 * Returns an ordinal scale for the specified domain. The arguments to this
 * constructor are optional, and equivalent to calling {@link #domain}.
 *
 * @class Represents an ordinal scale. <style
 * type="text/css">sub{line-height:0}</style> An ordinal scale represents a
 * pairwise mapping from <i>n</i> discrete values in the input domain to
 * <i>n</i> discrete values in the output range. For example, an ordinal scale
 * might map a domain of species ["setosa", "versicolor", "virginica"] to colors
 * ["red", "green", "blue"]. Thus, saying
 *
 * <pre>    .fillStyle(function(d) {
 *         switch (d.species) {
 *           case "setosa": return "red";
 *           case "versicolor": return "green";
 *           case "virginica": return "blue";
 *         }
 *       })</pre>
 *
 * is equivalent to
 *
 * <pre>    .fillStyle(pv.Scale.ordinal("setosa", "versicolor", "virginica")
 *         .range("red", "green", "blue")
 *         .by(function(d) d.species))</pre>
 *
 * If the mapping from species to color does not need to be specified
 * explicitly, the domain can be omitted. In this case it will be inferred
 * lazily from the data:
 *
 * <pre>    .fillStyle(pv.colors("red", "green", "blue")
 *         .by(function(d) d.species))</pre>
 *
 * When the domain is inferred, the first time the scale is invoked, the first
 * element from the range will be returned. Subsequent calls with unique values
 * will return subsequent elements from the range. If the inferred domain grows
 * larger than the range, range values will be reused. However, it is strongly
 * recommended that the domain and the range contain the same number of
 * elements.
 *
 * <p>A range can be discretized from a continuous interval (e.g., for pixel
 * positioning) by using {@link #split}, {@link #splitFlush} or
 * {@link #splitBanded} after the domain has been set. For example, if
 * <tt>states</tt> is an array of the fifty U.S. state names, the state name can
 * be encoded in the left position:
 *
 * <pre>    .left(pv.Scale.ordinal(states)
 *         .split(0, 640)
 *         .by(function(d) d.state))</pre>
 *
 * <p>N.B.: ordinal scales are not invertible (at least not yet), since the
 * domain and range and discontinuous. A workaround is to use a linear scale.
 *
 * @param {...} domain... optional domain values.
 * @extends pv.Scale
 * @see pv.colors
 */
pv.Scale.ordinal = function() {
  var d = [], i = {}, r = [], band = 0;

  /** @private */
  function scale(x) {
    if (!(x in i)) i[x] = d.push(x) - 1;
    return r[i[x] % r.length];
  }

  /**
   * Sets or gets the input domain. This method can be invoked several ways:
   *
   * <p>1. <tt>domain(values...)</tt>
   *
   * <p>Specifying the domain as a series of values is the most explicit and
   * recommended approach. However, if the domain values are derived from data,
   * you may find the second method more appropriate.
   *
   * <p>2. <tt>domain(array, f)</tt>
   *
   * <p>Rather than enumerating the domain values as explicit arguments to this
   * method, you can specify a single argument of an array. In addition, you can
   * specify an optional accessor function to extract the domain values from the
   * array.
   *
   * <p>3. <tt>domain()</tt>
   *
   * <p>Invoking the <tt>domain</tt> method with no arguments returns the
   * current domain as an array.
   *
   * @function
   * @name pv.Scale.ordinal.prototype.domain
   * @param {...} domain... domain values.
   * @returns {pv.Scale.ordinal} <tt>this</tt>, or the current domain.
   */
  scale.domain = function(array, f) {
    if (arguments.length) {
      array = (array instanceof Array)
          ? ((arguments.length > 1) ? pv.map(array, f) : array)
          : Array.prototype.slice.call(arguments);

      /* Filter the specified ordinals to their unique values. */
      d = [];
      var seen = {};
      for (var j = 0; j < array.length; j++) {
        var o = array[j];
        if (!(o in seen)) {
          seen[o] = true;
          d.push(o);
        }
      }

      i = pv.numerate(d);
      return this;
    }
    return d;
  };

  /**
   * Sets or gets the output range. This method can be invoked several ways:
   *
   * <p>1. <tt>range(values...)</tt>
   *
   * <p>Specifying the range as a series of values is the most explicit and
   * recommended approach. However, if the range values are derived from data,
   * you may find the second method more appropriate.
   *
   * <p>2. <tt>range(array, f)</tt>
   *
   * <p>Rather than enumerating the range values as explicit arguments to this
   * method, you can specify a single argument of an array. In addition, you can
   * specify an optional accessor function to extract the range values from the
   * array.
   *
   * <p>3. <tt>range()</tt>
   *
   * <p>Invoking the <tt>range</tt> method with no arguments returns the
   * current range as an array.
   *
   * @function
   * @name pv.Scale.ordinal.prototype.range
   * @param {...} range... range values.
   * @returns {pv.Scale.ordinal} <tt>this</tt>, or the current range.
   */
  scale.range = function(array, f) {
    if (arguments.length) {
      r = (array instanceof Array)
          ? ((arguments.length > 1) ? pv.map(array, f) : array)
          : Array.prototype.slice.call(arguments);
      if (typeof r[0] == "string") r = r.map(pv.color);
      return this;
    }
    return r;
  };

  /**
   * Sets the range from the given continuous interval. The interval
   * [<i>min</i>, <i>max</i>] is subdivided into <i>n</i> equispaced points,
   * where <i>n</i> is the number of (unique) values in the domain. The first
   * and last point are offset from the edge of the range by half the distance
   * between points.
   *
   * <p>This method must be called <i>after</i> the domain is set.
   *
   * @function
   * @name pv.Scale.ordinal.prototype.split
   * @param {number} min minimum value of the output range.
   * @param {number} max maximum value of the output range.
   * @returns {pv.Scale.ordinal} <tt>this</tt>.
   * @see #splitFlush
   * @see #splitBanded
   */
  scale.split = function(min, max) {
    var step = (max - min) / this.domain().length;
    r = pv.range(min + step / 2, max, step);
    return this;
  };

  /**
   * Sets the range from the given continuous interval. The interval
   * [<i>min</i>, <i>max</i>] is subdivided into <i>n</i> equispaced points,
   * where <i>n</i> is the number of (unique) values in the domain. The first
   * and last point are exactly on the edge of the range.
   *
   * <p>This method must be called <i>after</i> the domain is set.
   *
   * @function
   * @name pv.Scale.ordinal.prototype.splitFlush
   * @param {number} min minimum value of the output range.
   * @param {number} max maximum value of the output range.
   * @returns {pv.Scale.ordinal} <tt>this</tt>.
   * @see #split
   */
  scale.splitFlush = function(min, max) {
    var n = this.domain().length, step = (max - min) / (n - 1);
    r = (n == 1) ? [(min + max) / 2]
        : pv.range(min, max + step / 2, step);
    return this;
  };

  /**
   * Sets the range from the given continuous interval. The interval
   * [<i>min</i>, <i>max</i>] is subdivided into <i>n</i> equispaced bands,
   * where <i>n</i> is the number of (unique) values in the domain. The first
   * and last band are offset from the edge of the range by the distance between
   * bands.
   *
   * <p>The band width argument, <tt>band</tt>, is typically in the range [0, 1]
   * and defaults to 1. This fraction corresponds to the amount of space in the
   * range to allocate to the bands, as opposed to padding. A value of 0.5 means
   * that the band width will be equal to the padding width. The computed
   * absolute band width can be retrieved from the range as
   * <tt>scale.range().band</tt>.
   *
   * <p>If the band width argument is negative, this method will allocate bands
   * of a <i>fixed</i> width <tt>-band</tt>, rather than a relative fraction of
   * the available space.
   *
   * <p>Tip: to inset the bands by a fixed amount <tt>p</tt>, specify a minimum
   * value of <tt>min + p</tt> (or simply <tt>p</tt>, if <tt>min</tt> is
   * 0). Then set the mark width to <tt>scale.range().band - p</tt>.
   *
   * <p>This method must be called <i>after</i> the domain is set.
   *
   * @function
   * @name pv.Scale.ordinal.prototype.splitBanded
   * @param {number} min minimum value of the output range.
   * @param {number} max maximum value of the output range.
   * @param {number} [band] the fractional band width in [0, 1]; defaults to 1.
   * @returns {pv.Scale.ordinal} <tt>this</tt>.
   * @see #split
   */
  scale.splitBanded = function(min, max, band) {
    if (arguments.length < 3) band = 1;
    if (band < 0) {
      var n = this.domain().length,
          total = -band * n,
          remaining = max - min - total,
          padding = remaining / (n + 1);
      r = pv.range(min + padding, max, padding - band);
      r.band = -band;
    } else {
      var step = (max - min) / (this.domain().length + (1 - band));
      r = pv.range(min + step * (1 - band), max, step);
      r.band = step * band;
    }
    return this;
  };

  /**
   * Returns a view of this scale by the specified accessor function <tt>f</tt>.
   * Given a scale <tt>y</tt>, <tt>y.by(function(d) d.foo)</tt> is equivalent to
   * <tt>function(d) y(d.foo)</tt>. This method should be used judiciously; it
   * is typically more clear to invoke the scale directly, passing in the value
   * to be scaled.
   *
   * @function
   * @name pv.Scale.ordinal.prototype.by
   * @param {function} f an accessor function.
   * @returns {pv.Scale.ordinal} a view of this scale by the specified accessor
   * function.
   */
  scale.by = function(f) {
    function by() { return scale(f.apply(this, arguments)); }
    for (var method in scale) by[method] = scale[method];
    return by;
  };

  scale.domain.apply(scale, arguments);
  return scale;
};
/**
 * Constructs a default quantile scale. The arguments to this constructor are
 * optional, and equivalent to calling {@link #domain}. The default domain is
 * the empty set, and the default range is [0,1].
 *
 * @class Represents a quantile scale; a function that maps from a value within
 * a sortable domain to a quantized numeric range. Typically, the domain is a
 * set of numbers, but any sortable value (such as strings) can be used as the
 * domain of a quantile scale. The range defaults to [0,1], with 0 corresponding
 * to the smallest value in the domain, 1 the largest, .5 the median, etc.
 *
 * <p>By default, the number of quantiles in the range corresponds to the number
 * of values in the domain. The {@link #quantiles} method can be used to specify
 * an explicit number of quantiles; for example, <tt>quantiles(4)</tt> produces
 * a standard quartile scale. A quartile scale's range is a set of four discrete
 * values, such as [0, 1/3, 2/3, 1]. Calling the {@link #range} method will
 * scale these discrete values accordingly, similar to {@link
 * pv.Scale.ordinal#splitFlush}.
 *
 * <p>For example, given the strings ["c", "a", "b"], a default quantile scale:
 *
 * <pre>pv.Scale.quantile("c", "a", "b")</pre>
 *
 * will return 0 for "a", .5 for "b", and 1 for "c".
 *
 * @extends pv.Scale
 */
pv.Scale.quantile = function() {
  var n = -1, // number of quantiles
      j = -1, // max quantile index
      q = [], // quantile boundaries
      d = [], // domain
      y = pv.Scale.linear(); // range

  /** @private */
  function scale(x) {
    return y(Math.max(0, Math.min(j, pv.search.index(q, x) - 1)) / j);
  }

  /**
   * Sets or gets the quantile boundaries. By default, each element in the
   * domain is in its own quantile. If the argument to this method is a number,
   * it specifies the number of equal-sized quantiles by which to divide the
   * domain.
   *
   * <p>If no arguments are specified, this method returns the quantile
   * boundaries; the first element is always the minimum value of the domain,
   * and the last element is the maximum value of the domain. Thus, the length
   * of the returned array is always one greater than the number of quantiles.
   *
   * @function
   * @name pv.Scale.quantile.prototype.quantiles
   * @param {number} x the number of quantiles.
   */
  scale.quantiles = function(x) {
    if (arguments.length) {
      n = Number(x);
      if (n < 0) {
        q = [d[0]].concat(d);
        j = d.length - 1;
      } else {
        q = [];
        q[0] = d[0];
        for (var i = 1; i <= n; i++) {
          q[i] = d[~~(i * (d.length - 1) / n)];
        }
        j = n - 1;
      }
      return this;
    }
    return q;
  };

  /**
   * Sets or gets the input domain. This method can be invoked several ways:
   *
   * <p>1. <tt>domain(values...)</tt>
   *
   * <p>Specifying the domain as a series of values is the most explicit and
   * recommended approach. However, if the domain values are derived from data,
   * you may find the second method more appropriate.
   *
   * <p>2. <tt>domain(array, f)</tt>
   *
   * <p>Rather than enumerating the domain values as explicit arguments to this
   * method, you can specify a single argument of an array. In addition, you can
   * specify an optional accessor function to extract the domain values from the
   * array.
   *
   * <p>3. <tt>domain()</tt>
   *
   * <p>Invoking the <tt>domain</tt> method with no arguments returns the
   * current domain as an array.
   *
   * @function
   * @name pv.Scale.quantile.prototype.domain
   * @param {...} domain... domain values.
   * @returns {pv.Scale.quantile} <tt>this</tt>, or the current domain.
   */
  scale.domain = function(array, f) {
    if (arguments.length) {
      d = (array instanceof Array)
          ? pv.map(array, f)
          : Array.prototype.slice.call(arguments);
      d.sort(pv.naturalOrder);
      scale.quantiles(n); // recompute quantiles
      return this;
    }
    return d;
  };

  /**
   * Sets or gets the output range. This method can be invoked several ways:
   *
   * <p>1. <tt>range(min, ..., max)</tt>
   *
   * <p>The range may be specified as a series of numbers or colors. Most
   * commonly, two numbers are specified: the minimum and maximum pixel values.
   * For a color scale, values may be specified as {@link pv.Color}s or
   * equivalent strings. For a diverging scale, or other subdivided non-uniform
   * scales, multiple values can be specified. For example:
   *
   * <pre>    .range("red", "white", "green")</pre>
   *
   * <p>Currently, only numbers and colors are supported as range values. The
   * number of range values must exactly match the number of domain values, or
   * the behavior of the scale is undefined.
   *
   * <p>2. <tt>range()</tt>
   *
   * <p>Invoking the <tt>range</tt> method with no arguments returns the current
   * range as an array of numbers or colors.
   *
   * @function
   * @name pv.Scale.quantile.prototype.range
   * @param {...} range... range values.
   * @returns {pv.Scale.quantile} <tt>this</tt>, or the current range.
   */
  scale.range = function() {
    if (arguments.length) {
      y.range.apply(y, arguments);
      return this;
    }
    return y.range();
  };

  /**
   * Returns a view of this scale by the specified accessor function <tt>f</tt>.
   * Given a scale <tt>y</tt>, <tt>y.by(function(d) d.foo)</tt> is equivalent to
   * <tt>function(d) y(d.foo)</tt>.
   *
   * <p>This method is provided for convenience, such that scales can be
   * succinctly defined inline. For example, given an array of data elements
   * that have a <tt>score</tt> attribute with the domain [0, 1], the height
   * property could be specified as:
   *
   * <pre>.height(pv.Scale.linear().range(0, 480).by(function(d) d.score))</pre>
   *
   * This is equivalent to:
   *
   * <pre>.height(function(d) d.score * 480)</pre>
   *
   * This method should be used judiciously; it is typically more clear to
   * invoke the scale directly, passing in the value to be scaled.
   *
   * @function
   * @name pv.Scale.quantile.prototype.by
   * @param {function} f an accessor function.
   * @returns {pv.Scale.quantile} a view of this scale by the specified
   * accessor function.
   */
  scale.by = function(f) {
    function by() { return scale(f.apply(this, arguments)); }
    for (var method in scale) by[method] = scale[method];
    return by;
  };

  scale.domain.apply(scale, arguments);
  return scale;
};
/**
 * Returns a histogram operator for the specified data, with an optional
 * accessor function. If the data specified is not an array of numbers, an
 * accessor function must be specified to map the data to numeric values.
 *
 * @class Represents a histogram operator.
 *
 * @param {array} data an array of numbers or objects.
 * @param {function} [f] an optional accessor function.
 */
pv.histogram = function(data, f) {
  var frequency = true;
  return {

    /**
     * Returns the computed histogram bins. An optional array of numbers,
     * <tt>ticks</tt>, may be specified as the break points. If the ticks are
     * not specified, default ticks will be computed using a linear scale on the
     * data domain.
     *
     * <p>The returned array contains {@link pv.histogram.Bin}s. The <tt>x</tt>
     * attribute corresponds to the bin's start value (inclusive), while the
     * <tt>dx</tt> attribute stores the bin size (end - start). The <tt>y</tt>
     * attribute stores either the frequency count or probability, depending on
     * how the histogram operator has been configured.
     *
     * <p>The {@link pv.histogram.Bin} objects are themselves arrays, containing
     * the data elements present in each bin, i.e., the elements in the
     * <tt>data</tt> array (prior to invoking the accessor function, if any).
     * For example, if the data represented countries, and the accessor function
     * returned the GDP of each country, the returned bins would be arrays of
     * countries (not GDPs).
     *
     * @function
     * @name pv.histogram.prototype.bins
     * @param {array} [ticks]
     * @returns {array}
     */ /** @private */
    bins: function(ticks) {
      var x = pv.map(data, f), bins = [];

      /* Initialize default ticks. */
      if (!arguments.length) ticks = pv.Scale.linear(x).ticks();

      /* Initialize the bins. */
      for (var i = 0; i < ticks.length - 1; i++) {
        var bin = bins[i] = [];
        bin.x = ticks[i];
        bin.dx = ticks[i + 1] - ticks[i];
        bin.y = 0;
      }

      /* Count the number of samples per bin. */
      for (var i = 0; i < x.length; i++) {
        var j = pv.search.index(ticks, x[i]) - 1,
            bin = bins[Math.max(0, Math.min(bins.length - 1, j))];
        bin.y++;
        bin.push(data[i]);
      }

      /* Convert frequencies to probabilities. */
      if (!frequency) for (var i = 0; i < bins.length; i++) {
        bins[i].y /= x.length;
      }

      return bins;
    },

    /**
     * Sets or gets whether this histogram operator returns frequencies or
     * probabilities.
     *
     * @function
     * @name pv.histogram.prototype.frequency
     * @param {boolean} [x]
     * @returns {pv.histogram} this.
     */ /** @private */
    frequency: function(x) {
      if (arguments.length) {
        frequency = Boolean(x);
        return this;
      }
      return frequency;
    }
  };
};

/**
 * @class Represents a bin returned by the {@link pv.histogram} operator. Bins
 * are themselves arrays containing the data elements present in the given bin
 * (prior to the accessor function being invoked to convert the data object to a
 * numeric value). These bin arrays have additional attributes with meta
 * information about the bin.
 *
 * @name pv.histogram.Bin
 * @extends array
 * @see pv.histogram
 */

/**
 * The start value of the bin's range.
 *
 * @type number
 * @name pv.histogram.Bin.prototype.x
 */

/**
 * The magnitude value of the bin's range; end - start.
 *
 * @type number
 * @name pv.histogram.Bin.prototype.dx
 */

/**
 * The frequency or probability of the bin, depending on how the histogram
 * operator was configured.
 *
 * @type number
 * @name pv.histogram.Bin.prototype.y
 */
/**
 * Returns the {@link pv.Color} for the specified color format string. Colors
 * may have an associated opacity, or alpha channel. Color formats are specified
 * by CSS Color Modular Level 3, using either in RGB or HSL color space. For
 * example:<ul>
 *
 * <li>#f00 // #rgb
 * <li>#ff0000 // #rrggbb
 * <li>rgb(255, 0, 0)
 * <li>rgb(100%, 0%, 0%)
 * <li>hsl(0, 100%, 50%)
 * <li>rgba(0, 0, 255, 0.5)
 * <li>hsla(120, 100%, 50%, 1)
 *
 * </ul>The SVG 1.0 color keywords names are also supported, such as "aliceblue"
 * and "yellowgreen". The "transparent" keyword is supported for fully-
 * transparent black.
 *
 * <p>If the <tt>format</tt> argument is already an instance of <tt>Color</tt>,
 * the argument is returned with no further processing.
 *
 * @param {string} format the color specification string, such as "#f00".
 * @returns {pv.Color} the corresponding <tt>Color</tt>.
 * @see <a href="http://www.w3.org/TR/SVG/types.html#ColorKeywords">SVG color
 * keywords</a>
 * @see <a href="http://www.w3.org/TR/css3-color/">CSS3 color module</a>
 */
pv.color = function(format) {
  if (format.rgb) return format.rgb();

  /* Handle hsl, rgb. */
  var m1 = /([a-z]+)\((.*)\)/i.exec(format);
  if (m1) {
    var m2 = m1[2].split(","), a = 1;
    switch (m1[1]) {
      case "hsla":
      case "rgba": {
        a = parseFloat(m2[3]);
        if (!a) return pv.Color.transparent;
        break;
      }
    }
    switch (m1[1]) {
      case "hsla":
      case "hsl": {
        var h = parseFloat(m2[0]), // degrees
            s = parseFloat(m2[1]) / 100, // percentage
            l = parseFloat(m2[2]) / 100; // percentage
        return (new pv.Color.Hsl(h, s, l, a)).rgb();
      }
      case "rgba":
      case "rgb": {
        function parse(c) { // either integer or percentage
          var f = parseFloat(c);
          return (c[c.length - 1] == '%') ? Math.round(f * 2.55) : f;
        }
        var r = parse(m2[0]), g = parse(m2[1]), b = parse(m2[2]);
        return pv.rgb(r, g, b, a);
      }
    }
  }

  /* Named colors. */
  var named = pv.Color.names[format];
  if (named) return named;

  /* Hexadecimal colors: #rgb and #rrggbb. */
  if (format.charAt(0) == "#") {
    var r, g, b;
    if (format.length == 4) {
      r = format.charAt(1); r += r;
      g = format.charAt(2); g += g;
      b = format.charAt(3); b += b;
    } else if (format.length == 7) {
      r = format.substring(1, 3);
      g = format.substring(3, 5);
      b = format.substring(5, 7);
    }
    return pv.rgb(parseInt(r, 16), parseInt(g, 16), parseInt(b, 16), 1);
  }

  /* Otherwise, pass-through unsupported colors. */
  return new pv.Color(format, 1);
};

/**
 * Constructs a color with the specified color format string and opacity. This
 * constructor should not be invoked directly; use {@link pv.color} instead.
 *
 * @class Represents an abstract (possibly translucent) color. The color is
 * divided into two parts: the <tt>color</tt> attribute, an opaque color format
 * string, and the <tt>opacity</tt> attribute, a float in [0, 1]. The color
 * space is dependent on the implementing class; all colors support the
 * {@link #rgb} method to convert to RGB color space for interpolation.
 *
 * <p>See also the <a href="../../api/Color.html">Color guide</a>.
 *
 * @param {string} color an opaque color format string, such as "#f00".
 * @param {number} opacity the opacity, in [0,1].
 * @see pv.color
 */
pv.Color = function(color, opacity) {
  /**
   * An opaque color format string, such as "#f00".
   *
   * @type string
   * @see <a href="http://www.w3.org/TR/SVG/types.html#ColorKeywords">SVG color
   * keywords</a>
   * @see <a href="http://www.w3.org/TR/css3-color/">CSS3 color module</a>
   */
  this.color = color;

  /**
   * The opacity, a float in [0, 1].
   *
   * @type number
   */
  this.opacity = opacity;
};

/**
 * Returns a new color that is a brighter version of this color. The behavior of
 * this method may vary slightly depending on the underlying color space.
 * Although brighter and darker are inverse operations, the results of a series
 * of invocations of these two methods might be inconsistent because of rounding
 * errors.
 *
 * @param [k] {number} an optional scale factor; defaults to 1.
 * @see #darker
 * @returns {pv.Color} a brighter color.
 */
pv.Color.prototype.brighter = function(k) {
  return this.rgb().brighter(k);
};

/**
 * Returns a new color that is a brighter version of this color. The behavior of
 * this method may vary slightly depending on the underlying color space.
 * Although brighter and darker are inverse operations, the results of a series
 * of invocations of these two methods might be inconsistent because of rounding
 * errors.
 *
 * @param [k] {number} an optional scale factor; defaults to 1.
 * @see #brighter
 * @returns {pv.Color} a darker color.
 */
pv.Color.prototype.darker = function(k) {
  return this.rgb().darker(k);
};

/**
 * Constructs a new RGB color with the specified channel values.
 *
 * @param {number} r the red channel, an integer in [0,255].
 * @param {number} g the green channel, an integer in [0,255].
 * @param {number} b the blue channel, an integer in [0,255].
 * @param {number} [a] the alpha channel, a float in [0,1].
 * @returns pv.Color.Rgb
 */
pv.rgb = function(r, g, b, a) {
  return new pv.Color.Rgb(r, g, b, (arguments.length == 4) ? a : 1);
};

/**
 * Constructs a new RGB color with the specified channel values.
 *
 * @class Represents a color in RGB space.
 *
 * @param {number} r the red channel, an integer in [0,255].
 * @param {number} g the green channel, an integer in [0,255].
 * @param {number} b the blue channel, an integer in [0,255].
 * @param {number} a the alpha channel, a float in [0,1].
 * @extends pv.Color
 */
pv.Color.Rgb = function(r, g, b, a) {
  pv.Color.call(this, a ? ("rgb(" + r + "," + g + "," + b + ")") : "none", a);

  /**
   * The red channel, an integer in [0, 255].
   *
   * @type number
   */
  this.r = r;

  /**
   * The green channel, an integer in [0, 255].
   *
   * @type number
   */
  this.g = g;

  /**
   * The blue channel, an integer in [0, 255].
   *
   * @type number
   */
  this.b = b;

  /**
   * The alpha channel, a float in [0, 1].
   *
   * @type number
   */
  this.a = a;
};
pv.Color.Rgb.prototype = pv.extend(pv.Color);

/**
 * Constructs a new RGB color with the same green, blue and alpha channels as
 * this color, with the specified red channel.
 *
 * @param {number} r the red channel, an integer in [0,255].
 */
pv.Color.Rgb.prototype.red = function(r) {
  return pv.rgb(r, this.g, this.b, this.a);
};

/**
 * Constructs a new RGB color with the same red, blue and alpha channels as this
 * color, with the specified green channel.
 *
 * @param {number} g the green channel, an integer in [0,255].
 */
pv.Color.Rgb.prototype.green = function(g) {
  return pv.rgb(this.r, g, this.b, this.a);
};

/**
 * Constructs a new RGB color with the same red, green and alpha channels as
 * this color, with the specified blue channel.
 *
 * @param {number} b the blue channel, an integer in [0,255].
 */
pv.Color.Rgb.prototype.blue = function(b) {
  return pv.rgb(this.r, this.g, b, this.a);
};

/**
 * Constructs a new RGB color with the same red, green and blue channels as this
 * color, with the specified alpha channel.
 *
 * @param {number} a the alpha channel, a float in [0,1].
 */
pv.Color.Rgb.prototype.alpha = function(a) {
  return pv.rgb(this.r, this.g, this.b, a);
};

/**
 * Returns the RGB color equivalent to this color. This method is abstract and
 * must be implemented by subclasses.
 *
 * @returns {pv.Color.Rgb} an RGB color.
 * @function
 * @name pv.Color.prototype.rgb
 */

/**
 * Returns this.
 *
 * @returns {pv.Color.Rgb} this.
 */
pv.Color.Rgb.prototype.rgb = function() { return this; };

/**
 * Returns a new color that is a brighter version of this color. This method
 * applies an arbitrary scale factor to each of the three RGB components of this
 * color to create a brighter version of this color. Although brighter and
 * darker are inverse operations, the results of a series of invocations of
 * these two methods might be inconsistent because of rounding errors.
 *
 * @param [k] {number} an optional scale factor; defaults to 1.
 * @see #darker
 * @returns {pv.Color.Rgb} a brighter color.
 */
pv.Color.Rgb.prototype.brighter = function(k) {
  k = Math.pow(0.7, arguments.length ? k : 1);
  var r = this.r, g = this.g, b = this.b, i = 30;
  if (!r && !g && !b) return pv.rgb(i, i, i, this.a);
  if (r && (r < i)) r = i;
  if (g && (g < i)) g = i;
  if (b && (b < i)) b = i;
  return pv.rgb(
      Math.min(255, Math.floor(r / k)),
      Math.min(255, Math.floor(g / k)),
      Math.min(255, Math.floor(b / k)),
      this.a);
};

/**
 * Returns a new color that is a darker version of this color. This method
 * applies an arbitrary scale factor to each of the three RGB components of this
 * color to create a darker version of this color. Although brighter and darker
 * are inverse operations, the results of a series of invocations of these two
 * methods might be inconsistent because of rounding errors.
 *
 * @param [k] {number} an optional scale factor; defaults to 1.
 * @see #brighter
 * @returns {pv.Color.Rgb} a darker color.
 */
pv.Color.Rgb.prototype.darker = function(k) {
  k = Math.pow(0.7, arguments.length ? k : 1);
  return pv.rgb(
      Math.max(0, Math.floor(k * this.r)),
      Math.max(0, Math.floor(k * this.g)),
      Math.max(0, Math.floor(k * this.b)),
      this.a);
};

/**
 * Constructs a new HSL color with the specified values.
 *
 * @param {number} h the hue, an integer in [0, 360].
 * @param {number} s the saturation, a float in [0, 1].
 * @param {number} l the lightness, a float in [0, 1].
 * @param {number} [a] the opacity, a float in [0, 1].
 * @returns pv.Color.Hsl
 */
pv.hsl = function(h, s, l, a) {
  return new pv.Color.Hsl(h, s, l,  (arguments.length == 4) ? a : 1);
};

/**
 * Constructs a new HSL color with the specified values.
 *
 * @class Represents a color in HSL space.
 *
 * @param {number} h the hue, an integer in [0, 360].
 * @param {number} s the saturation, a float in [0, 1].
 * @param {number} l the lightness, a float in [0, 1].
 * @param {number} a the opacity, a float in [0, 1].
 * @extends pv.Color
 */
pv.Color.Hsl = function(h, s, l, a) {
  pv.Color.call(this, "hsl(" + h + "," + (s * 100) + "%," + (l * 100) + "%)", a);

  /**
   * The hue, an integer in [0, 360].
   *
   * @type number
   */
  this.h = h;

  /**
   * The saturation, a float in [0, 1].
   *
   * @type number
   */
  this.s = s;

  /**
   * The lightness, a float in [0, 1].
   *
   * @type number
   */
  this.l = l;

  /**
   * The opacity, a float in [0, 1].
   *
   * @type number
   */
  this.a = a;
};
pv.Color.Hsl.prototype = pv.extend(pv.Color);

/**
 * Constructs a new HSL color with the same saturation, lightness and alpha as
 * this color, and the specified hue.
 *
 * @param {number} h the hue, an integer in [0, 360].
 */
pv.Color.Hsl.prototype.hue = function(h) {
  return pv.hsl(h, this.s, this.l, this.a);
};

/**
 * Constructs a new HSL color with the same hue, lightness and alpha as this
 * color, and the specified saturation.
 *
 * @param {number} s the saturation, a float in [0, 1].
 */
pv.Color.Hsl.prototype.saturation = function(s) {
  return pv.hsl(this.h, s, this.l, this.a);
};

/**
 * Constructs a new HSL color with the same hue, saturation and alpha as this
 * color, and the specified lightness.
 *
 * @param {number} l the lightness, a float in [0, 1].
 */
pv.Color.Hsl.prototype.lightness = function(l) {
  return pv.hsl(this.h, this.s, l, this.a);
};

/**
 * Constructs a new HSL color with the same hue, saturation and lightness as
 * this color, and the specified alpha.
 *
 * @param {number} a the opacity, a float in [0, 1].
 */
pv.Color.Hsl.prototype.alpha = function(a) {
  return pv.hsl(this.h, this.s, this.l, a);
};

/**
 * Returns the RGB color equivalent to this HSL color.
 *
 * @returns {pv.Color.Rgb} an RGB color.
 */
pv.Color.Hsl.prototype.rgb = function() {
  var h = this.h, s = this.s, l = this.l;

  /* Some simple corrections for h, s and l. */
  h = h % 360; if (h < 0) h += 360;
  s = Math.max(0, Math.min(s, 1));
  l = Math.max(0, Math.min(l, 1));

  /* From FvD 13.37, CSS Color Module Level 3 */
  var m2 = (l <= .5) ? (l * (1 + s)) : (l + s - l * s);
  var m1 = 2 * l - m2;
  function v(h) {
    if (h > 360) h -= 360;
    else if (h < 0) h += 360;
    if (h < 60) return m1 + (m2 - m1) * h / 60;
    if (h < 180) return m2;
    if (h < 240) return m1 + (m2 - m1) * (240 - h) / 60;
    return m1;
  }
  function vv(h) {
    return Math.round(v(h) * 255);
  }

  return pv.rgb(vv(h + 120), vv(h), vv(h - 120), this.a);
};

/**
 * @private SVG color keywords, per CSS Color Module Level 3.
 *
 * @see <a href="http://www.w3.org/TR/SVG/types.html#ColorKeywords">SVG color
 * keywords</a>
 */
pv.Color.names = {
  aliceblue: "#f0f8ff",
  antiquewhite: "#faebd7",
  aqua: "#00ffff",
  aquamarine: "#7fffd4",
  azure: "#f0ffff",
  beige: "#f5f5dc",
  bisque: "#ffe4c4",
  black: "#000000",
  blanchedalmond: "#ffebcd",
  blue: "#0000ff",
  blueviolet: "#8a2be2",
  brown: "#a52a2a",
  burlywood: "#deb887",
  cadetblue: "#5f9ea0",
  chartreuse: "#7fff00",
  chocolate: "#d2691e",
  coral: "#ff7f50",
  cornflowerblue: "#6495ed",
  cornsilk: "#fff8dc",
  crimson: "#dc143c",
  cyan: "#00ffff",
  darkblue: "#00008b",
  darkcyan: "#008b8b",
  darkgoldenrod: "#b8860b",
  darkgray: "#a9a9a9",
  darkgreen: "#006400",
  darkgrey: "#a9a9a9",
  darkkhaki: "#bdb76b",
  darkmagenta: "#8b008b",
  darkolivegreen: "#556b2f",
  darkorange: "#ff8c00",
  darkorchid: "#9932cc",
  darkred: "#8b0000",
  darksalmon: "#e9967a",
  darkseagreen: "#8fbc8f",
  darkslateblue: "#483d8b",
  darkslategray: "#2f4f4f",
  darkslategrey: "#2f4f4f",
  darkturquoise: "#00ced1",
  darkviolet: "#9400d3",
  deeppink: "#ff1493",
  deepskyblue: "#00bfff",
  dimgray: "#696969",
  dimgrey: "#696969",
  dodgerblue: "#1e90ff",
  firebrick: "#b22222",
  floralwhite: "#fffaf0",
  forestgreen: "#228b22",
  fuchsia: "#ff00ff",
  gainsboro: "#dcdcdc",
  ghostwhite: "#f8f8ff",
  gold: "#ffd700",
  goldenrod: "#daa520",
  gray: "#808080",
  green: "#008000",
  greenyellow: "#adff2f",
  grey: "#808080",
  honeydew: "#f0fff0",
  hotpink: "#ff69b4",
  indianred: "#cd5c5c",
  indigo: "#4b0082",
  ivory: "#fffff0",
  khaki: "#f0e68c",
  lavender: "#e6e6fa",
  lavenderblush: "#fff0f5",
  lawngreen: "#7cfc00",
  lemonchiffon: "#fffacd",
  lightblue: "#add8e6",
  lightcoral: "#f08080",
  lightcyan: "#e0ffff",
  lightgoldenrodyellow: "#fafad2",
  lightgray: "#d3d3d3",
  lightgreen: "#90ee90",
  lightgrey: "#d3d3d3",
  lightpink: "#ffb6c1",
  lightsalmon: "#ffa07a",
  lightseagreen: "#20b2aa",
  lightskyblue: "#87cefa",
  lightslategray: "#778899",
  lightslategrey: "#778899",
  lightsteelblue: "#b0c4de",
  lightyellow: "#ffffe0",
  lime: "#00ff00",
  limegreen: "#32cd32",
  linen: "#faf0e6",
  magenta: "#ff00ff",
  maroon: "#800000",
  mediumaquamarine: "#66cdaa",
  mediumblue: "#0000cd",
  mediumorchid: "#ba55d3",
  mediumpurple: "#9370db",
  mediumseagreen: "#3cb371",
  mediumslateblue: "#7b68ee",
  mediumspringgreen: "#00fa9a",
  mediumturquoise: "#48d1cc",
  mediumvioletred: "#c71585",
  midnightblue: "#191970",
  mintcream: "#f5fffa",
  mistyrose: "#ffe4e1",
  moccasin: "#ffe4b5",
  navajowhite: "#ffdead",
  navy: "#000080",
  oldlace: "#fdf5e6",
  olive: "#808000",
  olivedrab: "#6b8e23",
  orange: "#ffa500",
  orangered: "#ff4500",
  orchid: "#da70d6",
  palegoldenrod: "#eee8aa",
  palegreen: "#98fb98",
  paleturquoise: "#afeeee",
  palevioletred: "#db7093",
  papayawhip: "#ffefd5",
  peachpuff: "#ffdab9",
  peru: "#cd853f",
  pink: "#ffc0cb",
  plum: "#dda0dd",
  powderblue: "#b0e0e6",
  purple: "#800080",
  red: "#ff0000",
  rosybrown: "#bc8f8f",
  royalblue: "#4169e1",
  saddlebrown: "#8b4513",
  salmon: "#fa8072",
  sandybrown: "#f4a460",
  seagreen: "#2e8b57",
  seashell: "#fff5ee",
  sienna: "#a0522d",
  silver: "#c0c0c0",
  skyblue: "#87ceeb",
  slateblue: "#6a5acd",
  slategray: "#708090",
  slategrey: "#708090",
  snow: "#fffafa",
  springgreen: "#00ff7f",
  steelblue: "#4682b4",
  tan: "#d2b48c",
  teal: "#008080",
  thistle: "#d8bfd8",
  tomato: "#ff6347",
  turquoise: "#40e0d0",
  violet: "#ee82ee",
  wheat: "#f5deb3",
  white: "#ffffff",
  whitesmoke: "#f5f5f5",
  yellow: "#ffff00",
  yellowgreen: "#9acd32",
  transparent: pv.Color.transparent = pv.rgb(0, 0, 0, 0)
};

/* Initialized named colors. */
(function() {
  var names = pv.Color.names;
  for (var name in names) names[name] = pv.color(names[name]);
})();
/**
 * Returns a new categorical color encoding using the specified colors.  The
 * arguments to this method are an array of colors; see {@link pv.color}. For
 * example, to create a categorical color encoding using the <tt>species</tt>
 * attribute:
 *
 * <pre>pv.colors("red", "green", "blue").by(function(d) d.species)</pre>
 *
 * The result of this expression can be used as a fill- or stroke-style
 * property. This assumes that the data's <tt>species</tt> attribute is a
 * string.
 *
 * @param {string} colors... categorical colors.
 * @see pv.Scale.ordinal
 * @returns {pv.Scale.ordinal} an ordinal color scale.
 */
pv.colors = function() {
  var scale = pv.Scale.ordinal();
  scale.range.apply(scale, arguments);
  return scale;
};

/**
 * A collection of standard color palettes for categorical encoding.
 *
 * @namespace A collection of standard color palettes for categorical encoding.
 */
pv.Colors = {};

/**
 * Returns a new 10-color scheme. The arguments to this constructor are
 * optional, and equivalent to calling {@link pv.Scale.OrdinalScale#domain}. The
 * following colors are used:
 *
 * <div style="background:#1f77b4;">#1f77b4</div>
 * <div style="background:#ff7f0e;">#ff7f0e</div>
 * <div style="background:#2ca02c;">#2ca02c</div>
 * <div style="background:#d62728;">#d62728</div>
 * <div style="background:#9467bd;">#9467bd</div>
 * <div style="background:#8c564b;">#8c564b</div>
 * <div style="background:#e377c2;">#e377c2</div>
 * <div style="background:#7f7f7f;">#7f7f7f</div>
 * <div style="background:#bcbd22;">#bcbd22</div>
 * <div style="background:#17becf;">#17becf</div>
 *
 * @param {number...} domain... domain values.
 * @returns {pv.Scale.ordinal} a new ordinal color scale.
 * @see pv.color
 */
pv.Colors.category10 = function() {
  var scale = pv.colors(
      "#1f77b4", "#ff7f0e", "#2ca02c", "#d62728", "#9467bd",
      "#8c564b", "#e377c2", "#7f7f7f", "#bcbd22", "#17becf");
  scale.domain.apply(scale, arguments);
  return scale;
};

/**
 * Returns a new 20-color scheme. The arguments to this constructor are
 * optional, and equivalent to calling {@link pv.Scale.OrdinalScale#domain}. The
 * following colors are used:
 *
 * <div style="background:#1f77b4;">#1f77b4</div>
 * <div style="background:#aec7e8;">#aec7e8</div>
 * <div style="background:#ff7f0e;">#ff7f0e</div>
 * <div style="background:#ffbb78;">#ffbb78</div>
 * <div style="background:#2ca02c;">#2ca02c</div>
 * <div style="background:#98df8a;">#98df8a</div>
 * <div style="background:#d62728;">#d62728</div>
 * <div style="background:#ff9896;">#ff9896</div>
 * <div style="background:#9467bd;">#9467bd</div>
 * <div style="background:#c5b0d5;">#c5b0d5</div>
 * <div style="background:#8c564b;">#8c564b</div>
 * <div style="background:#c49c94;">#c49c94</div>
 * <div style="background:#e377c2;">#e377c2</div>
 * <div style="background:#f7b6d2;">#f7b6d2</div>
 * <div style="background:#7f7f7f;">#7f7f7f</div>
 * <div style="background:#c7c7c7;">#c7c7c7</div>
 * <div style="background:#bcbd22;">#bcbd22</div>
 * <div style="background:#dbdb8d;">#dbdb8d</div>
 * <div style="background:#17becf;">#17becf</div>
 * <div style="background:#9edae5;">#9edae5</div>
 *
 * @param {number...} domain... domain values.
 * @returns {pv.Scale.ordinal} a new ordinal color scale.
 * @see pv.color
*/
pv.Colors.category20 = function() {
  var scale = pv.colors(
      "#1f77b4", "#aec7e8", "#ff7f0e", "#ffbb78", "#2ca02c",
      "#98df8a", "#d62728", "#ff9896", "#9467bd", "#c5b0d5",
      "#8c564b", "#c49c94", "#e377c2", "#f7b6d2", "#7f7f7f",
      "#c7c7c7", "#bcbd22", "#dbdb8d", "#17becf", "#9edae5");
  scale.domain.apply(scale, arguments);
  return scale;
};

/**
 * Returns a new alternative 19-color scheme. The arguments to this constructor
 * are optional, and equivalent to calling
 * {@link pv.Scale.OrdinalScale#domain}. The following colors are used:
 *
 * <div style="background:#9c9ede;">#9c9ede</div>
 * <div style="background:#7375b5;">#7375b5</div>
 * <div style="background:#4a5584;">#4a5584</div>
 * <div style="background:#cedb9c;">#cedb9c</div>
 * <div style="background:#b5cf6b;">#b5cf6b</div>
 * <div style="background:#8ca252;">#8ca252</div>
 * <div style="background:#637939;">#637939</div>
 * <div style="background:#e7cb94;">#e7cb94</div>
 * <div style="background:#e7ba52;">#e7ba52</div>
 * <div style="background:#bd9e39;">#bd9e39</div>
 * <div style="background:#8c6d31;">#8c6d31</div>
 * <div style="background:#e7969c;">#e7969c</div>
 * <div style="background:#d6616b;">#d6616b</div>
 * <div style="background:#ad494a;">#ad494a</div>
 * <div style="background:#843c39;">#843c39</div>
 * <div style="background:#de9ed6;">#de9ed6</div>
 * <div style="background:#ce6dbd;">#ce6dbd</div>
 * <div style="background:#a55194;">#a55194</div>
 * <div style="background:#7b4173;">#7b4173</div>
 *
 * @param {number...} domain... domain values.
 * @returns {pv.Scale.ordinal} a new ordinal color scale.
 * @see pv.color
 */
pv.Colors.category19 = function() {
  var scale = pv.colors(
      "#9c9ede", "#7375b5", "#4a5584", "#cedb9c", "#b5cf6b",
      "#8ca252", "#637939", "#e7cb94", "#e7ba52", "#bd9e39",
      "#8c6d31", "#e7969c", "#d6616b", "#ad494a", "#843c39",
      "#de9ed6", "#ce6dbd", "#a55194", "#7b4173");
  scale.domain.apply(scale, arguments);
  return scale;
};
/**
 * Returns a linear color ramp from the specified <tt>start</tt> color to the
 * specified <tt>end</tt> color. The color arguments may be specified either as
 * <tt>string</tt>s or as {@link pv.Color}s. This is equivalent to:
 *
 * <pre>    pv.Scale.linear().domain(0, 1).range(...)</pre>
 *
 * @param {string} start the start color; may be a <tt>pv.Color</tt>.
 * @param {string} end the end color; may be a <tt>pv.Color</tt>.
 * @returns {Function} a color ramp from <tt>start</tt> to <tt>end</tt>.
 * @see pv.Scale.linear
 */
pv.ramp = function(start, end) {
  var scale = pv.Scale.linear();
  scale.range.apply(scale, arguments);
  return scale;
};
/**
 * @private
 * @namespace
 */
pv.Scene = pv.SvgScene = {
  /* Various namespaces. */
  svg: "http://www.w3.org/2000/svg",
  xmlns: "http://www.w3.org/2000/xmlns",
  xlink: "http://www.w3.org/1999/xlink",
  xhtml: "http://www.w3.org/1999/xhtml",

  /** The pre-multipled scale, based on any enclosing transforms. */
  scale: 1,

  /** The set of supported events. */
  events: [
    "DOMMouseScroll", // for Firefox
    "mousewheel",
    "mousedown",
    "mouseup",
    "mouseover",
    "mouseout",
    "mousemove",
    "click",
    "dblclick"
  ],

  /** Implicit values for SVG and CSS properties. */
  implicit: {
    svg: {
      "shape-rendering": "auto",
      "pointer-events": "painted",
      "x": 0,
      "y": 0,
      "dy": 0,
      "text-anchor": "start",
      "transform": "translate(0,0)",
      "fill": "none",
      "fill-opacity": 1,
      "stroke": "none",
      "stroke-opacity": 1,
      "stroke-width": 1.5,
      "stroke-linejoin": "miter"
    },
    css: {
      "font": "10px sans-serif"
    }
  }
};

/**
 * Updates the display for the specified array of scene nodes.
 *
 * @param scenes {array} an array of scene nodes.
 */
pv.SvgScene.updateAll = function(scenes) {
  if (scenes.length
      && scenes[0].reverse
      && (scenes.type != "line")
      && (scenes.type != "area")) {
    var reversed = pv.extend(scenes);
    for (var i = 0, j = scenes.length - 1; j >= 0; i++, j--) {
      reversed[i] = scenes[j];
    }
    scenes = reversed;
  }
  this.removeSiblings(this[scenes.type](scenes));
};

/**
 * Creates a new SVG element of the specified type.
 *
 * @param type {string} an SVG element type, such as "rect".
 * @returns a new SVG element.
 */
pv.SvgScene.create = function(type) {
  return document.createElementNS(this.svg, type);
};

/**
 * Expects the element <i>e</i> to be the specified type. If the element does
 * not exist, a new one is created. If the element does exist but is the wrong
 * type, it is replaced with the specified element.
 *
 * @param e the current SVG element.
 * @param type {string} an SVG element type, such as "rect".
 * @param attributes an optional attribute map.
 * @param style an optional style map.
 * @returns a new SVG element.
 */
pv.SvgScene.expect = function(e, type, attributes, style) {
  if (e) {
    if (e.tagName == "a") e = e.firstChild;
    if (e.tagName != type) {
      var n = this.create(type);
      e.parentNode.replaceChild(n, e);
      e = n;
    }
  } else {
    e = this.create(type);
  }
  for (var name in attributes) {
    var value = attributes[name];
    if (value == this.implicit.svg[name]) value = null;
    if (value == null) e.removeAttribute(name);
    else e.setAttribute(name, value);
  }
  for (var name in style) {
    var value = style[name];
    if (value == this.implicit.css[name]) value = null;
    if (value == null) e.style.removeProperty(name);
    else e.style[name] = value;
  }
  return e;
};

/** TODO */
pv.SvgScene.append = function(e, scenes, index) {
  e.$scene = {scenes:scenes, index:index};
  e = this.title(e, scenes[index]);
  if (!e.parentNode) scenes.$g.appendChild(e);
  return e.nextSibling;
};

/**
 * Applies a title tooltip to the specified element <tt>e</tt>, using the
 * <tt>title</tt> property of the specified scene node <tt>s</tt>. Note that
 * this implementation does not create an SVG <tt>title</tt> element as a child
 * of <tt>e</tt>; although this is the recommended standard, it is only
 * supported in Opera. Instead, an anchor element is created around the element
 * <tt>e</tt>, and the <tt>xlink:title</tt> attribute is set accordingly.
 *
 * @param e an SVG element.
 * @param s a scene node.
 */
pv.SvgScene.title = function(e, s) {
  var a = e.parentNode;
  if (a && (a.tagName != "a")) a = null;
  if (s.title) {
    if (!a) {
      a = this.create("a");
      if (e.parentNode) e.parentNode.replaceChild(a, e);
      a.appendChild(e);
    }
    a.setAttributeNS(this.xlink, "title", s.title);
    return a;
  }
  if (a) a.parentNode.replaceChild(e, a);
  return e;
};

/** TODO */
pv.SvgScene.dispatch = pv.listener(function(e) {
  var t = e.target.$scene;
  if (t) {
    var type = e.type;

    /* Fixes for mousewheel support on Firefox & Opera. */
    switch (type) {
      case "DOMMouseScroll": {
        type = "mousewheel";
        e.wheel = -480 * e.detail;
        break;
      }
      case "mousewheel": {
        e.wheel = (window.opera ? 12 : 1) * e.wheelDelta;
        break;
      }
    }

    if (pv.Mark.dispatch(type, t.scenes, t.index)) e.preventDefault();
  }
});

/** @private Remove siblings following element <i>e</i>. */
pv.SvgScene.removeSiblings = function(e) {
  while (e) {
    var n = e.nextSibling;
    e.parentNode.removeChild(e);
    e = n;
  }
};

/** @private Do nothing when rendering undefined mark types. */
pv.SvgScene.undefined = function() {};
/**
 * @private Converts the specified b-spline curve segment to a bezier curve
 * compatible with SVG "C".
 *
 * @param p0 the first control point.
 * @param p1 the second control point.
 * @param p2 the third control point.
 * @param p3 the fourth control point.
 */
pv.SvgScene.pathBasis = (function() {

  /**
   * Matrix to transform basis (b-spline) control points to bezier control
   * points. Derived from FvD 11.2.8.
   */
  var basis = [
    [ 1/6, 2/3, 1/6,   0 ],
    [   0, 2/3, 1/3,   0 ],
    [   0, 1/3, 2/3,   0 ],
    [   0, 1/6, 2/3, 1/6 ]
  ];

  /**
   * Returns the point that is the weighted sum of the specified control points,
   * using the specified weights. This method requires that there are four
   * weights and four control points.
   */
  function weight(w, p0, p1, p2, p3) {
    return {
      x: w[0] * p0.left + w[1] * p1.left + w[2] * p2.left + w[3] * p3.left,
      y: w[0] * p0.top  + w[1] * p1.top  + w[2] * p2.top  + w[3] * p3.top
    };
  }

  var convert = function(p0, p1, p2, p3) {
    var b1 = weight(basis[1], p0, p1, p2, p3),
        b2 = weight(basis[2], p0, p1, p2, p3),
        b3 = weight(basis[3], p0, p1, p2, p3);
    return "C" + b1.x + "," + b1.y
         + "," + b2.x + "," + b2.y
         + "," + b3.x + "," + b3.y;
  };

  convert.segment = function(p0, p1, p2, p3) {
    var b0 = weight(basis[0], p0, p1, p2, p3),
        b1 = weight(basis[1], p0, p1, p2, p3),
        b2 = weight(basis[2], p0, p1, p2, p3),
        b3 = weight(basis[3], p0, p1, p2, p3);
    return "M" + b0.x + "," + b0.y
         + "C" + b1.x + "," + b1.y
         + "," + b2.x + "," + b2.y
         + "," + b3.x + "," + b3.y;
  };

  return convert;
})();

/**
 * @private Interpolates the given points using the basis spline interpolation.
 * Returns an SVG path without the leading M instruction to allow path
 * appending.
 *
 * @param points the array of points.
 */
pv.SvgScene.curveBasis = function(points) {
  if (points.length <= 2) return "";
  var path = "",
      p0 = points[0],
      p1 = p0,
      p2 = p0,
      p3 = points[1];
  path += this.pathBasis(p0, p1, p2, p3);
  for (var i = 2; i < points.length; i++) {
    p0 = p1;
    p1 = p2;
    p2 = p3;
    p3 = points[i];
    path += this.pathBasis(p0, p1, p2, p3);
  }
  /* Cycle through to get the last point. */
  path += this.pathBasis(p1, p2, p3, p3);
  path += this.pathBasis(p2, p3, p3, p3);
  return path;
};

/**
 * @private Interpolates the given points using the basis spline interpolation.
 * If points.length == tangents.length then a regular Hermite interpolation is
 * performed, if points.length == tangents.length + 2 then the first and last
 * segments are filled in with cubic bazier segments.  Returns an array of path
 * strings.
 *
 * @param points the array of points.
 */
pv.SvgScene.curveBasisSegments = function(points) {
  if (points.length <= 2) return "";
  var paths = [],
      p0 = points[0],
      p1 = p0,
      p2 = p0,
      p3 = points[1],
      firstPath = this.pathBasis.segment(p0, p1, p2, p3);

  p0 = p1;
  p1 = p2;
  p2 = p3;
  p3 = points[2];
  paths.push(firstPath + this.pathBasis(p0, p1, p2, p3)); // merge first & second path
  for (var i = 3; i < points.length; i++) {
    p0 = p1;
    p1 = p2;
    p2 = p3;
    p3 = points[i];
    paths.push(this.pathBasis.segment(p0, p1, p2, p3));
  }

  // merge last & second-to-last path
  paths.push(this.pathBasis.segment(p1, p2, p3, p3) + this.pathBasis(p2, p3, p3, p3));
  return paths;
};

/**
 * @private Interpolates the given points with respective tangents using the cubic
 * Hermite spline interpolation. If points.length == tangents.length then a regular
 * Hermite interpolation is performed, if points.length == tangents.length + 2 then
 * the first and last segments are filled in with cubic bazier segments.
 * Returns an SVG path without the leading M instruction to allow path appending.
 *
 * @param points the array of points.
 * @param tangents the array of tangent vectors.
 */
pv.SvgScene.curveHermite = function(points, tangents) {
  if (tangents.length < 1
      || (points.length != tangents.length
      && points.length != tangents.length + 2)) return "";
  var quad = points.length != tangents.length,
      path = "",
      p0 = points[0],
      p = points[1],
      t0 = tangents[0],
      t = t0,
      pi = 1;

  if (quad) {
    path += "Q" + (p.left - t0.x * 2 / 3) + ","  + (p.top - t0.y * 2 / 3)
        + "," + p.left + "," + p.top;
    p0 = points[1];
    pi = 2;
  }

  if (tangents.length > 1) {
    t = tangents[1];
    p = points[pi];
    pi++;
    path += "C" + (p0.left + t0.x) + "," + (p0.top + t0.y)
        + "," + (p.left - t.x) + "," + (p.top - t.y)
        + "," + p.left + "," + p.top;
    for (var i = 2; i < tangents.length; i++, pi++) {
      p = points[pi];
      t = tangents[i];
      path += "S" + (p.left - t.x) + "," + (p.top - t.y)
          + "," + p.left + "," + p.top;
    }
  }

  if (quad) {
    var lp = points[pi];
    path += "Q" + (p.left + t.x * 2 / 3) + ","  + (p.top + t.y * 2 / 3) + ","
        + lp.left + "," + lp.top;
  }

  return path;
};

/**
 * @private Interpolates the given points with respective tangents using the
 * cubic Hermite spline interpolation. Returns an array of path strings.
 *
 * @param points the array of points.
 * @param tangents the array of tangent vectors.
 */
pv.SvgScene.curveHermiteSegments = function(points, tangents) {
  if (tangents.length < 1
      || (points.length != tangents.length
      && points.length != tangents.length + 2)) return [];
  var quad = points.length != tangents.length,
      paths = [],
      p0 = points[0],
      p = p0,
      t0 = tangents[0],
      t = t0,
      pi = 1;

  if (quad) {
    p = points[1];
    paths.push("M" + p0.left + "," + p0.top
        + "Q" + (p.left - t.x * 2 / 3) + "," + (p.top - t.y * 2 / 3)
        + "," + p.left + "," + p.top);
    pi = 2;
  }

  for (var i = 1; i < tangents.length; i++, pi++) {
    p0 = p;
    t0 = t;
    p = points[pi];
    t = tangents[i];
    paths.push("M" + p0.left + "," + p0.top
        + "C" + (p0.left + t0.x) + "," + (p0.top + t0.y)
        + "," + (p.left - t.x) + "," + (p.top - t.y)
        + "," + p.left + "," + p.top);
  }

  if (quad) {
    var lp = points[pi];
    paths.push("M" + p.left + "," + p.top
        + "Q" + (p.left + t.x * 2 / 3) + ","  + (p.top + t.y * 2 / 3) + ","
        + lp.left + "," + lp.top);
  }

  return paths;
};

/**
 * @private Computes the tangents for the given points needed for cardinal
 * spline interpolation. Returns an array of tangent vectors. Note: that for n
 * points only the n-2 well defined tangents are returned.
 *
 * @param points the array of points.
 * @param tension the tension of hte cardinal spline.
 */
pv.SvgScene.cardinalTangents = function(points, tension) {
  var tangents = [],
      a = (1 - tension) / 2,
      p0 = points[0],
      p1 = points[1],
      p2 = points[2];

  for (var i = 3; i < points.length; i++) {
    tangents.push({x: a * (p2.left - p0.left), y: a * (p2.top - p0.top)});
    p0 = p1;
    p1 = p2;
    p2 = points[i];
  }

  tangents.push({x: a * (p2.left - p0.left), y: a * (p2.top - p0.top)});
  return tangents;
};

/**
 * @private Interpolates the given points using cardinal spline interpolation.
 * Returns an SVG path without the leading M instruction to allow path
 * appending.
 *
 * @param points the array of points.
 * @param tension the tension of hte cardinal spline.
 */
pv.SvgScene.curveCardinal = function(points, tension) {
  if (points.length <= 2) return "";
  return this.curveHermite(points, this.cardinalTangents(points, tension));
};

/**
 * @private Interpolates the given points using cardinal spline interpolation.
 * Returns an array of path strings.
 *
 * @param points the array of points.
 * @param tension the tension of hte cardinal spline.
 */
pv.SvgScene.curveCardinalSegments = function(points, tension) {
  if (points.length <= 2) return "";
  return this.curveHermiteSegments(points, this.cardinalTangents(points, tension));
};

/**
 * @private Interpolates the given points using Fritsch-Carlson Monotone cubic
 * Hermite interpolation. Returns an array of tangent vectors.
 *
 * @param points the array of points.
 */
pv.SvgScene.monotoneTangents = function(points) {
  var tangents = [],
      d = [],
      m = [],
      dx = [],
      k = 0;

  /* Compute the slopes of the secant lines between successive points. */
  for (k = 0; k < points.length-1; k++) {
    d[k] = (points[k+1].top - points[k].top)/(points[k+1].left - points[k].left);
  }

  /* Initialize the tangents at every point as the average of the secants. */
  m[0] = d[0];
  dx[0] = points[1].left - points[0].left;
  for (k = 1; k < points.length - 1; k++) {
    m[k] = (d[k-1]+d[k])/2;
    dx[k] = (points[k+1].left - points[k-1].left)/2;
  }
  m[k] = d[k-1];
  dx[k] = (points[k].left - points[k-1].left);

  /* Step 3. Very important, step 3. Yep. Wouldn't miss it. */
  for (k = 0; k < points.length - 1; k++) {
    if (d[k] == 0) {
      m[ k ] = 0;
      m[k+1] = 0;
    }
  }

  /* Step 4 + 5. Out of 5 or more steps. */
  for (k = 0; k < points.length - 1; k++) {
    if ((Math.abs(m[k]) < 1e-5) || (Math.abs(m[k+1]) < 1e-5)) continue;
    var ak = m[k] / d[k],
        bk = m[k + 1] / d[k],
        s = ak * ak + bk * bk; // monotone constant (?)
    if (s > 9) {
      var tk = 3 / Math.sqrt(s);
      m[k] = tk * ak * d[k];
      m[k + 1] = tk * bk * d[k];
    }
  }

  var len;
  for (var i = 0; i < points.length; i++) {
    len = 1 + m[i] * m[i]; // pv.vector(1, m[i]).norm().times(dx[i]/3)
    tangents.push({x: dx[i] / 3 / len, y: m[i] * dx[i] / 3 / len});
  }

  return tangents;
};

/**
 * @private Interpolates the given points using Fritsch-Carlson Monotone cubic
 * Hermite interpolation. Returns an SVG path without the leading M instruction
 * to allow path appending.
 *
 * @param points the array of points.
 */
pv.SvgScene.curveMonotone = function(points) {
  if (points.length <= 2) return "";
  return this.curveHermite(points, this.monotoneTangents(points));
}

/**
 * @private Interpolates the given points using Fritsch-Carlson Monotone cubic
 * Hermite interpolation.
 * Returns an array of path strings.
 *
 * @param points the array of points.
 */
pv.SvgScene.curveMonotoneSegments = function(points) {
  if (points.length <= 2) return "";
  return this.curveHermiteSegments(points, this.monotoneTangents(points));
};
pv.SvgScene.area = function(scenes) {
  var e = scenes.$g.firstChild;
  if (!scenes.length) return e;
  var s = scenes[0];

  /* segmented */
  if (s.segmented) return this.areaSegment(scenes);

  /* visible */
  if (!s.visible) return e;
  var fill = s.fillStyle, stroke = s.strokeStyle;
  if (!fill.opacity && !stroke.opacity) return e;

  /** @private Computes the straight path for the range [i, j]. */
  function path(i, j) {
    var p1 = [], p2 = [];
    for (var k = j; i <= k; i++, j--) {
      var si = scenes[i],
          sj = scenes[j],
          pi = si.left + "," + si.top,
          pj = (sj.left + sj.width) + "," + (sj.top + sj.height);

      /* interpolate */
      if (i < k) {
        var sk = scenes[i + 1], sl = scenes[j - 1];
        switch (s.interpolate) {
          case "step-before": {
            pi += "V" + sk.top;
            pj += "H" + (sl.left + sl.width);
            break;
          }
          case "step-after": {
            pi += "H" + sk.left;
            pj += "V" + (sl.top + sl.height);
            break;
          }
        }
      }

      p1.push(pi);
      p2.push(pj);
    }
    return p1.concat(p2).join("L");
  }

  /** @private Computes the curved path for the range [i, j]. */
  function pathCurve(i, j) {
    var pointsT = [], pointsB = [], pathT, pathB;

    for (var k = j; i <= k; i++, j--) {
      var sj = scenes[j];
      pointsT.push(scenes[i]);
      pointsB.push({left: sj.left + sj.width, top: sj.top + sj.height});
    }

    if (s.interpolate == "basis") {
      pathT = pv.SvgScene.curveBasis(pointsT);
      pathB = pv.SvgScene.curveBasis(pointsB);
    } else if (s.interpolate == "cardinal") {
      pathT = pv.SvgScene.curveCardinal(pointsT, s.tension);
      pathB = pv.SvgScene.curveCardinal(pointsB, s.tension);
    } else { // monotone
      pathT = pv.SvgScene.curveMonotone(pointsT);
      pathB = pv.SvgScene.curveMonotone(pointsB);
    }

    return pointsT[0].left + "," + pointsT[0].top + pathT
         + "L" + pointsB[0].left + "," + pointsB[0].top + pathB;
  }

  /* points */
  var d = [], si, sj;
  for (var i = 0; i < scenes.length; i++) {
    si = scenes[i]; if (!si.width && !si.height) continue;
    for (var j = i + 1; j < scenes.length; j++) {
      sj = scenes[j]; if (!sj.width && !sj.height) break;
    }
    if (i && (s.interpolate != "step-after")) i--;
    if ((j < scenes.length) && (s.interpolate != "step-before")) j++;
    d.push(((j - i > 2
        && (s.interpolate == "basis"
        || s.interpolate == "cardinal"
        || s.interpolate == "monotone"))
        ? pathCurve : path)(i, j - 1));
    i = j - 1;
  }
  if (!d.length) return e;

  e = this.expect(e, "path", {
      "shape-rendering": s.antialias ? null : "crispEdges",
      "pointer-events": s.events,
      "cursor": s.cursor,
      "d": "M" + d.join("ZM") + "Z",
      "fill": fill.color,
      "fill-opacity": fill.opacity || null,
      "stroke": stroke.color,
      "stroke-opacity": stroke.opacity || null,
      "stroke-width": stroke.opacity ? s.lineWidth / this.scale : null
    });
  return this.append(e, scenes, 0);
};

pv.SvgScene.areaSegment = function(scenes) {
  var e = scenes.$g.firstChild, s = scenes[0], pathsT, pathsB;
  if (s.interpolate == "basis"
      || s.interpolate == "cardinal"
      || s.interpolate == "monotone") {
    var pointsT = [], pointsB = [];

    for (var i = 0, n = scenes.length; i < n; i++) {
      var sj = scenes[n - i - 1];
      pointsT.push(scenes[i]);
      pointsB.push({left: sj.left + sj.width, top: sj.top + sj.height});
    }

    if (s.interpolate == "basis") {
      pathsT = this.curveBasisSegments(pointsT);
      pathsB = this.curveBasisSegments(pointsB);
    } else if (s.interpolate == "cardinal") {
      pathsT = this.curveCardinalSegments(pointsT, s.tension);
      pathsB = this.curveCardinalSegments(pointsB, s.tension);
    } else { // monotone
      pathsT = this.curveMonotoneSegments(pointsT);
      pathsB = this.curveMonotoneSegments(pointsB);
    }
  }

  for (var i = 0, n = scenes.length - 1; i < n; i++) {
    var s1 = scenes[i], s2 = scenes[i + 1];

    /* visible */
    if (!s1.visible || !s2.visible) continue;
    var fill = s1.fillStyle, stroke = s1.strokeStyle;
    if (!fill.opacity && !stroke.opacity) continue;

    var d;
    if (pathsT) {
      var pathT = pathsT[i],
          pathB = "L" + pathsB[n - i - 1].substr(1);

      d = pathT + pathB + "Z";
    } else {
      /* interpolate */
      var si = s1, sj = s2;
      switch (s1.interpolate) {
        case "step-before": si = s2; break;
        case "step-after": sj = s1; break;
      }

      /* path */
      d = "M" + s1.left + "," + si.top
        + "L" + s2.left + "," + sj.top
        + "L" + (s2.left + s2.width) + "," + (sj.top + sj.height)
        + "L" + (s1.left + s1.width) + "," + (si.top + si.height)
        + "Z";
    }

    e = this.expect(e, "path", {
        "shape-rendering": s1.antialias ? null : "crispEdges",
        "pointer-events": s1.events,
        "cursor": s1.cursor,
        "d": d,
        "fill": fill.color,
        "fill-opacity": fill.opacity || null,
        "stroke": stroke.color,
        "stroke-opacity": stroke.opacity || null,
        "stroke-width": stroke.opacity ? s1.lineWidth / this.scale : null
      });
    e = this.append(e, scenes, i);
  }
  return e;
};
pv.SvgScene.bar = function(scenes) {
  var e = scenes.$g.firstChild;
  for (var i = 0; i < scenes.length; i++) {
    var s = scenes[i];

    /* visible */
    if (!s.visible) continue;
    var fill = s.fillStyle, stroke = s.strokeStyle;
    if (!fill.opacity && !stroke.opacity) continue;

    e = this.expect(e, "rect", {
        "shape-rendering": s.antialias ? null : "crispEdges",
        "pointer-events": s.events,
        "cursor": s.cursor,
        "x": s.left,
        "y": s.top,
        "width": Math.max(1E-10, s.width),
        "height": Math.max(1E-10, s.height),
        "fill": fill.color,
        "fill-opacity": fill.opacity || null,
        "stroke": stroke.color,
        "stroke-opacity": stroke.opacity || null,
        "stroke-width": stroke.opacity ? s.lineWidth / this.scale : null
      });
    e = this.append(e, scenes, i);
  }
  return e;
};
pv.SvgScene.dot = function(scenes) {
  var e = scenes.$g.firstChild;
  for (var i = 0; i < scenes.length; i++) {
    var s = scenes[i];

    /* visible */
    if (!s.visible) continue;
    var fill = s.fillStyle, stroke = s.strokeStyle;
    if (!fill.opacity && !stroke.opacity) continue;

    /* points */
    var radius = s.radius, path = null;
    switch (s.shape) {
      case "cross": {
        path = "M" + -radius + "," + -radius
            + "L" + radius + "," + radius
            + "M" + radius + "," + -radius
            + "L" + -radius + "," + radius;
        break;
      }
      case "triangle": {
        var h = radius, w = radius * 1.1547; // 2 / Math.sqrt(3)
        path = "M0," + h
            + "L" + w +"," + -h
            + " " + -w + "," + -h
            + "Z";
        break;
      }
      case "diamond": {
        radius *= Math.SQRT2;
        path = "M0," + -radius
            + "L" + radius + ",0"
            + " 0," + radius
            + " " + -radius + ",0"
            + "Z";
        break;
      }
      case "square": {
        path = "M" + -radius + "," + -radius
            + "L" + radius + "," + -radius
            + " " + radius + "," + radius
            + " " + -radius + "," + radius
            + "Z";
        break;
      }
      case "tick": {
        path = "M0,0L0," + -s.size;
        break;
      }
      case "bar": {
        path = "M0," + (s.size / 2) + "L0," + -(s.size / 2);
        break;
      }
    }

    /* Use <circle> for circles, <path> for everything else. */
    var svg = {
      "shape-rendering": s.antialias ? null : "crispEdges",
      "pointer-events": s.events,
      "cursor": s.cursor,
      "fill": fill.color,
      "fill-opacity": fill.opacity || null,
      "stroke": stroke.color,
      "stroke-opacity": stroke.opacity || null,
      "stroke-width": stroke.opacity ? s.lineWidth / this.scale : null
    };
    if (path) {
      svg.transform = "translate(" + s.left + "," + s.top + ")";
      if (s.angle) svg.transform += " rotate(" + 180 * s.angle / Math.PI + ")";
      svg.d = path;
      e = this.expect(e, "path", svg);
    } else {
      svg.cx = s.left;
      svg.cy = s.top;
      svg.r = radius;
      e = this.expect(e, "circle", svg);
    }
    e = this.append(e, scenes, i);
  }
  return e;
};
pv.SvgScene.image = function(scenes) {
  var e = scenes.$g.firstChild;
  for (var i = 0; i < scenes.length; i++) {
    var s = scenes[i];

    /* visible */
    if (!s.visible) continue;

    /* fill */
    e = this.fill(e, scenes, i);

    /* image */
    if (s.image) {
      e = this.expect(e, "foreignObject", {
          "cursor": s.cursor,
          "x": s.left,
          "y": s.top,
          "width": s.width,
          "height": s.height
        });
      var c = e.firstChild || e.appendChild(document.createElementNS(this.xhtml, "canvas"));
      c.$scene = {scenes:scenes, index:i};
      c.style.width = s.width;
      c.style.height = s.height;
      c.width = s.imageWidth;
      c.height = s.imageHeight;
      c.getContext("2d").putImageData(s.image, 0, 0);
    } else {
      e = this.expect(e, "image", {
          "preserveAspectRatio": "none",
          "cursor": s.cursor,
          "x": s.left,
          "y": s.top,
          "width": s.width,
          "height": s.height
        });
      e.setAttributeNS(this.xlink, "href", s.url);
    }
    e = this.append(e, scenes, i);

    /* stroke */
    e = this.stroke(e, scenes, i);
  }
  return e;
};
pv.SvgScene.label = function(scenes) {
  var e = scenes.$g.firstChild;
  for (var i = 0; i < scenes.length; i++) {
    var s = scenes[i];

    /* visible */
    if (!s.visible) continue;
    var fill = s.textStyle;
    if (!fill.opacity || !s.text) continue;

    /* text-baseline, text-align */
    var x = 0, y = 0, dy = 0, anchor = "start";
    switch (s.textBaseline) {
      case "middle": dy = ".35em"; break;
      case "top": dy = ".71em"; y = s.textMargin; break;
      case "bottom": y = "-" + s.textMargin; break;
    }
    switch (s.textAlign) {
      case "right": anchor = "end"; x = "-" + s.textMargin; break;
      case "center": anchor = "middle"; break;
      case "left": x = s.textMargin; break;
    }

    e = this.expect(e, "text", {
        "pointer-events": s.events,
        "cursor": s.cursor,
        "x": x,
        "y": y,
        "dy": dy,
        "transform": "translate(" + s.left + "," + s.top + ")"
            + (s.textAngle ? " rotate(" + 180 * s.textAngle / Math.PI + ")" : "")
            + (this.scale != 1 ? " scale(" + 1 / this.scale + ")" : ""),
        "fill": fill.color,
        "fill-opacity": fill.opacity || null,
        "text-anchor": anchor
      }, {
        "font": s.font,
        "text-shadow": s.textShadow,
        "text-decoration": s.textDecoration
      });
    if (e.firstChild) e.firstChild.nodeValue = s.text;
    else e.appendChild(document.createTextNode(s.text));
    e = this.append(e, scenes, i);
  }
  return e;
};
pv.SvgScene.line = function(scenes) {
  var e = scenes.$g.firstChild;
  if (scenes.length < 2) return e;
  var s = scenes[0];

  /* segmented */
  if (s.segmented) return this.lineSegment(scenes);

  /* visible */
  if (!s.visible) return e;
  var fill = s.fillStyle, stroke = s.strokeStyle;
  if (!fill.opacity && !stroke.opacity) return e;

  /* points */
  var d = "M" + s.left + "," + s.top;

  if (scenes.length > 2 && (s.interpolate == "basis" || s.interpolate == "cardinal" || s.interpolate == "monotone")) {
    switch (s.interpolate) {
      case "basis": d += this.curveBasis(scenes); break;
      case "cardinal": d += this.curveCardinal(scenes, s.tension); break;
      case "monotone": d += this.curveMonotone(scenes); break;
    }
  } else {
    for (var i = 1; i < scenes.length; i++) {
      d += this.pathSegment(scenes[i - 1], scenes[i]);
    }
  }

  e = this.expect(e, "path", {
      "shape-rendering": s.antialias ? null : "crispEdges",
      "pointer-events": s.events,
      "cursor": s.cursor,
      "d": d,
      "fill": fill.color,
      "fill-opacity": fill.opacity || null,
      "stroke": stroke.color,
      "stroke-opacity": stroke.opacity || null,
      "stroke-width": stroke.opacity ? s.lineWidth / this.scale : null,
      "stroke-linejoin": s.lineJoin
    });
  return this.append(e, scenes, 0);
};

pv.SvgScene.lineSegment = function(scenes) {
  var e = scenes.$g.firstChild;

  var s = scenes[0];
  var paths;
  switch (s.interpolate) {
    case "basis": paths = this.curveBasisSegments(scenes); break;
    case "cardinal": paths = this.curveCardinalSegments(scenes, s.tension); break;
    case "monotone": paths = this.curveMonotoneSegments(scenes); break;
  }

  for (var i = 0, n = scenes.length - 1; i < n; i++) {
    var s1 = scenes[i], s2 = scenes[i + 1];

    /* visible */
    if (!s1.visible || !s2.visible) continue;
    var stroke = s1.strokeStyle, fill = pv.Color.transparent;
    if (!stroke.opacity) continue;

    /* interpolate */
    var d;
    if ((s1.interpolate == "linear") && (s1.lineJoin == "miter")) {
      fill = stroke;
      stroke = pv.Color.transparent;
      d = this.pathJoin(scenes[i - 1], s1, s2, scenes[i + 2]);
    } else if(paths) {
      d = paths[i];
    } else {
      d = "M" + s1.left + "," + s1.top + this.pathSegment(s1, s2);
    }

    e = this.expect(e, "path", {
        "shape-rendering": s1.antialias ? null : "crispEdges",
        "pointer-events": s1.events,
        "cursor": s1.cursor,
        "d": d,
        "fill": fill.color,
        "fill-opacity": fill.opacity || null,
        "stroke": stroke.color,
        "stroke-opacity": stroke.opacity || null,
        "stroke-width": stroke.opacity ? s1.lineWidth / this.scale : null,
        "stroke-linejoin": s1.lineJoin
      });
    e = this.append(e, scenes, i);
  }
  return e;
};

/** @private Returns the path segment for the specified points. */
pv.SvgScene.pathSegment = function(s1, s2) {
  var l = 1; // sweep-flag
  switch (s1.interpolate) {
    case "polar-reverse":
      l = 0;
    case "polar": {
      var dx = s2.left - s1.left,
          dy = s2.top - s1.top,
          e = 1 - s1.eccentricity,
          r = Math.sqrt(dx * dx + dy * dy) / (2 * e);
      if ((e <= 0) || (e > 1)) break; // draw a straight line
      return "A" + r + "," + r + " 0 0," + l + " " + s2.left + "," + s2.top;
    }
    case "step-before": return "V" + s2.top + "H" + s2.left;
    case "step-after": return "H" + s2.left + "V" + s2.top;
  }
  return "L" + s2.left + "," + s2.top;
};

/** @private Line-line intersection, per Akenine-Moller 16.16.1. */
pv.SvgScene.lineIntersect = function(o1, d1, o2, d2) {
  return o1.plus(d1.times(o2.minus(o1).dot(d2.perp()) / d1.dot(d2.perp())));
}

/** @private Returns the miter join path for the specified points. */
pv.SvgScene.pathJoin = function(s0, s1, s2, s3) {
  /*
   * P1-P2 is the current line segment. V is a vector that is perpendicular to
   * the line segment, and has length lineWidth / 2. ABCD forms the initial
   * bounding box of the line segment (i.e., the line segment if we were to do
   * no joins).
   */
  var p1 = pv.vector(s1.left, s1.top),
      p2 = pv.vector(s2.left, s2.top),
      p = p2.minus(p1),
      v = p.perp().norm(),
      w = v.times(s1.lineWidth / (2 * this.scale)),
      a = p1.plus(w),
      b = p2.plus(w),
      c = p2.minus(w),
      d = p1.minus(w);

  /*
   * Start join. P0 is the previous line segment's start point. We define the
   * cutting plane as the average of the vector perpendicular to P0-P1, and
   * the vector perpendicular to P1-P2. This insures that the cross-section of
   * the line on the cutting plane is equal if the line-width is unchanged.
   * Note that we don't implement miter limits, so these can get wild.
   */
  if (s0 && s0.visible) {
    var v1 = p1.minus(s0.left, s0.top).perp().norm().plus(v);
    d = this.lineIntersect(p1, v1, d, p);
    a = this.lineIntersect(p1, v1, a, p);
  }

  /* Similarly, for end join. */
  if (s3 && s3.visible) {
    var v2 = pv.vector(s3.left, s3.top).minus(p2).perp().norm().plus(v);
    c = this.lineIntersect(p2, v2, c, p);
    b = this.lineIntersect(p2, v2, b, p);
  }

  return "M" + a.x + "," + a.y
       + "L" + b.x + "," + b.y
       + " " + c.x + "," + c.y
       + " " + d.x + "," + d.y;
};
pv.SvgScene.panel = function(scenes) {
  var g = scenes.$g, e = g && g.firstChild;
  for (var i = 0; i < scenes.length; i++) {
    var s = scenes[i];

    /* visible */
    if (!s.visible) continue;

    /* svg */
    if (!scenes.parent) {
      s.canvas.style.display = "inline-block";
      if (g && (g.parentNode != s.canvas)) {
        g = s.canvas.firstChild;
        e = g && g.firstChild;
      }
      if (!g) {
        g = s.canvas.appendChild(this.create("svg"));
        g.setAttribute("font-size", "10px");
        g.setAttribute("font-family", "sans-serif");
        g.setAttribute("fill", "none");
        g.setAttribute("stroke", "none");
        g.setAttribute("stroke-width", 1.5);
        for (var j = 0; j < this.events.length; j++) {
          g.addEventListener(this.events[j], this.dispatch, false);
        }
        e = g.firstChild;
      }
      scenes.$g = g;
      g.setAttribute("width", s.width + s.left + s.right);
      g.setAttribute("height", s.height + s.top + s.bottom);
    }

    /* clip (nest children) */
    if (s.overflow == "hidden") {
      var id = pv.id().toString(36),
          c = this.expect(e, "g", {"clip-path": "url(#" + id + ")"});
      if (!c.parentNode) g.appendChild(c);
      scenes.$g = g = c;
      e = c.firstChild;

      e = this.expect(e, "clipPath", {"id": id});
      var r = e.firstChild || e.appendChild(this.create("rect"));
      r.setAttribute("x", s.left);
      r.setAttribute("y", s.top);
      r.setAttribute("width", s.width);
      r.setAttribute("height", s.height);
      if (!e.parentNode) g.appendChild(e);
      e = e.nextSibling;
    }

    /* fill */
    e = this.fill(e, scenes, i);

    /* transform (push) */
    var k = this.scale,
        t = s.transform,
        x = s.left + t.x,
        y = s.top + t.y;
    this.scale *= t.k;

    /* children */
    for (var j = 0; j < s.children.length; j++) {
      s.children[j].$g = e = this.expect(e, "g", {
          "transform": "translate(" + x + "," + y + ")"
              + (t.k != 1 ? " scale(" + t.k + ")" : "")
        });
      this.updateAll(s.children[j]);
      if (!e.parentNode) g.appendChild(e);
      e = e.nextSibling;
    }

    /* transform (pop) */
    this.scale = k;

    /* stroke */
    e = this.stroke(e, scenes, i);

    /* clip (restore group) */
    if (s.overflow == "hidden") {
      scenes.$g = g = c.parentNode;
      e = c.nextSibling;
    }
  }
  return e;
};

pv.SvgScene.fill = function(e, scenes, i) {
  var s = scenes[i], fill = s.fillStyle;
  if (fill.opacity || s.events == "all") {
    e = this.expect(e, "rect", {
        "shape-rendering": s.antialias ? null : "crispEdges",
        "pointer-events": s.events,
        "cursor": s.cursor,
        "x": s.left,
        "y": s.top,
        "width": s.width,
        "height": s.height,
        "fill": fill.color,
        "fill-opacity": fill.opacity,
        "stroke": null
      });
    e = this.append(e, scenes, i);
  }
  return e;
};

pv.SvgScene.stroke = function(e, scenes, i) {
  var s = scenes[i], stroke = s.strokeStyle;
  if (stroke.opacity || s.events == "all") {
    e = this.expect(e, "rect", {
        "shape-rendering": s.antialias ? null : "crispEdges",
        "pointer-events": s.events == "all" ? "stroke" : s.events,
        "cursor": s.cursor,
        "x": s.left,
        "y": s.top,
        "width": Math.max(1E-10, s.width),
        "height": Math.max(1E-10, s.height),
        "fill": null,
        "stroke": stroke.color,
        "stroke-opacity": stroke.opacity,
        "stroke-width": s.lineWidth / this.scale
      });
    e = this.append(e, scenes, i);
  }
  return e;
};
pv.SvgScene.rule = function(scenes) {
  var e = scenes.$g.firstChild;
  for (var i = 0; i < scenes.length; i++) {
    var s = scenes[i];

    /* visible */
    if (!s.visible) continue;
    var stroke = s.strokeStyle;
    if (!stroke.opacity) continue;

    e = this.expect(e, "line", {
        "shape-rendering": s.antialias ? null : "crispEdges",
        "pointer-events": s.events,
        "cursor": s.cursor,
        "x1": s.left,
        "y1": s.top,
        "x2": s.left + s.width,
        "y2": s.top + s.height,
        "stroke": stroke.color,
        "stroke-opacity": stroke.opacity,
        "stroke-width": s.lineWidth / this.scale
      });
    e = this.append(e, scenes, i);
  }
  return e;
};
pv.SvgScene.wedge = function(scenes) {
  var e = scenes.$g.firstChild;
  for (var i = 0; i < scenes.length; i++) {
    var s = scenes[i];

    /* visible */
    if (!s.visible) continue;
    var fill = s.fillStyle, stroke = s.strokeStyle;
    if (!fill.opacity && !stroke.opacity) continue;

    /* points */
    var r1 = s.innerRadius, r2 = s.outerRadius, a = Math.abs(s.angle), p;
    if (a >= 2 * Math.PI) {
      if (r1) {
        p = "M0," + r2
            + "A" + r2 + "," + r2 + " 0 1,1 0," + (-r2)
            + "A" + r2 + "," + r2 + " 0 1,1 0," + r2
            + "M0," + r1
            + "A" + r1 + "," + r1 + " 0 1,1 0," + (-r1)
            + "A" + r1 + "," + r1 + " 0 1,1 0," + r1
            + "Z";
      } else {
        p = "M0," + r2
            + "A" + r2 + "," + r2 + " 0 1,1 0," + (-r2)
            + "A" + r2 + "," + r2 + " 0 1,1 0," + r2
            + "Z";
      }
    } else {
      var sa = Math.min(s.startAngle, s.endAngle),
          ea = Math.max(s.startAngle, s.endAngle),
          c1 = Math.cos(sa), c2 = Math.cos(ea),
          s1 = Math.sin(sa), s2 = Math.sin(ea);
      if (r1) {
        p = "M" + r2 * c1 + "," + r2 * s1
            + "A" + r2 + "," + r2 + " 0 "
            + ((a < Math.PI) ? "0" : "1") + ",1 "
            + r2 * c2 + "," + r2 * s2
            + "L" + r1 * c2 + "," + r1 * s2
            + "A" + r1 + "," + r1 + " 0 "
            + ((a < Math.PI) ? "0" : "1") + ",0 "
            + r1 * c1 + "," + r1 * s1 + "Z";
      } else {
        p = "M" + r2 * c1 + "," + r2 * s1
            + "A" + r2 + "," + r2 + " 0 "
            + ((a < Math.PI) ? "0" : "1") + ",1 "
            + r2 * c2 + "," + r2 * s2 + "L0,0Z";
      }
    }

    e = this.expect(e, "path", {
        "shape-rendering": s.antialias ? null : "crispEdges",
        "pointer-events": s.events,
        "cursor": s.cursor,
        "transform": "translate(" + s.left + "," + s.top + ")",
        "d": p,
        "fill": fill.color,
        "fill-rule": "evenodd",
        "fill-opacity": fill.opacity || null,
        "stroke": stroke.color,
        "stroke-opacity": stroke.opacity || null,
        "stroke-width": stroke.opacity ? s.lineWidth / this.scale : null
      });
    e = this.append(e, scenes, i);
  }
  return e;
};
/**
 * Constructs a new mark with default properties. Marks, with the exception of
 * the root panel, are not typically constructed directly; instead, they are
 * added to a panel or an existing mark via {@link pv.Mark#add}.
 *
 * @class Represents a data-driven graphical mark. The <tt>Mark</tt> class is
 * the base class for all graphical marks in Protovis; it does not provide any
 * specific rendering functionality, but together with {@link Panel} establishes
 * the core framework.
 *
 * <p>Concrete mark types include familiar visual elements such as bars, lines
 * and labels. Although a bar mark may be used to construct a bar chart, marks
 * know nothing about charts; it is only through their specification and
 * composition that charts are produced. These building blocks permit many
 * combinatorial possibilities.
 *
 * <p>Marks are associated with <b>data</b>: a mark is generated once per
 * associated datum, mapping the datum to visual <b>properties</b> such as
 * position and color. Thus, a single mark specification represents a set of
 * visual elements that share the same data and visual encoding. The type of
 * mark defines the names of properties and their meaning. A property may be
 * static, ignoring the associated datum and returning a constant; or, it may be
 * dynamic, derived from the associated datum or index. Such dynamic encodings
 * can be specified succinctly using anonymous functions. Special properties
 * called event handlers can be registered to add interactivity.
 *
 * <p>Protovis uses <b>inheritance</b> to simplify the specification of related
 * marks: a new mark can be derived from an existing mark, inheriting its
 * properties. The new mark can then override properties to specify new
 * behavior, potentially in terms of the old behavior. In this way, the old mark
 * serves as the <b>prototype</b> for the new mark. Most mark types share the
 * same basic properties for consistency and to facilitate inheritance.
 *
 * <p>The prioritization of redundant properties is as follows:<ol>
 *
 * <li>If the <tt>width</tt> property is not specified (i.e., null), its value
 * is the width of the parent panel, minus this mark's left and right margins;
 * the left and right margins are zero if not specified.
 *
 * <li>Otherwise, if the <tt>right</tt> margin is not specified, its value is
 * the width of the parent panel, minus this mark's width and left margin; the
 * left margin is zero if not specified.
 *
 * <li>Otherwise, if the <tt>left</tt> property is not specified, its value is
 * the width of the parent panel, minus this mark's width and the right margin.
 *
 * </ol>This prioritization is then duplicated for the <tt>height</tt>,
 * <tt>bottom</tt> and <tt>top</tt> properties, respectively.
 *
 * <p>While most properties are <i>variable</i>, some mark types, such as lines
 * and areas, generate a single visual element rather than a distinct visual
 * element per datum. With these marks, some properties may be <b>fixed</b>.
 * Fixed properties can vary per mark, but not <i>per datum</i>! These
 * properties are evaluated solely for the first (0-index) datum, and typically
 * are specified as a constant. However, it is valid to use a function if the
 * property varies between panels or is dynamically generated.
 *
 * <p>See also the <a href="../../api/">Protovis guide</a>.
 */
pv.Mark = function() {
  /*
   * TYPE 0 constant defs
   * TYPE 1 function defs
   * TYPE 2 constant properties
   * TYPE 3 function properties
   * in order of evaluation!
   */
  this.$properties = [];
  this.$handlers = {};
};

/** @private Records which properties are defined on this mark type. */
pv.Mark.prototype.properties = {};

/** @private Records the cast function for each property. */
pv.Mark.cast = {};

/**
 * @private Defines and registers a property method for the property with the
 * given name.  This method should be called on a mark class prototype to define
 * each exposed property. (Note this refers to the JavaScript
 * <tt>prototype</tt>, not the Protovis mark prototype, which is the {@link
 * #proto} field.)
 *
 * <p>The created property method supports several modes of invocation: <ol>
 *
 * <li>If invoked with a <tt>Function</tt> argument, this function is evaluated
 * for each associated datum. The return value of the function is used as the
 * computed property value. The context of the function (<tt>this</tt>) is this
 * mark. The arguments to the function are the associated data of this mark and
 * any enclosing panels. For example, a linear encoding of numerical data to
 * height is specified as
 *
 * <pre>m.height(function(d) d * 100);</pre>
 *
 * The expression <tt>d * 100</tt> will be evaluated for the height property of
 * each mark instance. The return value of the property method (e.g.,
 * <tt>m.height</tt>) is this mark (<tt>m</tt>)).<p>
 *
 * <li>If invoked with a non-function argument, the property is treated as a
 * constant. The return value of the property method (e.g., <tt>m.height</tt>)
 * is this mark.<p>
 *
 * <li>If invoked with no arguments, the computed property value for the current
 * mark instance in the scene graph is returned. This facilitates <i>property
 * chaining</i>, where one mark's properties are defined in terms of another's.
 * For example, to offset a mark's location from its prototype, you might say
 *
 * <pre>m.top(function() this.proto.top() + 10);</pre>
 *
 * Note that the index of the mark being evaluated (in the above example,
 * <tt>this.proto</tt>) is inherited from the <tt>Mark</tt> class and set by
 * this mark. So, if the fifth element's top property is being evaluated, the
 * fifth instance of <tt>this.proto</tt> will similarly be queried for the value
 * of its top property. If the mark being evaluated has a different number of
 * instances, or its data is unrelated, the behavior of this method is
 * undefined. In these cases it may be better to index the <tt>scene</tt>
 * explicitly to specify the exact instance.
 *
 * </ol><p>Property names should follow standard JavaScript method naming
 * conventions, using lowerCamel-style capitalization.
 *
 * <p>In addition to creating the property method, every property is registered
 * in the {@link #properties} map on the <tt>prototype</tt>. Although this is an
 * instance field, it is considered immutable and shared by all instances of a
 * given mark type. The <tt>properties</tt> map can be queried to see if a mark
 * type defines a particular property, such as width or height.
 *
 * @param {string} name the property name.
 * @param {function} [cast] the cast function for this property.
 */
pv.Mark.prototype.property = function(name, cast) {
  if (!this.hasOwnProperty("properties")) {
    this.properties = pv.extend(this.properties);
  }
  this.properties[name] = true;

  /*
   * Define the setter-getter globally, since the default behavior should be the
   * same for all properties, and since the Protovis inheritance chain is
   * independent of the JavaScript inheritance chain. For example, anchors
   * define a "name" property that is evaluated on derived marks, even though
   * those marks don't normally have a name.
   */
  pv.Mark.prototype.propertyMethod(name, false, pv.Mark.cast[name] = cast);
  return this;
};

/**
 * @private Defines a setter-getter for the specified property.
 *
 * <p>If a cast function has been assigned to the specified property name, the
 * property function is wrapped by the cast function, or, if a constant is
 * specified, the constant is immediately cast. Note, however, that if the
 * property value is null, the cast function is not invoked.
 *
 * @param {string} name the property name.
 * @param {boolean} [def] whether is a property or a def.
 * @param {function} [cast] the cast function for this property.
 */
pv.Mark.prototype.propertyMethod = function(name, def, cast) {
  if (!cast) cast = pv.Mark.cast[name];
  this[name] = function(v) {

      /* If this is a def, use it rather than property. */
      if (def && this.scene) {
        var defs = this.scene.defs;
        if (arguments.length) {
          defs[name] = {
            id: (v == null) ? 0 : pv.id(),
            value: ((v != null) && cast) ? cast(v) : v
          };
          return this;
        }
        return defs[name] ? defs[name].value : null;
      }

      /* If arguments are specified, set the property value. */
      if (arguments.length) {
        var type = !def << 1 | (typeof v == "function");
        this.propertyValue(name, (type & 1 && cast) ? function() {
            var x = v.apply(this, arguments);
            return (x != null) ? cast(x) : null;
          } : (((v != null) && cast) ? cast(v) : v)).type = type;
        return this;
      }

      return this.instance()[name];
    };
};

/** @private Sets the value of the property <i>name</i> to <i>v</i>. */
pv.Mark.prototype.propertyValue = function(name, v) {
  var properties = this.$properties, p = {name: name, id: pv.id(), value: v};
  for (var i = 0; i < properties.length; i++) {
    if (properties[i].name == name) {
      properties.splice(i, 1);
      break;
    }
  }
  properties.push(p);
  return p;
};

/* Define all global properties. */
pv.Mark.prototype
    .property("data")
    .property("visible", Boolean)
    .property("left", Number)
    .property("right", Number)
    .property("top", Number)
    .property("bottom", Number)
    .property("cursor", String)
    .property("title", String)
    .property("reverse", Boolean)
    .property("antialias", Boolean)
    .property("events", String);

/**
 * The mark type; a lower camelCase name. The type name controls rendering
 * behavior, and unless the rendering engine is extended, must be one of the
 * built-in concrete mark types: area, bar, dot, image, label, line, panel,
 * rule, or wedge.
 *
 * @type string
 * @name pv.Mark.prototype.type
 */

/**
 * The mark prototype, possibly undefined, from which to inherit property
 * functions. The mark prototype is not necessarily of the same type as this
 * mark. Any properties defined on this mark will override properties inherited
 * either from the prototype or from the type-specific defaults.
 *
 * @type pv.Mark
 * @name pv.Mark.prototype.proto
 */

/**
 * The enclosing parent panel. The parent panel is generally undefined only for
 * the root panel; however, it is possible to create "offscreen" marks that are
 * used only for inheritance purposes.
 *
 * @type pv.Panel
 * @name pv.Mark.prototype.parent
 */

/**
 * The child index. -1 if the enclosing parent panel is null; otherwise, the
 * zero-based index of this mark into the parent panel's <tt>children</tt> array.
 *
 * @type number
 */
pv.Mark.prototype.childIndex = -1;

/**
 * The mark index. The value of this field depends on which instance (i.e.,
 * which element of the data array) is currently being evaluated. During the
 * build phase, the index is incremented over each datum; when handling events,
 * the index is set to the instance that triggered the event.
 *
 * @type number
 */
pv.Mark.prototype.index = -1;

/**
 * The current scale factor, based on any enclosing transforms. The current
 * scale can be used to create scale-independent graphics. For example, to
 * define a dot that has a radius of 10 irrespective of any zooming, say:
 *
 * <pre>dot.radius(function() 10 / this.scale)</pre>
 *
 * Note that the stroke width and font size are defined irrespective of scale
 * (i.e., in screen space) already. Also note that when a transform is applied
 * to a panel, the scale affects only the child marks, not the panel itself.
 *
 * @type number
 * @see pv.Panel#transform
 */
pv.Mark.prototype.scale = 1;

/**
 * @private The scene graph. The scene graph is an array of objects; each object
 * (or "node") corresponds to an instance of this mark and an element in the
 * data array. The scene graph can be traversed to lookup previously-evaluated
 * properties.
 *
 * @name pv.Mark.prototype.scene
 */

/**
 * The root parent panel. This may be undefined for "offscreen" marks that are
 * created for inheritance purposes only.
 *
 * @type pv.Panel
 * @name pv.Mark.prototype.root
 */

/**
 * The data property; an array of objects. The size of the array determines the
 * number of marks that will be instantiated; each element in the array will be
 * passed to property functions to compute the property values. Typically, the
 * data property is specified as a constant array, such as
 *
 * <pre>m.data([1, 2, 3, 4, 5]);</pre>
 *
 * However, it is perfectly acceptable to define the data property as a
 * function. This function might compute the data dynamically, allowing
 * different data to be used per enclosing panel. For instance, in the stacked
 * area graph example (see {@link #scene}), the data function on the area mark
 * dereferences each series.
 *
 * @type array
 * @name pv.Mark.prototype.data
 */

/**
 * The visible property; a boolean determining whether or not the mark instance
 * is visible. If a mark instance is not visible, its other properties will not
 * be evaluated. Similarly, for panels no child marks will be rendered.
 *
 * @type boolean
 * @name pv.Mark.prototype.visible
 */

/**
 * The left margin; the distance, in pixels, between the left edge of the
 * enclosing panel and the left edge of this mark. Note that in some cases this
 * property may be redundant with the right property, or with the conjunction of
 * right and width.
 *
 * @type number
 * @name pv.Mark.prototype.left
 */

/**
 * The right margin; the distance, in pixels, between the right edge of the
 * enclosing panel and the right edge of this mark. Note that in some cases this
 * property may be redundant with the left property, or with the conjunction of
 * left and width.
 *
 * @type number
 * @name pv.Mark.prototype.right
 */

/**
 * The top margin; the distance, in pixels, between the top edge of the
 * enclosing panel and the top edge of this mark. Note that in some cases this
 * property may be redundant with the bottom property, or with the conjunction
 * of bottom and height.
 *
 * @type number
 * @name pv.Mark.prototype.top
 */

/**
 * The bottom margin; the distance, in pixels, between the bottom edge of the
 * enclosing panel and the bottom edge of this mark. Note that in some cases
 * this property may be redundant with the top property, or with the conjunction
 * of top and height.
 *
 * @type number
 * @name pv.Mark.prototype.bottom
 */

/**
 * The cursor property; corresponds to the CSS cursor property. This is
 * typically used in conjunction with event handlers to indicate interactivity.
 *
 * @type string
 * @name pv.Mark.prototype.cursor
 * @see <a href="http://www.w3.org/TR/CSS2/ui.html#propdef-cursor">CSS2 cursor</a>
 */

/**
 * The title property; corresponds to the HTML/SVG title property, allowing the
 * general of simple plain text tooltips.
 *
 * @type string
 * @name pv.Mark.prototype.title
 */

/**
 * The events property; corresponds to the SVG pointer-events property,
 * specifying how the mark should participate in mouse events. The default value
 * is "painted". Supported values are:
 *
 * <p>"painted": The given mark may receive events when the mouse is over a
 * "painted" area. The painted areas are the interior (i.e., fill) of the mark
 * if a 'fillStyle' is specified, and the perimeter (i.e., stroke) of the mark
 * if a 'strokeStyle' is specified.
 *
 * <p>"all": The given mark may receive events when the mouse is over either the
 * interior (i.e., fill) or the perimeter (i.e., stroke) of the mark, regardless
 * of the specified fillStyle and strokeStyle.
 *
 * <p>"none": The given mark may not receive events.
 *
 * @type string
 * @name pv.Mark.prototype.events
 */

/**
 * The reverse property; a boolean determining whether marks are ordered from
 * front-to-back or back-to-front. SVG does not support explicit z-ordering;
 * shapes are rendered in the order they appear. Thus, by default, marks are
 * rendered in data order. Setting the reverse property to false reverses the
 * order in which they are rendered; however, the properties are still evaluated
 * (i.e., built) in forward order.
 *
 * @type boolean
 * @name pv.Mark.prototype.reverse
 */

/**
 * Default properties for all mark types. By default, the data array is the
 * parent data as a single-element array; if the data property is not specified,
 * this causes each mark to be instantiated as a singleton with the parents
 * datum. The visible property is true by default, and the reverse property is
 * false.
 *
 * @type pv.Mark
 */
pv.Mark.prototype.defaults = new pv.Mark()
    .data(function(d) { return [d]; })
    .visible(true)
    .antialias(true)
    .events("painted");

/**
 * Sets the prototype of this mark to the specified mark. Any properties not
 * defined on this mark may be inherited from the specified prototype mark, or
 * its prototype, and so on. The prototype mark need not be the same type of
 * mark as this mark. (Note that for inheritance to be useful, properties with
 * the same name on different mark types should have equivalent meaning.)
 *
 * @param {pv.Mark} proto the new prototype.
 * @returns {pv.Mark} this mark.
 * @see #add
 */
pv.Mark.prototype.extend = function(proto) {
  this.proto = proto;
  return this;
};

/**
 * Adds a new mark of the specified type to the enclosing parent panel, whilst
 * simultaneously setting the prototype of the new mark to be this mark.
 *
 * @param {function} type the type of mark to add; a constructor, such as
 * <tt>pv.Bar</tt>.
 * @returns {pv.Mark} the new mark.
 * @see #extend
 */
pv.Mark.prototype.add = function(type) {
  return this.parent.add(type).extend(this);
};

/**
 * Defines a custom property on this mark. Custom properties are currently
 * fixed, in that they are initialized once per mark set (i.e., per parent panel
 * instance). Custom properties can be used to store local state for the mark,
 * such as data needed by other properties (e.g., a custom scale) or interaction
 * state.
 *
 * <p>WARNING We plan on changing this feature in a future release to define
 * standard properties, as opposed to <i>fixed</i> properties that behave
 * idiosyncratically within event handlers. Furthermore, we recommend storing
 * state in an external data structure, rather than tying it to the
 * visualization specification as with defs.
 *
 * @param {string} name the name of the local variable.
 * @param {function} [v] an optional initializer; may be a constant or a
 * function.
 */
pv.Mark.prototype.def = function(name, v) {
  this.propertyMethod(name, true);
  return this[name](arguments.length > 1 ? v : null);
};

/**
 * Returns an anchor with the specified name. All marks support the five
 * standard anchor names:<ul>
 *
 * <li>top
 * <li>left
 * <li>center
 * <li>bottom
 * <li>right
 *
 * </ul>In addition to positioning properties (left, right, top bottom), the
 * anchors support text rendering properties (text-align, text-baseline). Text is
 * rendered to appear inside the mark by default.
 *
 * <p>To facilitate stacking, anchors are defined in terms of their opposite
 * edge. For example, the top anchor defines the bottom property, such that the
 * mark extends upwards; the bottom anchor instead defines the top property,
 * such that the mark extends downwards. See also {@link pv.Layout.Stack}.
 *
 * <p>While anchor names are typically constants, the anchor name is a true
 * property, which means you can specify a function to compute the anchor name
 * dynamically. See the {@link pv.Anchor#name} property for details.
 *
 * @param {string} name the anchor name; either a string or a property function.
 * @returns {pv.Anchor} the new anchor.
 */
pv.Mark.prototype.anchor = function(name) {
  var target = this, scene;

  /* Default anchor name. */
  if (!name) name = "center";

  /** @private Find the instances of target that match source. */
  function instances(source) {
    var mark = target, index = [];

    /* Mirrored descent. */
    while (!(scene = mark.scene)) {
      source = source.parent;
      index.push({index: source.index, childIndex: mark.childIndex});
      mark = mark.parent;
    }
    while (index.length) {
      var i = index.pop();
      scene = scene[i.index].children[i.childIndex];
    }

    /*
     * When the anchor target is also an ancestor, as in the case of adding
     * to a panel anchor, only generate one instance per panel. Also, set
     * the margins to zero, since they are offset by the enclosing panel.
     */
    if (target.hasOwnProperty("index")) {
      var s = pv.extend(scene[target.index]);
      s.right = s.top = s.left = s.bottom = 0;
      return [s];
    }
    return scene;
  }

  return new pv.Anchor(this)
    .name(name)
    .def("$mark.anchor", function() {
        scene = this.scene.target = instances(this);
      })
    .data(function() {
        return scene.map(function(s) { return s.data; });
      })
    .visible(function() {
        return scene[this.index].visible;
      })
    .left(function() {
        var s = scene[this.index], w = s.width || 0;
        switch (this.name()) {
          case "bottom":
          case "top":
          case "center": return s.left + w / 2;
          case "left": return null;
        }
        return s.left + w;
      })
    .top(function() {
        var s = scene[this.index], h = s.height || 0;
        switch (this.name()) {
          case "left":
          case "right":
          case "center": return s.top + h / 2;
          case "top": return null;
        }
        return s.top + h;
      })
    .right(function() {
        var s = scene[this.index];
        return this.name() == "left" ? s.right + (s.width || 0) : null;
      })
    .bottom(function() {
        var s = scene[this.index];
        return this.name() == "top" ? s.bottom + (s.height || 0) : null;
      })
    .textAlign(function() {
        switch (this.name()) {
          case "bottom":
          case "top":
          case "center": return "center";
          case "right": return "right";
        }
        return "left";
      })
    .textBaseline(function() {
        switch (this.name()) {
          case "right":
          case "left":
          case "center": return "middle";
          case "top": return "top";
        }
        return "bottom";
      });
};

/**
 * Returns the anchor target of this mark, if it is derived from an anchor;
 * otherwise returns null. For example, if a label is derived from a bar anchor,
 *
 * <pre>bar.anchor("top").add(pv.Label);</pre>
 *
 * then property functions on the label can refer to the bar via the
 * <tt>anchorTarget</tt> method. This method is also useful for mark types
 * defining properties on custom anchors.
 *
 * @returns {pv.Mark} the anchor target of this mark; possibly null.
 */
pv.Mark.prototype.anchorTarget = function() {
  return this.proto.anchorTarget();
};

/**
 * Alias for setting the left, right, top and bottom properties simultaneously.
 *
 * @see #left
 * @see #right
 * @see #top
 * @see #bottom
 * @returns {pv.Mark} this.
 */
pv.Mark.prototype.margin = function(n) {
  return this.left(n).right(n).top(n).bottom(n);
};

/**
 * @private Returns the current instance of this mark in the scene graph. This
 * is typically equivalent to <tt>this.scene[this.index]</tt>, however if the
 * scene or index is unset, the default instance of the mark is returned. If no
 * default is set, the default is the last instance. Similarly, if the scene or
 * index of the parent panel is unset, the default instance of this mark in the
 * last instance of the enclosing panel is returned, and so on.
 *
 * @returns a node in the scene graph.
 */
pv.Mark.prototype.instance = function(defaultIndex) {
  var scene = this.scene || this.parent.instance(-1).children[this.childIndex],
      index = !arguments.length || this.hasOwnProperty("index") ? this.index : defaultIndex;
  return scene[index < 0 ? scene.length - 1 : index];
};

/**
 * @private Returns the first instance of this mark in the scene graph. This
 * method can only be called when the mark is bound to the scene graph (for
 * example, from an event handler, or within a property function).
 *
 * @returns a node in the scene graph.
 */
pv.Mark.prototype.first = function() {
  return this.scene[0];
};

/**
 * @private Returns the last instance of this mark in the scene graph. This
 * method can only be called when the mark is bound to the scene graph (for
 * example, from an event handler, or within a property function). In addition,
 * note that mark instances are built sequentially, so the last instance of this
 * mark may not yet be constructed.
 *
 * @returns a node in the scene graph.
 */
pv.Mark.prototype.last = function() {
  return this.scene[this.scene.length - 1];
};

/**
 * @private Returns the previous instance of this mark in the scene graph, or
 * null if this is the first instance.
 *
 * @returns a node in the scene graph, or null.
 */
pv.Mark.prototype.sibling = function() {
  return (this.index == 0) ? null : this.scene[this.index - 1];
};

/**
 * @private Returns the current instance in the scene graph of this mark, in the
 * previous instance of the enclosing parent panel. May return null if this
 * instance could not be found.
 *
 * @returns a node in the scene graph, or null.
 */
pv.Mark.prototype.cousin = function() {
  var p = this.parent, s = p && p.sibling();
  return (s && s.children) ? s.children[this.childIndex][this.index] : null;
};

/**
 * Renders this mark, including recursively rendering all child marks if this is
 * a panel. This method finds all instances of this mark and renders them. This
 * method descends recursively to the level of the mark to be rendered, finding
 * all visible instances of the mark. After the marks are rendered, the scene
 * and index attributes are removed from the mark to restore them to a clean
 * state.
 *
 * <p>If an enclosing panel has an index property set (as is the case inside in
 * an event handler), then only instances of this mark inside the given instance
 * of the panel will be rendered; otherwise, all visible instances of the mark
 * will be rendered.
 */
pv.Mark.prototype.render = function() {
  var parent = this.parent,
      stack = pv.Mark.stack;

  /* For the first render, take it from the top. */
  if (parent && !this.root.scene) {
    this.root.render();
    return;
  }

  /* Record the path to this mark. */
  var indexes = [];
  for (var mark = this; mark.parent; mark = mark.parent) {
    indexes.unshift(mark.childIndex);
  }

  /** @private */
  function render(mark, depth, scale) {
    mark.scale = scale;
    if (depth < indexes.length) {
      stack.unshift(null);
      if (mark.hasOwnProperty("index")) {
        renderInstance(mark, depth, scale);
      } else {
        for (var i = 0, n = mark.scene.length; i < n; i++) {
          mark.index = i;
          renderInstance(mark, depth, scale);
        }
        delete mark.index;
      }
      stack.shift();
    } else {
      mark.build();

      /*
       * In the update phase, the scene is rendered by creating and updating
       * elements and attributes in the SVG image. No properties are evaluated
       * during the update phase; instead the values computed previously in the
       * build phase are simply translated into SVG. The update phase is
       * decoupled (see pv.Scene) to allow different rendering engines.
       */
      pv.Scene.scale = scale;
      pv.Scene.updateAll(mark.scene);
    }
    delete mark.scale;
  }

  /**
   * @private Recursively renders the current instance of the specified mark.
   * This is slightly tricky because `index` and `scene` properties may or may
   * not already be set; if they are set, it means we are rendering only a
   * specific instance; if they are unset, we are rendering all instances.
   * Furthermore, we must preserve the original context of these properties when
   * rendering completes.
   *
   * <p>Another tricky aspect is that the `scene` attribute should be set for
   * any preceding children, so as to allow property chaining. This is
   * consistent with first-pass rendering.
   */
  function renderInstance(mark, depth, scale) {
    var s = mark.scene[mark.index], i;
    if (s.visible) {
      var childIndex = indexes[depth],
          child = mark.children[childIndex];

      /* Set preceding child scenes. */
      for (i = 0; i < childIndex; i++) {
        mark.children[i].scene = s.children[i];
      }

      /* Set current child scene, if necessary. */
      stack[0] = s.data;
      if (child.scene) {
        render(child, depth + 1, scale * s.transform.k);
      } else {
        child.scene = s.children[childIndex];
        render(child, depth + 1, scale * s.transform.k);
        delete child.scene;
      }

      /* Clear preceding child scenes. */
      for (i = 0; i < childIndex; i++) {
        delete mark.children[i].scene;
      }
    }
  }

  /* Bind this mark's property definitions. */
  this.bind();

  /* The render context is the first ancestor with an explicit index. */
  while (parent && !parent.hasOwnProperty("index")) parent = parent.parent;

  /* Recursively render all instances of this mark. */
  this.context(
      parent ? parent.scene : undefined,
      parent ? parent.index : -1,
      function() { render(this.root, 0, 1); });
};

/** @private Stores the current data stack. */
pv.Mark.stack = [];

/**
 * @private In the bind phase, inherited property definitions are cached so they
 * do not need to be queried during build.
 */
pv.Mark.prototype.bind = function() {
  var seen = {}, types = [[], [], [], []], data, visible;

  /** Scans the proto chain for the specified mark. */
  function bind(mark) {
    do {
      var properties = mark.$properties;
      for (var i = properties.length - 1; i >= 0 ; i--) {
        var p = properties[i];
        if (!(p.name in seen)) {
          seen[p.name] = p;
          switch (p.name) {
            case "data": data = p; break;
            case "visible": visible = p; break;
            default: types[p.type].push(p); break;
          }
        }
      }
    } while (mark = mark.proto);
  }

  /* Scan the proto chain for all defined properties. */
  bind(this);
  bind(this.defaults);
  types[1].reverse();
  types[3].reverse();

  /* Any undefined properties are null. */
  var mark = this;
  do for (var name in mark.properties) {
    if (!(name in seen)) {
      types[2].push(seen[name] = {name: name, type: 2, value: null});
    }
  } while (mark = mark.proto);

  /* Define setter-getter for inherited defs. */
  var defs = types[0].concat(types[1]);
  for (var i = 0; i < defs.length; i++) {
    this.propertyMethod(defs[i].name, true);
  }

  /* Setup binds to evaluate constants before functions. */
  this.binds = {
    properties: seen,
    data: data,
    defs: defs,
    required: [visible],
    optional: pv.blend(types)
  };
};

/**
 * @private Evaluates properties and computes implied properties. Properties are
 * stored in the {@link #scene} array for each instance of this mark.
 *
 * <p>As marks are built recursively, the {@link #index} property is updated to
 * match the current index into the data array for each mark. Note that the
 * index property is only set for the mark currently being built and its
 * enclosing parent panels. The index property for other marks is unset, but is
 * inherited from the global <tt>Mark</tt> class prototype. This allows mark
 * properties to refer to properties on other marks <i>in the same panel</i>
 * conveniently; however, in general it is better to reference mark instances
 * specifically through the scene graph rather than depending on the magical
 * behavior of {@link #index}.
 *
 * <p>The root scene array has a special property, <tt>data</tt>, which stores
 * the current data stack. The first element in this stack is the current datum,
 * followed by the datum of the enclosing parent panel, and so on. The data
 * stack should not be accessed directly; instead, property functions are passed
 * the current data stack as arguments.
 *
 * <p>The evaluation of the <tt>data</tt> and <tt>visible</tt> properties is
 * special. The <tt>data</tt> property is evaluated first; unlike the other
 * properties, the data stack is from the parent panel, rather than the current
 * mark, since the data is not defined until the data property is evaluated.
 * The <tt>visisble</tt> property is subsequently evaluated for each instance;
 * only if true will the {@link #buildInstance} method be called, evaluating
 * other properties and recursively building the scene graph.
 *
 * <p>If this mark is being re-built, any old instances of this mark that no
 * longer exist (because the new data array contains fewer elements) will be
 * cleared using {@link #clearInstance}.
 *
 * @param parent the instance of the parent panel from the scene graph.
 */
pv.Mark.prototype.build = function() {
  var scene = this.scene, stack = pv.Mark.stack;
  if (!scene) {
    scene = this.scene = [];
    scene.mark = this;
    scene.type = this.type;
    scene.childIndex = this.childIndex;
    if (this.parent) {
      scene.parent = this.parent.scene;
      scene.parentIndex = this.parent.index;
    }
  }

  /* Evaluate defs. */
  if (this.binds.defs.length) {
    var defs = scene.defs;
    if (!defs) scene.defs = defs = {};
    for (var i = 0; i < this.binds.defs.length; i++) {
      var p = this.binds.defs[i], d = defs[p.name];
      if (!d || (p.id > d.id)) {
        defs[p.name] = {
          id: 0, // this def will be re-evaluated on next build
          value: (p.type & 1) ? p.value.apply(this, stack) : p.value
        };
      }
    }
  }

  /* Evaluate special data property. */
  var data = this.binds.data;
  data = data.type & 1 ? data.value.apply(this, stack) : data.value;

  /* Create, update and delete scene nodes. */
  stack.unshift(null);
  scene.length = data.length;
  for (var i = 0; i < data.length; i++) {
    pv.Mark.prototype.index = this.index = i;
    var s = scene[i];
    if (!s) scene[i] = s = {};
    s.data = stack[0] = data[i];
    this.buildInstance(s);
  }
  pv.Mark.prototype.index = -1;
  delete this.index;
  stack.shift();

  return this;
};

/**
 * @private Evaluates the specified array of properties for the specified
 * instance <tt>s</tt> in the scene graph.
 *
 * @param s a node in the scene graph; the instance of the mark to build.
 * @param properties an array of properties.
 */
pv.Mark.prototype.buildProperties = function(s, properties) {
  for (var i = 0, n = properties.length; i < n; i++) {
    var p = properties[i], v = p.value; // assume case 2 (constant)
    switch (p.type) {
      case 0:
      case 1: v = this.scene.defs[p.name].value; break;
      case 3: v = v.apply(this, pv.Mark.stack); break;
    }
    s[p.name] = v;
  }
};

/**
 * @private Evaluates all of the properties for this mark for the specified
 * instance <tt>s</tt> in the scene graph. The set of properties to evaluate is
 * retrieved from the {@link #properties} array for this mark type (see {@link
 * #type}).  After these properties are evaluated, any <b>implied</b> properties
 * may be computed by the mark and set on the scene graph; see
 * {@link #buildImplied}.
 *
 * <p>For panels, this method recursively builds the scene graph for all child
 * marks as well. In general, this method should not need to be overridden by
 * concrete mark types.
 *
 * @param s a node in the scene graph; the instance of the mark to build.
 */
pv.Mark.prototype.buildInstance = function(s) {
  this.buildProperties(s, this.binds.required);
  if (s.visible) {
    this.buildProperties(s, this.binds.optional);
    this.buildImplied(s);
  }
};

/**
 * @private Computes the implied properties for this mark for the specified
 * instance <tt>s</tt> in the scene graph. Implied properties are those with
 * dependencies on multiple other properties; for example, the width property
 * may be implied if the left and right properties are set. This method can be
 * overridden by concrete mark types to define new implied properties, if
 * necessary.
 *
 * @param s a node in the scene graph; the instance of the mark to build.
 */
pv.Mark.prototype.buildImplied = function(s) {
  var l = s.left;
  var r = s.right;
  var t = s.top;
  var b = s.bottom;

  /* Assume width and height are zero if not supported by this mark type. */
  var p = this.properties;
  var w = p.width ? s.width : 0;
  var h = p.height ? s.height : 0;

  /* Compute implied width, right and left. */
  var width = this.parent ? this.parent.width() : (w + l + r);
  if (w == null) {
    w = width - (r = r || 0) - (l = l || 0);
  } else if (r == null) {
    r = width - w - (l = l || 0);
  } else if (l == null) {
    l = width - w - (r = r || 0);
  }

  /* Compute implied height, bottom and top. */
  var height = this.parent ? this.parent.height() : (h + t + b);
  if (h == null) {
    h = height - (t = t || 0) - (b = b || 0);
  } else if (b == null) {
    b = height - h - (t = t || 0);
  } else if (t == null) {
    t = height - h - (b = b || 0);
  }

  s.left = l;
  s.right = r;
  s.top = t;
  s.bottom = b;

  /* Only set width and height if they are supported by this mark type. */
  if (p.width) s.width = w;
  if (p.height) s.height = h;

  /* Set any null colors to pv.Color.transparent. */
  if (p.textStyle && !s.textStyle) s.textStyle = pv.Color.transparent;
  if (p.fillStyle && !s.fillStyle) s.fillStyle = pv.Color.transparent;
  if (p.strokeStyle && !s.strokeStyle) s.strokeStyle = pv.Color.transparent;
};

/**
 * Returns the current location of the mouse (cursor) relative to this mark's
 * parent. The <i>x</i> coordinate corresponds to the left margin, while the
 * <i>y</i> coordinate corresponds to the top margin.
 *
 * @returns {pv.Vector} the mouse location.
 */
pv.Mark.prototype.mouse = function() {

  /* Compute xy-coordinates relative to the panel. */
  var x = pv.event.pageX || 0,
      y = pv.event.pageY || 0,
      n = this.root.canvas();
  do {
    x -= n.offsetLeft;
    y -= n.offsetTop;
  } while (n = n.offsetParent);

  /* Compute the inverse transform of all enclosing panels. */
  var t = pv.Transform.identity,
      p = this.properties.transform ? this : this.parent,
      pz = [];
  do { pz.push(p); } while (p = p.parent);
  while (p = pz.pop()) t = t.translate(p.left(), p.top()).times(p.transform());
  t = t.invert();

  return pv.vector(x * t.k + t.x, y * t.k + t.y);
};

/**
 * Registers an event handler for the specified event type with this mark. When
 * an event of the specified type is triggered, the specified handler will be
 * invoked. The handler is invoked in a similar method to property functions:
 * the context is <tt>this</tt> mark instance, and the arguments are the full
 * data stack. Event handlers can use property methods to manipulate the display
 * properties of the mark:
 *
 * <pre>m.event("click", function() this.fillStyle("red"));</pre>
 *
 * Alternatively, the external data can be manipulated and the visualization
 * redrawn:
 *
 * <pre>m.event("click", function(d) {
 *     data = all.filter(function(k) k.name == d);
 *     vis.render();
 *   });</pre>
 *
 * The return value of the event handler determines which mark gets re-rendered.
 * Use defs ({@link #def}) to set temporary state from event handlers.
 *
 * <p>The complete set of event types is defined by SVG; see the reference
 * below. The set of supported event types is:<ul>
 *
 * <li>click
 * <li>mousedown
 * <li>mouseup
 * <li>mouseover
 * <li>mousemove
 * <li>mouseout
 *
 * </ul>Since Protovis does not specify any concept of focus, it does not
 * support key events; these should be handled outside the visualization using
 * standard JavaScript. In the future, support for interaction may be extended
 * to support additional event types, particularly those most relevant to
 * interactive visualization, such as selection.
 *
 * <p>TODO In the current implementation, event handlers are not inherited from
 * prototype marks. They must be defined explicitly on each interactive mark. In
 * addition, only one event handler for a given event type can be defined; when
 * specifying multiple event handlers for the same type, only the last one will
 * be used.
 *
 * @see <a href="http://www.w3.org/TR/SVGTiny12/interact.html#SVGEvents">SVG events</a>
 * @param {string} type the event type.
 * @param {function} handler the event handler.
 * @returns {pv.Mark} this.
 */
pv.Mark.prototype.event = function(type, handler) {
  this.$handlers[type] = pv.functor(handler);
  return this;
};

/** @private Evaluates the function <i>f</i> with the specified context. */
pv.Mark.prototype.context = function(scene, index, f) {
  var proto = pv.Mark.prototype,
      stack = pv.Mark.stack,
      oscene = pv.Mark.scene,
      oindex = proto.index;

  /** @private Sets the context. */
  function apply(scene, index) {
    pv.Mark.scene = scene;
    proto.index = index;
    if (!scene) return;

    var that = scene.mark,
        mark = that,
        ancestors = [];

    /* Set ancestors' scene and index; populate data stack. */
    do {
      ancestors.push(mark);
      stack.push(scene[index].data);
      mark.index = index;
      mark.scene = scene;
      index = scene.parentIndex;
      scene = scene.parent;
    } while (mark = mark.parent);

    /* Set ancestors' scale; requires top-down. */
    for (var i = ancestors.length - 1, k = 1; i > 0; i--) {
      mark = ancestors[i];
      mark.scale = k;
      k *= mark.scene[mark.index].transform.k;
    }

    /* Set children's scene and scale. */
    if (that.children) for (var i = 0, n = that.children.length; i < n; i++) {
      mark = that.children[i];
      mark.scene = that.scene[that.index].children[i];
      mark.scale = k;
    }
  }

  /** @private Clears the context. */
  function clear(scene, index) {
    if (!scene) return;
    var that = scene.mark,
        mark;

    /* Reset children. */
    if (that.children) for (var i = 0, n = that.children.length; i < n; i++) {
      mark = that.children[i];
      delete mark.scene;
      delete mark.scale;
    }

    /* Reset ancestors. */
    mark = that;
    do {
      stack.pop();
      if (mark.parent) {
        delete mark.scene;
        delete mark.scale;
      }
      delete mark.index;
    } while (mark = mark.parent);
  }

  /* Context switch, invoke the function, then switch back. */
  clear(oscene, oindex);
  apply(scene, index);
  try {
    f.apply(this, stack);
  } finally {
    clear(scene, index);
    apply(oscene, oindex);
  }
};

/** @private Execute the event listener, then re-render. */
pv.Mark.dispatch = function(type, scene, index) {
  var m = scene.mark, p = scene.parent, l = m.$handlers[type];
  if (!l) return p && pv.Mark.dispatch(type, p, scene.parentIndex);
  m.context(scene, index, function() {
      m = l.apply(m, pv.Mark.stack);
      if (m && m.render) m.render();
    });
  return true;
};
/**
 * Constructs a new mark anchor with default properties.
 *
 * @class Represents an anchor on a given mark. An anchor is itself a mark, but
 * without a visual representation. It serves only to provide useful default
 * properties that can be inherited by other marks. Each type of mark can define
 * any number of named anchors for convenience. If the concrete mark type does
 * not define an anchor implementation specifically, one will be inherited from
 * the mark's parent class.
 *
 * <p>For example, the bar mark provides anchors for its four sides: left,
 * right, top and bottom. Adding a label to the top anchor of a bar,
 *
 * <pre>bar.anchor("top").add(pv.Label);</pre>
 *
 * will render a text label on the top edge of the bar; the top anchor defines
 * the appropriate position properties (top and left), as well as text-rendering
 * properties for convenience (textAlign and textBaseline).
 *
 * <p>Note that anchors do not <i>inherit</i> from their targets; the positional
 * properties are copied from the scene graph, which guarantees that the anchors
 * are positioned correctly, even if the positional properties are not defined
 * deterministically. (In addition, it also improves performance by avoiding
 * re-evaluating expensive properties.) If you want the anchor to inherit from
 * the target, use {@link pv.Mark#extend} before adding. For example:
 *
 * <pre>bar.anchor("top").extend(bar).add(pv.Label);</pre>
 *
 * The anchor defines it's own positional properties, but other properties (such
 * as the title property, say) can be inherited using the above idiom. Also note
 * that you can override positional properties in the anchor for custom
 * behavior.
 *
 * @extends pv.Mark
 * @param {pv.Mark} target the anchor target.
 */
pv.Anchor = function(target) {
  pv.Mark.call(this);
  this.target = target;
  this.parent = target.parent;
};

pv.Anchor.prototype = pv.extend(pv.Mark)
    .property("name", String);

/**
 * The anchor name. The set of supported anchor names is dependent on the
 * concrete mark type; see the mark type for details. For example, bars support
 * left, right, top and bottom anchors.
 *
 * <p>While anchor names are typically constants, the anchor name is a true
 * property, which means you can specify a function to compute the anchor name
 * dynamically. For instance, if you wanted to alternate top and bottom anchors,
 * saying
 *
 * <pre>m.anchor(function() (this.index % 2) ? "top" : "bottom").add(pv.Dot);</pre>
 *
 * would have the desired effect.
 *
 * @type string
 * @name pv.Anchor.prototype.name
 */

/**
 * Returns the anchor target of this mark, if it is derived from an anchor;
 * otherwise returns null. For example, if a label is derived from a bar anchor,
 *
 * <pre>bar.anchor("top").add(pv.Label);</pre>
 *
 * then property functions on the label can refer to the bar via the
 * <tt>anchorTarget</tt> method. This method is also useful for mark types
 * defining properties on custom anchors.
 *
 * @returns {pv.Mark} the anchor target of this mark; possibly null.
 */
pv.Anchor.prototype.anchorTarget = function() {
  return this.target;
};
/**
 * Constructs a new area mark with default properties. Areas are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents an area mark: the solid area between two series of
 * connected line segments. Unsurprisingly, areas are used most frequently for
 * area charts.
 *
 * <p>Just as a line represents a polyline, the <tt>Area</tt> mark type
 * represents a <i>polygon</i>. However, an area is not an arbitrary polygon;
 * vertices are paired either horizontally or vertically into parallel
 * <i>spans</i>, and each span corresponds to an associated datum. Either the
 * width or the height must be specified, but not both; this determines whether
 * the area is horizontally-oriented or vertically-oriented.  Like lines, areas
 * can be stroked and filled with arbitrary colors.
 *
 * <p>See also the <a href="../../api/Area.html">Area guide</a>.
 *
 * @extends pv.Mark
 */
pv.Area = function() {
  pv.Mark.call(this);
};

pv.Area.prototype = pv.extend(pv.Mark)
    .property("width", Number)
    .property("height", Number)
    .property("lineWidth", Number)
    .property("strokeStyle", pv.color)
    .property("fillStyle", pv.color)
    .property("segmented", Boolean)
    .property("interpolate", String)
    .property("tension", Number);

pv.Area.prototype.type = "area";

/**
 * The width of a given span, in pixels; used for horizontal spans. If the width
 * is specified, the height property should be 0 (the default). Either the top
 * or bottom property should be used to space the spans vertically, typically as
 * a multiple of the index.
 *
 * @type number
 * @name pv.Area.prototype.width
 */

/**
 * The height of a given span, in pixels; used for vertical spans. If the height
 * is specified, the width property should be 0 (the default). Either the left
 * or right property should be used to space the spans horizontally, typically
 * as a multiple of the index.
 *
 * @type number
 * @name pv.Area.prototype.height
 */

/**
 * The width of stroked lines, in pixels; used in conjunction with
 * <tt>strokeStyle</tt> to stroke the perimeter of the area. Unlike the
 * {@link Line} mark type, the entire perimeter is stroked, rather than just one
 * edge. The default value of this property is 1.5, but since the default stroke
 * style is null, area marks are not stroked by default.
 *
 * <p>This property is <i>fixed</i> for non-segmented areas. See
 * {@link pv.Mark}.
 *
 * @type number
 * @name pv.Area.prototype.lineWidth
 */

/**
 * The style of stroked lines; used in conjunction with <tt>lineWidth</tt> to
 * stroke the perimeter of the area. Unlike the {@link Line} mark type, the
 * entire perimeter is stroked, rather than just one edge. The default value of
 * this property is null, meaning areas are not stroked by default.
 *
 * <p>This property is <i>fixed</i> for non-segmented areas. See
 * {@link pv.Mark}.
 *
 * @type string
 * @name pv.Area.prototype.strokeStyle
 * @see pv.color
 */

/**
 * The area fill style; if non-null, the interior of the polygon forming the
 * area is filled with the specified color. The default value of this property
 * is a categorical color.
 *
 * <p>This property is <i>fixed</i> for non-segmented areas. See
 * {@link pv.Mark}.
 *
 * @type string
 * @name pv.Area.prototype.fillStyle
 * @see pv.color
 */

/**
 * Whether the area is segmented; whether variations in fill style, stroke
 * style, and the other properties are treated as fixed. Rendering segmented
 * areas is noticeably slower than non-segmented areas.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type boolean
 * @name pv.Area.prototype.segmented
 */

/**
 * How to interpolate between values. Linear interpolation ("linear") is the
 * default, producing a straight line between points. For piecewise constant
 * functions (i.e., step functions), either "step-before" or "step-after" can be
 * specified. To draw open uniform b-splines, specify "basis". To draw cardinal
 * splines, specify "cardinal"; see also {@link #tension}.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type string
 * @name pv.Area.prototype.interpolate
 */

/**
 * The tension of cardinal splines; used in conjunction with
 * interpolate("cardinal"). A value between 0 and 1 draws cardinal splines with
 * the given tension. In some sense, the tension can be interpreted as the
 * "length" of the tangent; a tension of 1 will yield all zero tangents (i.e.,
 * linear interpolation), and a tension of 0 yields a Catmull-Rom spline. The
 * default value is 0.7.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type number
 * @name pv.Area.prototype.tension
 */

/**
 * Default properties for areas. By default, there is no stroke and the fill
 * style is a categorical color.
 *
 * @type pv.Area
 */
pv.Area.prototype.defaults = new pv.Area()
    .extend(pv.Mark.prototype.defaults)
    .lineWidth(1.5)
    .fillStyle(pv.Colors.category20().by(pv.parent))
    .interpolate("linear")
    .tension(.7);

/** @private Sets width and height to zero if null. */
pv.Area.prototype.buildImplied = function(s) {
  if (s.height == null) s.height = 0;
  if (s.width == null) s.width = 0;
  pv.Mark.prototype.buildImplied.call(this, s);
};

/** @private Records which properties may be fixed. */
pv.Area.fixed = {
  lineWidth: 1,
  lineJoin: 1,
  strokeStyle: 1,
  fillStyle: 1,
  segmented: 1,
  interpolate: 1,
  tension: 1
};

/**
 * @private Make segmented required, such that this fixed property is always
 * evaluated, even if the first segment is not visible. Also cache which
 * properties are normally fixed.
 */
pv.Area.prototype.bind = function() {
  pv.Mark.prototype.bind.call(this);
  var binds = this.binds,
      required = binds.required,
      optional = binds.optional;
  for (var i = 0, n = optional.length; i < n; i++) {
    var p = optional[i];
    p.fixed = p.name in pv.Area.fixed;
    if (p.name == "segmented") {
      required.push(p);
      optional.splice(i, 1);
      i--;
      n--;
    }
  }

  /* Cache the original arrays so they can be restored on build. */
  this.binds.$required = required;
  this.binds.$optional = optional;
};

/**
 * @private Override the default build behavior such that fixed properties are
 * determined dynamically, based on the value of the (always) fixed segmented
 * property. Any fixed properties are only evaluated on the first instance,
 * although their values are propagated to subsequent instances, so that they
 * are available for property chaining and the like.
 */
pv.Area.prototype.buildInstance = function(s) {
  var binds = this.binds;

  /* Handle fixed properties on secondary instances. */
  if (this.index) {
    var fixed = binds.fixed;

    /* Determine which properties are fixed. */
    if (!fixed) {
      fixed = binds.fixed = [];
      function f(p) { return !p.fixed || (fixed.push(p), false); }
      binds.required = binds.required.filter(f);
      if (!this.scene[0].segmented) binds.optional = binds.optional.filter(f);
    }

    /* Copy fixed property values from the first instance. */
    for (var i = 0, n = fixed.length; i < n; i++) {
      var p = fixed[i].name;
      s[p] = this.scene[0][p];
    }
  }

  /* Evaluate all properties on the first instance. */
  else {
    binds.required = binds.$required;
    binds.optional = binds.$optional;
    binds.fixed = null;
  }

  pv.Mark.prototype.buildInstance.call(this, s);
};

/**
 * Constructs a new area anchor with default properties. Areas support five
 * different anchors:<ul>
 *
 * <li>top
 * <li>left
 * <li>center
 * <li>bottom
 * <li>right
 *
 * </ul>In addition to positioning properties (left, right, top bottom), the
 * anchors support text rendering properties (text-align, text-baseline). Text
 * is rendered to appear inside the area. The area anchor also propagates the
 * interpolate, eccentricity, and tension properties such that an anchored area
 * or line will match positions between control points.
 *
 * <p>For consistency with the other mark types, the anchor positions are
 * defined in terms of their opposite edge. For example, the top anchor defines
 * the bottom property, such that an area added to the top anchor grows upward.
 *
 * @param {string} name the anchor name; either a string or a property function.
 * @returns {pv.Anchor}
 */
pv.Area.prototype.anchor = function(name) {
  var scene;
  return pv.Mark.prototype.anchor.call(this, name)
    .def("$area.anchor", function() {
        scene = this.scene.target;
      })
    .interpolate(function() {
       return scene[this.index].interpolate;
      })
    .eccentricity(function() {
       return scene[this.index].eccentricity;
      })
    .tension(function() {
        return scene[this.index].tension;
      });
};
/**
 * Constructs a new bar mark with default properties. Bars are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents a bar: an axis-aligned rectangle that can be stroked and
 * filled. Bars are used for many chart types, including bar charts, histograms
 * and Gantt charts. Bars can also be used as decorations, for example to draw a
 * frame border around a panel; in fact, a panel is a special type (a subclass)
 * of bar.
 *
 * <p>Bars can be positioned in several ways. Most commonly, one of the four
 * corners is fixed using two margins, and then the width and height properties
 * determine the extent of the bar relative to this fixed location. For example,
 * using the bottom and left properties fixes the bottom-left corner; the width
 * then extends to the right, while the height extends to the top. As an
 * alternative to the four corners, a bar can be positioned exclusively using
 * margins; this is convenient as an inset from the containing panel, for
 * example. See {@link pv.Mark} for details on the prioritization of redundant
 * positioning properties.
 *
 * <p>See also the <a href="../../api/Bar.html">Bar guide</a>.
 *
 * @extends pv.Mark
 */
pv.Bar = function() {
  pv.Mark.call(this);
};

pv.Bar.prototype = pv.extend(pv.Mark)
    .property("width", Number)
    .property("height", Number)
    .property("lineWidth", Number)
    .property("strokeStyle", pv.color)
    .property("fillStyle", pv.color);

pv.Bar.prototype.type = "bar";

/**
 * The width of the bar, in pixels. If the left position is specified, the bar
 * extends rightward from the left edge; if the right position is specified, the
 * bar extends leftward from the right edge.
 *
 * @type number
 * @name pv.Bar.prototype.width
 */

/**
 * The height of the bar, in pixels. If the bottom position is specified, the
 * bar extends upward from the bottom edge; if the top position is specified,
 * the bar extends downward from the top edge.
 *
 * @type number
 * @name pv.Bar.prototype.height
 */

/**
 * The width of stroked lines, in pixels; used in conjunction with
 * <tt>strokeStyle</tt> to stroke the bar's border.
 *
 * @type number
 * @name pv.Bar.prototype.lineWidth
 */

/**
 * The style of stroked lines; used in conjunction with <tt>lineWidth</tt> to
 * stroke the bar's border. The default value of this property is null, meaning
 * bars are not stroked by default.
 *
 * @type string
 * @name pv.Bar.prototype.strokeStyle
 * @see pv.color
 */

/**
 * The bar fill style; if non-null, the interior of the bar is filled with the
 * specified color. The default value of this property is a categorical color.
 *
 * @type string
 * @name pv.Bar.prototype.fillStyle
 * @see pv.color
 */

/**
 * Default properties for bars. By default, there is no stroke and the fill
 * style is a categorical color.
 *
 * @type pv.Bar
 */
pv.Bar.prototype.defaults = new pv.Bar()
    .extend(pv.Mark.prototype.defaults)
    .lineWidth(1.5)
    .fillStyle(pv.Colors.category20().by(pv.parent));
/**
 * Constructs a new dot mark with default properties. Dots are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents a dot; a dot is simply a sized glyph centered at a given
 * point that can also be stroked and filled. The <tt>size</tt> property is
 * proportional to the area of the rendered glyph to encourage meaningful visual
 * encodings. Dots can visually encode up to eight dimensions of data, though
 * this may be unwise due to integrality. See {@link pv.Mark} for details on the
 * prioritization of redundant positioning properties.
 *
 * <p>See also the <a href="../../api/Dot.html">Dot guide</a>.
 *
 * @extends pv.Mark
 */
pv.Dot = function() {
  pv.Mark.call(this);
};

pv.Dot.prototype = pv.extend(pv.Mark)
    .property("size", Number)
    .property("radius", Number)
    .property("shape", String)
    .property("angle", Number)
    .property("lineWidth", Number)
    .property("strokeStyle", pv.color)
    .property("fillStyle", pv.color);

pv.Dot.prototype.type = "dot";

/**
 * The size of the dot, in square pixels. Square pixels are used such that the
 * area of the dot is linearly proportional to the value of the size property,
 * facilitating representative encodings.
 *
 * @see #radius
 * @type number
 * @name pv.Dot.prototype.size
 */

/**
 * The radius of the dot, in pixels. This is an alternative to using
 * {@link #size}.
 *
 * @see #size
 * @type number
 * @name pv.Dot.prototype.radius
 */

/**
 * The shape name. Several shapes are supported:<ul>
 *
 * <li>cross
 * <li>triangle
 * <li>diamond
 * <li>square
 * <li>circle
 * <li>tick
 * <li>bar
 *
 * </ul>These shapes can be further changed using the {@link #angle} property;
 * for instance, a cross can be turned into a plus by rotating. Similarly, the
 * tick, which is vertical by default, can be rotated horizontally. Note that
 * some shapes (cross and tick) do not have interior areas, and thus do not
 * support fill style meaningfully.
 *
 * <p>Note: it may be more natural to use the {@link pv.Rule} mark for
 * horizontal and vertical ticks. The tick shape is only necessary if angled
 * ticks are needed.
 *
 * @type string
 * @name pv.Dot.prototype.shape
 */

/**
 * The rotation angle, in radians. Used to rotate shapes, such as to turn a
 * cross into a plus.
 *
 * @type number
 * @name pv.Dot.prototype.angle
 */

/**
 * The width of stroked lines, in pixels; used in conjunction with
 * <tt>strokeStyle</tt> to stroke the dot's shape.
 *
 * @type number
 * @name pv.Dot.prototype.lineWidth
 */

/**
 * The style of stroked lines; used in conjunction with <tt>lineWidth</tt> to
 * stroke the dot's shape. The default value of this property is a categorical
 * color.
 *
 * @type string
 * @name pv.Dot.prototype.strokeStyle
 * @see pv.color
 */

/**
 * The fill style; if non-null, the interior of the dot is filled with the
 * specified color. The default value of this property is null, meaning dots are
 * not filled by default.
 *
 * @type string
 * @name pv.Dot.prototype.fillStyle
 * @see pv.color
 */

/**
 * Default properties for dots. By default, there is no fill and the stroke
 * style is a categorical color. The default shape is "circle" with size 20.
 *
 * @type pv.Dot
 */
pv.Dot.prototype.defaults = new pv.Dot()
    .extend(pv.Mark.prototype.defaults)
    .size(20)
    .shape("circle")
    .lineWidth(1.5)
    .strokeStyle(pv.Colors.category10().by(pv.parent));

/**
 * Constructs a new dot anchor with default properties. Dots support five
 * different anchors:<ul>
 *
 * <li>top
 * <li>left
 * <li>center
 * <li>bottom
 * <li>right
 *
 * </ul>In addition to positioning properties (left, right, top bottom), the
 * anchors support text rendering properties (text-align, text-baseline). Text is
 * rendered to appear outside the dot. Note that this behavior is different from
 * other mark anchors, which default to rendering text <i>inside</i> the mark.
 *
 * <p>For consistency with the other mark types, the anchor positions are
 * defined in terms of their opposite edge. For example, the top anchor defines
 * the bottom property, such that a bar added to the top anchor grows upward.
 *
 * @param {string} name the anchor name; either a string or a property function.
 * @returns {pv.Anchor}
 */
pv.Dot.prototype.anchor = function(name) {
  var scene;
  return pv.Mark.prototype.anchor.call(this, name)
    .def("$wedge.anchor", function() {
        scene = this.scene.target;
      })
    .left(function() {
        var s = scene[this.index];
        switch (this.name()) {
          case "bottom":
          case "top":
          case "center": return s.left;
          case "left": return null;
        }
        return s.left + s.radius;
      })
    .right(function() {
        var s = scene[this.index];
        return this.name() == "left" ? s.right + s.radius : null;
      })
    .top(function() {
        var s = scene[this.index];
        switch (this.name()) {
          case "left":
          case "right":
          case "center": return s.top;
          case "top": return null;
        }
        return s.top + s.radius;
      })
    .bottom(function() {
        var s = scene[this.index];
        return this.name() == "top" ? s.bottom + s.radius : null;
      })
    .textAlign(function() {
        switch (this.name()) {
          case "left": return "right";
          case "bottom":
          case "top":
          case "center": return "center";
        }
        return "left";
      })
    .textBaseline(function() {
        switch (this.name()) {
          case "right":
          case "left":
          case "center": return "middle";
          case "bottom": return "top";
        }
        return "bottom";
      });
};

/** @private Sets radius based on size or vice versa. */
pv.Dot.prototype.buildImplied = function(s) {
  if (s.radius == null) s.radius = Math.sqrt(s.size);
  else if (s.size == null) s.size = s.radius * s.radius;
  pv.Mark.prototype.buildImplied.call(this, s);
};
/**
 * Constructs a new label mark with default properties. Labels are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents a text label, allowing textual annotation of other marks or
 * arbitrary text within the visualization. The character data must be plain
 * text (unicode), though the text can be styled using the {@link #font}
 * property. If rich text is needed, external HTML elements can be overlaid on
 * the canvas by hand.
 *
 * <p>Labels are positioned using the box model, similarly to {@link Dot}. Thus,
 * a label has no width or height, but merely a text anchor location. The text
 * is positioned relative to this anchor location based on the
 * {@link #textAlign}, {@link #textBaseline} and {@link #textMargin} properties.
 * Furthermore, the text may be rotated using {@link #textAngle}.
 *
 * <p>Labels ignore events, so as to not interfere with event handlers on
 * underlying marks, such as bars. In the future, we may support event handlers
 * on labels.
 *
 * <p>See also the <a href="../../api/Label.html">Label guide</a>.
 *
 * @extends pv.Mark
 */
pv.Label = function() {
  pv.Mark.call(this);
};

pv.Label.prototype = pv.extend(pv.Mark)
    .property("text", String)
    .property("font", String)
    .property("textAngle", Number)
    .property("textStyle", pv.color)
    .property("textAlign", String)
    .property("textBaseline", String)
    .property("textMargin", Number)
    .property("textDecoration", String)
    .property("textShadow", String);

pv.Label.prototype.type = "label";

/**
 * The character data to render; a string. The default value of the text
 * property is the identity function, meaning the label's associated datum will
 * be rendered using its <tt>toString</tt>.
 *
 * @type string
 * @name pv.Label.prototype.text
 */

/**
 * The font format, per the CSS Level 2 specification. The default font is "10px
 * sans-serif", for consistency with the HTML 5 canvas element specification.
 * Note that since text is not wrapped, any line-height property will be
 * ignored. The other font-style, font-variant, font-weight, font-size and
 * font-family properties are supported.
 *
 * @see <a href="http://www.w3.org/TR/CSS2/fonts.html#font-shorthand">CSS2 fonts</a>
 * @type string
 * @name pv.Label.prototype.font
 */

/**
 * The rotation angle, in radians. Text is rotated clockwise relative to the
 * anchor location. For example, with the default left alignment, an angle of
 * Math.PI / 2 causes text to proceed downwards. The default angle is zero.
 *
 * @type number
 * @name pv.Label.prototype.textAngle
 */

/**
 * The text color. The name "textStyle" is used for consistency with "fillStyle"
 * and "strokeStyle", although it might be better to rename this property (and
 * perhaps use the same name as "strokeStyle"). The default color is black.
 *
 * @type string
 * @name pv.Label.prototype.textStyle
 * @see pv.color
 */

/**
 * The horizontal text alignment. One of:<ul>
 *
 * <li>left
 * <li>center
 * <li>right
 *
 * </ul>The default horizontal alignment is left.
 *
 * @type string
 * @name pv.Label.prototype.textAlign
 */

/**
 * The vertical text alignment. One of:<ul>
 *
 * <li>top
 * <li>middle
 * <li>bottom
 *
 * </ul>The default vertical alignment is bottom.
 *
 * @type string
 * @name pv.Label.prototype.textBaseline
 */

/**
 * The text margin; may be specified in pixels, or in font-dependent units (such
 * as ".1ex"). The margin can be used to pad text away from its anchor location,
 * in a direction dependent on the horizontal and vertical alignment
 * properties. For example, if the text is left- and middle-aligned, the margin
 * shifts the text to the right. The default margin is 3 pixels.
 *
 * @type number
 * @name pv.Label.prototype.textMargin
 */

/**
 * A list of shadow effects to be applied to text, per the CSS Text Level 3
 * text-shadow property. An example specification is "0.1em 0.1em 0.1em
 * rgba(0,0,0,.5)"; the first length is the horizontal offset, the second the
 * vertical offset, and the third the blur radius.
 *
 * @see <a href="http://www.w3.org/TR/css3-text/#text-shadow">CSS3 text</a>
 * @type string
 * @name pv.Label.prototype.textShadow
 */

/**
 * A list of decoration to be applied to text, per the CSS Text Level 3
 * text-decoration property. An example specification is "underline".
 *
 * @see <a href="http://www.w3.org/TR/css3-text/#text-decoration">CSS3 text</a>
 * @type string
 * @name pv.Label.prototype.textDecoration
 */

/**
 * Default properties for labels. See the individual properties for the default
 * values.
 *
 * @type pv.Label
 */
pv.Label.prototype.defaults = new pv.Label()
    .extend(pv.Mark.prototype.defaults)
    .events("none")
    .text(pv.identity)
    .font("14px Roboto")
    .textAngle(0)
    .textStyle("#333")
    .textAlign("left")
    .textBaseline("bottom")
    .textMargin(3);
/**
 * Constructs a new line mark with default properties. Lines are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents a series of connected line segments, or <i>polyline</i>,
 * that can be stroked with a configurable color and thickness. Each
 * articulation point in the line corresponds to a datum; for <i>n</i> points,
 * <i>n</i>-1 connected line segments are drawn. The point is positioned using
 * the box model. Arbitrary paths are also possible, allowing radar plots and
 * other custom visualizations.
 *
 * <p>Like areas, lines can be stroked and filled with arbitrary colors. In most
 * cases, lines are only stroked, but the fill style can be used to construct
 * arbitrary polygons.
 *
 * <p>See also the <a href="../../api/Line.html">Line guide</a>.
 *
 * @extends pv.Mark
 */
pv.Line = function() {
  pv.Mark.call(this);
};

pv.Line.prototype = pv.extend(pv.Mark)
    .property("lineWidth", Number)
    .property("lineJoin", String)
    .property("strokeStyle", pv.color)
    .property("fillStyle", pv.color)
    .property("segmented", Boolean)
    .property("interpolate", String)
    .property("eccentricity", Number)
    .property("tension", Number);

pv.Line.prototype.type = "line";

/**
 * The width of stroked lines, in pixels; used in conjunction with
 * <tt>strokeStyle</tt> to stroke the line.
 *
 * @type number
 * @name pv.Line.prototype.lineWidth
 */

/**
 * The style of stroked lines; used in conjunction with <tt>lineWidth</tt> to
 * stroke the line. The default value of this property is a categorical color.
 *
 * @type string
 * @name pv.Line.prototype.strokeStyle
 * @see pv.color
 */

/**
 * The type of corners where two lines meet. Accepted values are "bevel",
 * "round" and "miter". The default value is "miter".
 *
 * <p>For segmented lines, only "miter" joins and "linear" interpolation are
 * currently supported. Any other value, including null, will disable joins,
 * producing disjoint line segments. Note that the miter joins must be computed
 * manually (at least in the current SVG renderer); since this calculation may
 * be expensive and unnecessary for small lines, specifying null can improve
 * performance significantly.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type string
 * @name pv.Line.prototype.lineJoin
 */

/**
 * The line fill style; if non-null, the interior of the line is closed and
 * filled with the specified color. The default value of this property is a
 * null, meaning that lines are not filled by default.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type string
 * @name pv.Line.prototype.fillStyle
 * @see pv.color
 */

/**
 * Whether the line is segmented; whether variations in stroke style, line width
 * and the other properties are treated as fixed. Rendering segmented lines is
 * noticeably slower than non-segmented lines.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type boolean
 * @name pv.Line.prototype.segmented
 */

/**
 * How to interpolate between values. Linear interpolation ("linear") is the
 * default, producing a straight line between points. For piecewise constant
 * functions (i.e., step functions), either "step-before" or "step-after" can be
 * specified. To draw a clockwise circular arc between points, specify "polar";
 * to draw a counterclockwise circular arc between points, specify
 * "polar-reverse". To draw open uniform b-splines, specify "basis". To draw
 * cardinal splines, specify "cardinal"; see also {@link #tension}.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type string
 * @name pv.Line.prototype.interpolate
 */

/**
 * The eccentricity of polar line segments; used in conjunction with
 * interpolate("polar"). The default value of 0 means that line segments are
 * drawn as circular arcs. A value of 1 draws a straight line. A value between 0
 * and 1 draws an elliptical arc with the given eccentricity.
 *
 * @type number
 * @name pv.Line.prototype.eccentricity
 */

/**
 * The tension of cardinal splines; used in conjunction with
 * interpolate("cardinal"). A value between 0 and 1 draws cardinal splines with
 * the given tension. In some sense, the tension can be interpreted as the
 * "length" of the tangent; a tension of 1 will yield all zero tangents (i.e.,
 * linear interpolation), and a tension of 0 yields a Catmull-Rom spline. The
 * default value is 0.7.
 *
 * <p>This property is <i>fixed</i>. See {@link pv.Mark}.
 *
 * @type number
 * @name pv.Line.prototype.tension
 */

/**
 * Default properties for lines. By default, there is no fill and the stroke
 * style is a categorical color. The default interpolation is linear.
 *
 * @type pv.Line
 */
pv.Line.prototype.defaults = new pv.Line()
    .extend(pv.Mark.prototype.defaults)
    .lineJoin("miter")
    .lineWidth(1.5)
    .strokeStyle(pv.Colors.category10().by(pv.parent))
    .interpolate("linear")
    .eccentricity(0)
    .tension(.7);

/** @private Reuse Area's implementation for segmented bind & build. */
pv.Line.prototype.bind = pv.Area.prototype.bind;
pv.Line.prototype.buildInstance = pv.Area.prototype.buildInstance;

/**
 * Constructs a new line anchor with default properties. Lines support five
 * different anchors:<ul>
 *
 * <li>top
 * <li>left
 * <li>center
 * <li>bottom
 * <li>right
 *
 * </ul>In addition to positioning properties (left, right, top bottom), the
 * anchors support text rendering properties (text-align, text-baseline). Text is
 * rendered to appear outside the line. Note that this behavior is different
 * from other mark anchors, which default to rendering text <i>inside</i> the
 * mark.
 *
 * <p>For consistency with the other mark types, the anchor positions are
 * defined in terms of their opposite edge. For example, the top anchor defines
 * the bottom property, such that a bar added to the top anchor grows upward.
 *
 * @param {string} name the anchor name; either a string or a property function.
 * @returns {pv.Anchor}
 */
pv.Line.prototype.anchor = function(name) {
  return pv.Area.prototype.anchor.call(this, name)
    .textAlign(function(d) {
        switch (this.name()) {
          case "left": return "right";
          case "bottom":
          case "top":
          case "center": return "center";
          case "right": return "left";
        }
      })
    .textBaseline(function(d) {
        switch (this.name()) {
          case "right":
          case "left":
          case "center": return "middle";
          case "top": return "bottom";
          case "bottom": return "top";
        }
      });
};
/**
 * Constructs a new rule with default properties. Rules are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents a horizontal or vertical rule. Rules are frequently used
 * for axes and grid lines. For example, specifying only the bottom property
 * draws horizontal rules, while specifying only the left draws vertical
 * rules. Rules can also be used as thin bars. The visual style is controlled in
 * the same manner as lines.
 *
 * <p>Rules are positioned exclusively the standard box model properties. The
 * following combinations of properties are supported:
 *
 * <table>
 * <thead><th style="width:12em;">Properties</th><th>Orientation</th></thead>
 * <tbody>
 * <tr><td>left</td><td>vertical</td></tr>
 * <tr><td>right</td><td>vertical</td></tr>
 * <tr><td>left, bottom, top</td><td>vertical</td></tr>
 * <tr><td>right, bottom, top</td><td>vertical</td></tr>
 * <tr><td>top</td><td>horizontal</td></tr>
 * <tr><td>bottom</td><td>horizontal</td></tr>
 * <tr><td>top, left, right</td><td>horizontal</td></tr>
 * <tr><td>bottom, left, right</td><td>horizontal</td></tr>
 * <tr><td>left, top, height</td><td>vertical</td></tr>
 * <tr><td>left, bottom, height</td><td>vertical</td></tr>
 * <tr><td>right, top, height</td><td>vertical</td></tr>
 * <tr><td>right, bottom, height</td><td>vertical</td></tr>
 * <tr><td>left, top, width</td><td>horizontal</td></tr>
 * <tr><td>left, bottom, width</td><td>horizontal</td></tr>
 * <tr><td>right, top, width</td><td>horizontal</td></tr>
 * <tr><td>right, bottom, width</td><td>horizontal</td></tr>
 * </tbody>
 * </table>
 *
 * <p>Small rules can be used as tick marks; alternatively, a {@link Dot} with
 * the "tick" shape can be used.
 *
 * <p>See also the <a href="../../api/Rule.html">Rule guide</a>.
 *
 * @see pv.Line
 * @extends pv.Mark
 */
pv.Rule = function() {
  pv.Mark.call(this);
};

pv.Rule.prototype = pv.extend(pv.Mark)
    .property("width", Number)
    .property("height", Number)
    .property("lineWidth", Number)
    .property("strokeStyle", pv.color);

pv.Rule.prototype.type = "rule";

/**
 * The width of the rule, in pixels. If the left position is specified, the rule
 * extends rightward from the left edge; if the right position is specified, the
 * rule extends leftward from the right edge.
 *
 * @type number
 * @name pv.Rule.prototype.width
 */

/**
 * The height of the rule, in pixels. If the bottom position is specified, the
 * rule extends upward from the bottom edge; if the top position is specified,
 * the rule extends downward from the top edge.
 *
 * @type number
 * @name pv.Rule.prototype.height
 */

/**
 * The width of stroked lines, in pixels; used in conjunction with
 * <tt>strokeStyle</tt> to stroke the rule. The default value is 1 pixel.
 *
 * @type number
 * @name pv.Rule.prototype.lineWidth
 */

/**
 * The style of stroked lines; used in conjunction with <tt>lineWidth</tt> to
 * stroke the rule. The default value of this property is black.
 *
 * @type string
 * @name pv.Rule.prototype.strokeStyle
 * @see pv.color
 */

/**
 * Default properties for rules. By default, a single-pixel black line is
 * stroked.
 *
 * @type pv.Rule
 */
pv.Rule.prototype.defaults = new pv.Rule()
    .extend(pv.Mark.prototype.defaults)
    .lineWidth(1)
    .strokeStyle("black")
    .antialias(false);

/**
 * Constructs a new rule anchor with default properties. Rules support five
 * different anchors:<ul>
 *
 * <li>top
 * <li>left
 * <li>center
 * <li>bottom
 * <li>right
 *
 * </ul>In addition to positioning properties (left, right, top bottom), the
 * anchors support text rendering properties (text-align, text-baseline). Text is
 * rendered to appear outside the rule. Note that this behavior is different
 * from other mark anchors, which default to rendering text <i>inside</i> the
 * mark.
 *
 * <p>For consistency with the other mark types, the anchor positions are
 * defined in terms of their opposite edge. For example, the top anchor defines
 * the bottom property, such that a bar added to the top anchor grows upward.
 *
 * @param {string} name the anchor name; either a string or a property function.
 * @returns {pv.Anchor}
 */
pv.Rule.prototype.anchor = pv.Line.prototype.anchor;

/** @private Sets width or height based on orientation. */
pv.Rule.prototype.buildImplied = function(s) {
  var l = s.left, r = s.right, t = s.top, b = s.bottom;

  /* Determine horizontal or vertical orientation. */
  if ((s.width != null)
      || ((l == null) && (r == null))
      || ((r != null) && (l != null))) {
    s.height = 0;
  } else {
    s.width = 0;
  }

  pv.Mark.prototype.buildImplied.call(this, s);
};
/**
 * Constructs a new, empty panel with default properties. Panels, with the
 * exception of the root panel, are not typically constructed directly; instead,
 * they are added to an existing panel or mark via {@link pv.Mark#add}.
 *
 * @class Represents a container mark. Panels allow repeated or nested
 * structures, commonly used in small multiple displays where a small
 * visualization is tiled to facilitate comparison across one or more
 * dimensions. Other types of visualizations may benefit from repeated and
 * possibly overlapping structure as well, such as stacked area charts. Panels
 * can also offset the position of marks to provide padding from surrounding
 * content.
 *
 * <p>All Protovis displays have at least one panel; this is the root panel to
 * which marks are rendered. The box model properties (four margins, width and
 * height) are used to offset the positions of contained marks. The data
 * property determines the panel count: a panel is generated once per associated
 * datum. When nested panels are used, property functions can declare additional
 * arguments to access the data associated with enclosing panels.
 *
 * <p>Panels can be rendered inline, facilitating the creation of sparklines.
 * This allows designers to reuse browser layout features, such as text flow and
 * tables; designers can also overlay HTML elements such as rich text and
 * images.
 *
 * <p>All panels have a <tt>children</tt> array (possibly empty) containing the
 * child marks in the order they were added. Panels also have a <tt>root</tt>
 * field which points to the root (outermost) panel; the root panel's root field
 * points to itself.
 *
 * <p>See also the <a href="../../api/">Protovis guide</a>.
 *
 * @extends pv.Bar
 */
pv.Panel = function() {
  pv.Bar.call(this);

  /**
   * The child marks; zero or more {@link pv.Mark}s in the order they were
   * added.
   *
   * @see #add
   * @type pv.Mark[]
   */
  this.children = [];
  this.root = this;

  /**
   * The internal $dom field is set by the Protovis loader; see lang/init.js. It
   * refers to the script element that contains the Protovis specification, so
   * that the panel knows where in the DOM to insert the generated SVG element.
   *
   * @private
   */
  this.$dom = pv.$ && pv.$.s;
};

pv.Panel.prototype = pv.extend(pv.Bar)
    .property("transform")
    .property("overflow", String)
    .property("canvas", function(c) {
        return (typeof c == "string")
            ? document.getElementById(c)
            : c; // assume that c is the passed-in element
      });

pv.Panel.prototype.type = "panel";

/**
 * The canvas element; either the string ID of the canvas element in the current
 * document, or a reference to the canvas element itself. If null, a canvas
 * element will be created and inserted into the document at the location of the
 * script element containing the current Protovis specification. This property
 * only applies to root panels and is ignored on nested panels.
 *
 * <p>Note: the "canvas" element here refers to a <tt>div</tt> (or other suitable
 * HTML container element), <i>not</i> a <tt>canvas</tt> element. The name of
 * this property is a historical anachronism from the first implementation that
 * used HTML 5 canvas, rather than SVG.
 *
 * @type string
 * @name pv.Panel.prototype.canvas
 */

/**
 * Specifies whether child marks are clipped when they overflow this panel.
 * This affects the clipping of all this panel's descendant marks.
 *
 * @type string
 * @name pv.Panel.prototype.overflow
 * @see <a href="http://www.w3.org/TR/CSS2/visufx.html#overflow">CSS2</a>
 */

/**
 * The transform to be applied to child marks. The default transform is
 * identity, which has no effect. Note that the panel's own fill and stroke are
 * not affected by the transform, and panel's transform only affects the
 * <tt>scale</tt> of child marks, not the panel itself.
 *
 * @type pv.Transform
 * @name pv.Panel.prototype.transform
 * @see pv.Mark#scale
 */

/**
 * Default properties for panels. By default, the margins are zero, the fill
 * style is transparent.
 *
 * @type pv.Panel
 */
pv.Panel.prototype.defaults = new pv.Panel()
    .extend(pv.Bar.prototype.defaults)
    .fillStyle(null) // override Bar default
    .overflow("visible");

/**
 * Returns an anchor with the specified name. This method is overridden such
 * that adding to a panel's anchor adds to the panel, rather than to the panel's
 * parent.
 *
 * @param {string} name the anchor name; either a string or a property function.
 * @returns {pv.Anchor} the new anchor.
 */
pv.Panel.prototype.anchor = function(name) {
  var anchor = pv.Bar.prototype.anchor.call(this, name);
  anchor.parent = this;
  return anchor;
};

/**
 * Adds a new mark of the specified type to this panel. Unlike the normal
 * {@link Mark#add} behavior, adding a mark to a panel does not cause the mark
 * to inherit from the panel. Since the contained marks are offset by the panel
 * margins already, inheriting properties is generally undesirable; of course,
 * it is always possible to change this behavior by calling {@link Mark#extend}
 * explicitly.
 *
 * @param {function} type the type of the new mark to add.
 * @returns {pv.Mark} the new mark.
 */
pv.Panel.prototype.add = function(type) {
  var child = new type();
  child.parent = this;
  child.root = this.root;
  child.childIndex = this.children.length;
  this.children.push(child);
  return child;
};

/** @private Bind this panel, then any child marks recursively. */
pv.Panel.prototype.bind = function() {
  pv.Mark.prototype.bind.call(this);
  for (var i = 0; i < this.children.length; i++) {
    this.children[i].bind();
  }
};

/**
 * @private Evaluates all of the properties for this panel for the specified
 * instance <tt>s</tt> in the scene graph, including recursively building the
 * scene graph for child marks.
 *
 * @param s a node in the scene graph; the instance of the panel to build.
 * @see Mark#scene
 */
pv.Panel.prototype.buildInstance = function(s) {
  pv.Bar.prototype.buildInstance.call(this, s);
  if (!s.visible) return;
  if (!s.children) s.children = [];

  /*
   * Multiply the current scale factor by this panel's transform. Also clear the
   * default index as we recurse into child marks; it will be reset to the
   * current index when the next panel instance is built.
   */
  var scale = this.scale * s.transform.k, child, n = this.children.length;
  pv.Mark.prototype.index = -1;

  /*
   * Build each child, passing in the parent (this panel) scene graph node. The
   * child mark's scene is initialized from the corresponding entry in the
   * existing scene graph, such that properties from the previous build can be
   * reused; this is largely to facilitate the recycling of SVG elements.
   */
  for (var i = 0; i < n; i++) {
    child = this.children[i];
    child.scene = s.children[i]; // possibly undefined
    child.scale = scale;
    child.build();
  }

  /*
   * Once the child marks have been built, the new scene graph nodes are removed
   * from the child marks and placed into the scene graph. The nodes cannot
   * remain on the child nodes because this panel (or a parent panel) may be
   * instantiated multiple times!
   */
  for (var i = 0; i < n; i++) {
    child = this.children[i];
    s.children[i] = child.scene;
    delete child.scene;
    delete child.scale;
  }

  /* Delete any expired child scenes. */
  s.children.length = n;
};

/**
 * @private Computes the implied properties for this panel for the specified
 * instance <tt>s</tt> in the scene graph. Panels have two implied
 * properties:<ul>
 *
 * <li>The <tt>canvas</tt> property references the DOM element, typically a DIV,
 * that contains the SVG element that is used to display the visualization. This
 * property may be specified as a string, referring to the unique ID of the
 * element in the DOM. The string is converted to a reference to the DOM
 * element. The width and height of the SVG element is inferred from this DOM
 * element. If no canvas property is specified, a new SVG element is created and
 * inserted into the document, using the panel dimensions; see
 * {@link #createCanvas}.
 *
 * <li>The <tt>children</tt> array, while not a property per se, contains the
 * scene graph for each child mark. This array is initialized to be empty, and
 * is populated above in {@link #buildInstance}.
 *
 * </ul>The current implementation creates the SVG element, if necessary, during
 * the build phase; in the future, it may be preferrable to move this to the
 * update phase, although then the canvas property would be undefined. In
 * addition, DOM inspection is necessary to define the implied width and height
 * properties that may be inferred from the DOM.
 *
 * @param s a node in the scene graph; the instance of the panel to build.
 */
pv.Panel.prototype.buildImplied = function(s) {
  if (!this.parent) {
    var c = s.canvas;
    if (c) {
      /* Clear the container if it's not associated with this panel. */
      if (c.$panel != this) {
        c.$panel = this;
        while (c.lastChild) c.removeChild(c.lastChild);
      }

      /* If width and height weren't specified, inspect the container. */
      var w, h;
      if (s.width == null) {
        w = parseFloat(pv.css(c, "width"));
        s.width = w - s.left - s.right;
      }
      if (s.height == null) {
        h = parseFloat(pv.css(c, "height"));
        s.height = h - s.top - s.bottom;
      }
    } else {
      var cache = this.$canvas || (this.$canvas = []);
      if (!(c = cache[this.index])) {
        c = cache[this.index] = document.createElement("span");
        if (this.$dom) { // script element for text/javascript+protovis
          this.$dom.parentNode.insertBefore(c, this.$dom);
        } else { // find the last element in the body
          var n = document.body;
          while (n.lastChild && n.lastChild.tagName) n = n.lastChild;
          if (n != document.body) n = n.parentNode;
          n.appendChild(c);
        }
      }
    }
    s.canvas = c;
  }
  if (!s.transform) s.transform = pv.Transform.identity;
  pv.Mark.prototype.buildImplied.call(this, s);
};
/**
 * Constructs a new image with default properties. Images are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents an image, either a static resource or a dynamically-
 * generated pixel buffer. Images share the same layout and style properties as
 * bars. The external image resource is specified via the {@link #url}
 * property. The optional fill, if specified, appears beneath the image, while
 * the optional stroke appears above the image.
 *
 * <p>Dynamic images such as heatmaps are supported using the {@link #image}
 * psuedo-property. This function is passed the <i>x</i> and <i>y</i> index, in
 * addition to the current data stack. The return value is a {@link pv.Color},
 * or null for transparent. A string can also be returned, which will be parsed
 * into a color; however, it is typically much faster to return an object with
 * <tt>r</tt>, <tt>g</tt>, <tt>b</tt> and <tt>a</tt> attributes, to avoid the
 * cost of parsing and object instantiation.
 *
 * <p>See {@link pv.Bar} for details on positioning properties.
 *
 * @extends pv.Bar
 */
pv.Image = function() {
  pv.Bar.call(this);
};

pv.Image.prototype = pv.extend(pv.Bar)
    .property("url", String)
    .property("imageWidth", Number)
    .property("imageHeight", Number);

pv.Image.prototype.type = "image";

/**
 * The URL of the image to display. The set of supported image types is
 * browser-dependent; PNG and JPEG are recommended.
 *
 * @type string
 * @name pv.Image.prototype.url
 */

/**
 * The width of the image in pixels. For static images, this property is
 * computed implicitly from the loaded image resources. For dynamic images, this
 * property can be used to specify the width of the pixel buffer; otherwise, the
 * value is derived from the <tt>width</tt> property.
 *
 * @type number
 * @name pv.Image.prototype.imageWidth
 */

/**
 * The height of the image in pixels. For static images, this property is
 * computed implicitly from the loaded image resources. For dynamic images, this
 * property can be used to specify the height of the pixel buffer; otherwise, the
 * value is derived from the <tt>height</tt> property.
 *
 * @type number
 * @name pv.Image.prototype.imageHeight
 */

/**
 * Default properties for images. By default, there is no stroke or fill style.
 *
 * @type pv.Image
 */
pv.Image.prototype.defaults = new pv.Image()
    .extend(pv.Bar.prototype.defaults)
    .fillStyle(null);

/**
 * Specifies the dynamic image function. By default, no image function is
 * specified and the <tt>url</tt> property is used to load a static image
 * resource. If an image function is specified, it will be invoked for each
 * pixel in the image, based on the related <tt>imageWidth</tt> and
 * <tt>imageHeight</tt> properties.
 *
 * <p>For example, given a two-dimensional array <tt>heatmap</tt>, containing
 * numbers in the range [0, 1] in row-major order, a simple monochrome heatmap
 * image can be specified as:
 *
 * <pre>vis.add(pv.Image)
 *     .imageWidth(heatmap[0].length)
 *     .imageHeight(heatmap.length)
 *     .image(pv.ramp("white", "black").by(function(x, y) heatmap[y][x]));</pre>
 *
 * For fastest performance, use an ordinal scale which caches the fixed color
 * palette, or return an object literal with <tt>r</tt>, <tt>g</tt>, <tt>b</tt>
 * and <tt>a</tt> attributes. A {@link pv.Color} or string can also be returned,
 * though this typically results in slower performance.
 *
 * @param {function} f the new sizing function.
 * @returns {pv.Layout.Pack} this.
 */
pv.Image.prototype.image = function(f) {
  /** @private */
  this.$image = function() {
      var c = f.apply(this, arguments);
      return c == null ? pv.Color.transparent
          : typeof c == "string" ? pv.color(c)
          : c;
    };
  return this;
};

/** @private Scan the proto chain for an image function. */
pv.Image.prototype.bind = function() {
  pv.Bar.prototype.bind.call(this);
  var binds = this.binds, mark = this;
  do {
    binds.image = mark.$image;
  } while (!binds.image && (mark = mark.proto));
};

/** @private */
pv.Image.prototype.buildImplied = function(s) {
  pv.Bar.prototype.buildImplied.call(this, s);
  if (!s.visible) return;

  /* Compute the implied image dimensions. */
  if (s.imageWidth == null) s.imageWidth = s.width;
  if (s.imageHeight == null) s.imageHeight = s.height;

  /* Compute the pixel values. */
  if ((s.url == null) && this.binds.image) {

    /* Cache the canvas element to reuse across renders. */
    var canvas = this.$canvas || (this.$canvas = document.createElement("canvas")),
        context = canvas.getContext("2d"),
        w = s.imageWidth,
        h = s.imageHeight,
        stack = pv.Mark.stack,
        data;

    /* Evaluate the image function, storing into a CanvasPixelArray. */
    canvas.width = w;
    canvas.height = h;
    data = (s.image = context.createImageData(w, h)).data;
    stack.unshift(null, null);
    for (var y = 0, p = 0; y < h; y++) {
      stack[1] = y;
      for (var x = 0; x < w; x++) {
        stack[0] = x;
        var color = this.binds.image.apply(this, stack);
        data[p++] = color.r;
        data[p++] = color.g;
        data[p++] = color.b;
        data[p++] = 255 * color.a;
      }
    }
    stack.splice(0, 2);
  }
};
/**
 * Constructs a new wedge with default properties. Wedges are not typically
 * constructed directly, but by adding to a panel or an existing mark via
 * {@link pv.Mark#add}.
 *
 * @class Represents a wedge, or pie slice. Specified in terms of start and end
 * angle, inner and outer radius, wedges can be used to construct donut charts
 * and polar bar charts as well. If the {@link #angle} property is used, the end
 * angle is implied by adding this value to start angle. By default, the start
 * angle is the previously-generated wedge's end angle. This design allows
 * explicit control over the wedge placement if desired, while offering
 * convenient defaults for the construction of radial graphs.
 *
 * <p>The center point of the circle is positioned using the standard box model.
 * The wedge can be stroked and filled, similar to {@link pv.Bar}.
 *
 * <p>See also the <a href="../../api/Wedge.html">Wedge guide</a>.
 *
 * @extends pv.Mark
 */
pv.Wedge = function() {
  pv.Mark.call(this);
};

pv.Wedge.prototype = pv.extend(pv.Mark)
    .property("startAngle", Number)
    .property("endAngle", Number)
    .property("angle", Number)
    .property("innerRadius", Number)
    .property("outerRadius", Number)
    .property("lineWidth", Number)
    .property("strokeStyle", pv.color)
    .property("fillStyle", pv.color);

pv.Wedge.prototype.type = "wedge";

/**
 * The start angle of the wedge, in radians. The start angle is measured
 * clockwise from the 3 o'clock position. The default value of this property is
 * the end angle of the previous instance (the {@link Mark#sibling}), or -PI / 2
 * for the first wedge; for pie and donut charts, typically only the
 * {@link #angle} property needs to be specified.
 *
 * @type number
 * @name pv.Wedge.prototype.startAngle
 */

/**
 * The end angle of the wedge, in radians. If not specified, the end angle is
 * implied as the start angle plus the {@link #angle}.
 *
 * @type number
 * @name pv.Wedge.prototype.endAngle
 */

/**
 * The angular span of the wedge, in radians. This property is used if end angle
 * is not specified.
 *
 * @type number
 * @name pv.Wedge.prototype.angle
 */

/**
 * The inner radius of the wedge, in pixels. The default value of this property
 * is zero; a positive value will produce a donut slice rather than a pie slice.
 * The inner radius can vary per-wedge.
 *
 * @type number
 * @name pv.Wedge.prototype.innerRadius
 */

/**
 * The outer radius of the wedge, in pixels. This property is required. For
 * pies, only this radius is required; for donuts, the inner radius must be
 * specified as well. The outer radius can vary per-wedge.
 *
 * @type number
 * @name pv.Wedge.prototype.outerRadius
 */

/**
 * The width of stroked lines, in pixels; used in conjunction with
 * <tt>strokeStyle</tt> to stroke the wedge's border.
 *
 * @type number
 * @name pv.Wedge.prototype.lineWidth
 */

/**
 * The style of stroked lines; used in conjunction with <tt>lineWidth</tt> to
 * stroke the wedge's border. The default value of this property is null,
 * meaning wedges are not stroked by default.
 *
 * @type string
 * @name pv.Wedge.prototype.strokeStyle
 * @see pv.color
 */

/**
 * The wedge fill style; if non-null, the interior of the wedge is filled with
 * the specified color. The default value of this property is a categorical
 * color.
 *
 * @type string
 * @name pv.Wedge.prototype.fillStyle
 * @see pv.color
 */

/**
 * Default properties for wedges. By default, there is no stroke and the fill
 * style is a categorical color.
 *
 * @type pv.Wedge
 */
pv.Wedge.prototype.defaults = new pv.Wedge()
    .extend(pv.Mark.prototype.defaults)
    .startAngle(function() {
        var s = this.sibling();
        return s ? s.endAngle : -Math.PI / 2;
      })
    .innerRadius(0)
    .lineWidth(1.5)
    .strokeStyle(null)
    .fillStyle(pv.Colors.category20().by(pv.index));

/**
 * Returns the mid-radius of the wedge, which is defined as half-way between the
 * inner and outer radii.
 *
 * @see #innerRadius
 * @see #outerRadius
 * @returns {number} the mid-radius, in pixels.
 */
pv.Wedge.prototype.midRadius = function() {
  return (this.innerRadius() + this.outerRadius()) / 2;
};

/**
 * Returns the mid-angle of the wedge, which is defined as half-way between the
 * start and end angles.
 *
 * @see #startAngle
 * @see #endAngle
 * @returns {number} the mid-angle, in radians.
 */
pv.Wedge.prototype.midAngle = function() {
  return (this.startAngle() + this.endAngle()) / 2;
};

/**
 * Constructs a new wedge anchor with default properties. Wedges support five
 * different anchors:<ul>
 *
 * <li>outer
 * <li>inner
 * <li>center
 * <li>start
 * <li>end
 *
 * </ul>In addition to positioning properties (left, right, top bottom), the
 * anchors support text rendering properties (text-align, text-baseline,
 * textAngle). Text is rendered to appear inside the wedge.
 *
 * @param {string} name the anchor name; either a string or a property function.
 * @returns {pv.Anchor}
 */
pv.Wedge.prototype.anchor = function(name) {
  function partial(s) { return s.innerRadius || s.angle < 2 * Math.PI; }
  function midRadius(s) { return (s.innerRadius + s.outerRadius) / 2; }
  function midAngle(s) { return (s.startAngle + s.endAngle) / 2; }
  var scene;
  return pv.Mark.prototype.anchor.call(this, name)
    .def("$wedge.anchor", function() {
        scene = this.scene.target;
      })
    .left(function() {
        var s = scene[this.index];
        if (partial(s)) switch (this.name()) {
          case "outer": return s.left + s.outerRadius * Math.cos(midAngle(s));
          case "inner": return s.left + s.innerRadius * Math.cos(midAngle(s));
          case "start": return s.left + midRadius(s) * Math.cos(s.startAngle);
          case "center": return s.left + midRadius(s) * Math.cos(midAngle(s));
          case "end": return s.left + midRadius(s) * Math.cos(s.endAngle);
        }
        return s.left;
      })
    .top(function() {
        var s = scene[this.index];
        if (partial(s)) switch (this.name()) {
          case "outer": return s.top + s.outerRadius * Math.sin(midAngle(s));
          case "inner": return s.top + s.innerRadius * Math.sin(midAngle(s));
          case "start": return s.top + midRadius(s) * Math.sin(s.startAngle);
          case "center": return s.top + midRadius(s) * Math.sin(midAngle(s));
          case "end": return s.top + midRadius(s) * Math.sin(s.endAngle);
        }
        return s.top;
      })
    .textAlign(function() {
        var s = scene[this.index];
        if (partial(s)) switch (this.name()) {
          case "outer": return pv.Wedge.upright(midAngle(s)) ? "right" : "left";
          case "inner": return pv.Wedge.upright(midAngle(s)) ? "left" : "right";
        }
        return "center";
      })
    .textBaseline(function() {
        var s = scene[this.index];
        if (partial(s)) switch (this.name()) {
          case "start": return pv.Wedge.upright(s.startAngle) ? "top" : "bottom";
          case "end": return pv.Wedge.upright(s.endAngle) ? "bottom" : "top";
        }
        return "middle";
      })
    .textAngle(function() {
        var s = scene[this.index], a = 0;
        if (partial(s)) switch (this.name()) {
          case "center":
          case "inner":
          case "outer": a = midAngle(s); break;
          case "start": a = s.startAngle; break;
          case "end": a = s.endAngle; break;
        }
        return pv.Wedge.upright(a) ? a : (a + Math.PI);
      });
};

/**
 * Returns true if the specified angle is considered "upright", as in, text
 * rendered at that angle would appear upright. If the angle is not upright,
 * text is rotated 180 degrees to be upright, and the text alignment properties
 * are correspondingly changed.
 *
 * @param {number} angle an angle, in radius.
 * @returns {boolean} true if the specified angle is upright.
 */
pv.Wedge.upright = function(angle) {
  angle = angle % (2 * Math.PI);
  angle = (angle < 0) ? (2 * Math.PI + angle) : angle;
  return (angle < Math.PI / 2) || (angle >= 3 * Math.PI / 2);
};

/** @private Sets angle based on endAngle or vice versa. */
pv.Wedge.prototype.buildImplied = function(s) {
  if (s.angle == null) s.angle = s.endAngle - s.startAngle;
  else if (s.endAngle == null) s.endAngle = s.startAngle + s.angle;
  pv.Mark.prototype.buildImplied.call(this, s);
};
/**
 * Abstract; not implemented. There is no explicit constructor; this class
 * merely serves to document the attributes that are used on particles in
 * physics simulations.
 *
 * @class A weighted particle that can participate in a force simulation.
 *
 * @name pv.Particle
 */

/**
 * The next particle in the simulation. Particles form a singly-linked list.
 *
 * @field
 * @type pv.Particle
 * @name pv.Particle.prototype.next
 */

/**
 * The <i>x</i>-position of the particle.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.x
 */

/**
 * The <i>y</i>-position of the particle.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.y
 */

/**
 * The <i>x</i>-velocity of the particle.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.vx
 */

/**
 * The <i>y</i>-velocity of the particle.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.vy
 */

/**
 * The <i>x</i>-position of the particle at -dt.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.px
 */

/**
 * The <i>y</i>-position of the particle at -dt.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.py
 */

/**
 * The <i>x</i>-force on the particle.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.fx
 */

/**
 * The <i>y</i>-force on the particle.
 *
 * @field
 * @type number
 * @name pv.Particle.prototype.fy
 */
/**
 * Constructs a new empty simulation.
 *
 * @param {array} particles
 * @returns {pv.Simulation} a new simulation for the specified particles.
 * @see pv.Simulation
 */
pv.simulation = function(particles) {
  return new pv.Simulation(particles);
};

/**
 * Constructs a new simulation for the specified particles.
 *
 * @class Represents a particle simulation. Particles are massive points in
 * two-dimensional space. Forces can be applied to these particles, causing them
 * to move. Constraints can also be applied to restrict particle movement, for
 * example, constraining particles to a fixed position, or simulating collision
 * between circular particles with area.
 *
 * <p>The simulation uses <a
 * href="http://en.wikipedia.org/wiki/Verlet_integration">Position Verlet</a>
 * integration, due to the ease with which <a
 * href="http://www.teknikus.dk/tj/gdc2001.htm">geometric constraints</a> can be
 * implemented. For each time step, Verlet integration is performed, new forces
 * are accumulated, and then constraints are applied.
 *
 * <p>The simulation makes two simplifying assumptions: all particles are
 * equal-mass, and the time step of the simulation is fixed. It would be easy to
 * incorporate variable-mass particles as a future enhancement. Variable time
 * steps are also possible, but are likely to introduce instability in the
 * simulation.
 *
 * <p>This class can be used directly to simulate particle interaction.
 * Alternatively, for network diagrams, see {@link pv.Layout.Force}.
 *
 * @param {array} particles an array of {@link pv.Particle}s to simulate.
 * @see pv.Layout.Force
 * @see pv.Force
 * @see pv.Constraint
 */
pv.Simulation = function(particles) {
  for (var i = 0; i < particles.length; i++) this.particle(particles[i]);
};

/**
 * The particles in the simulation. Particles are stored as a linked list; this
 * field represents the first particle in the simulation.
 *
 * @field
 * @type pv.Particle
 * @name pv.Simulation.prototype.particles
 */

/**
 * The forces in the simulation. Forces are stored as a linked list; this field
 * represents the first force in the simulation.
 *
 * @field
 * @type pv.Force
 * @name pv.Simulation.prototype.forces
 */

/**
 * The constraints in the simulation. Constraints are stored as a linked list;
 * this field represents the first constraint in the simulation.
 *
 * @field
 * @type pv.Constraint
 * @name pv.Simulation.prototype.constraints
 */

/**
 * Adds the specified particle to the simulation.
 *
 * @param {pv.Particle} p the new particle.
 * @returns {pv.Simulation} this.
 */
pv.Simulation.prototype.particle = function(p) {
  p.next = this.particles;
  /* Default velocities and forces to zero if unset. */
  if (isNaN(p.px)) p.px = p.x;
  if (isNaN(p.py)) p.py = p.y;
  if (isNaN(p.fx)) p.fx = 0;
  if (isNaN(p.fy)) p.fy = 0;
  this.particles = p;
  return this;
};

/**
 * Adds the specified force to the simulation.
 *
 * @param {pv.Force} f the new force.
 * @returns {pv.Simulation} this.
 */
pv.Simulation.prototype.force = function(f) {
  f.next = this.forces;
  this.forces = f;
  return this;
};

/**
 * Adds the specified constraint to the simulation.
 *
 * @param {pv.Constraint} c the new constraint.
 * @returns {pv.Simulation} this.
 */
pv.Simulation.prototype.constraint = function(c) {
  c.next = this.constraints;
  this.constraints = c;
  return this;
};

/**
 * Apply constraints, and then set the velocities to zero.
 *
 * @returns {pv.Simulation} this.
 */
pv.Simulation.prototype.stabilize = function(n) {
  var c;
  if (!arguments.length) n = 3; // TODO use cooling schedule
  for (var i = 0; i < n; i++) {
    var q = new pv.Quadtree(this.particles);
    for (c = this.constraints; c; c = c.next) c.apply(this.particles, q);
  }
  for (var p = this.particles; p; p = p.next) {
    p.px = p.x;
    p.py = p.y;
  }
  return this;
};

/**
 * Advances the simulation one time-step.
 */
pv.Simulation.prototype.step = function() {
  var p, f, c;

  /*
   * Assumptions:
   * - The mass (m) of every particles is 1.
   * - The time step (dt) is 1.
   */

  /* Position Verlet integration. */
  for (p = this.particles; p; p = p.next) {
    var px = p.px, py = p.py;
    p.px = p.x;
    p.py = p.y;
    p.x += p.vx = ((p.x - px) + p.fx);
    p.y += p.vy = ((p.y - py) + p.fy);
  }

  /* Apply constraints, then accumulate new forces. */
  var q = new pv.Quadtree(this.particles);
  for (c = this.constraints; c; c = c.next) c.apply(this.particles, q);
  for (p = this.particles; p; p = p.next) p.fx = p.fy = 0;
  for (f = this.forces; f; f = f.next) f.apply(this.particles, q);
};
/**
 * Constructs a new quadtree for the specified array of particles.
 *
 * @class Represents a quadtree: a two-dimensional recursive spatial
 * subdivision. This particular implementation uses square partitions, dividing
 * each square into four equally-sized squares. Each particle exists in a unique
 * node; if multiple particles are in the same position, some particles may be
 * stored on internal nodes rather than leaf nodes.
 *
 * <p>This quadtree can be used to accelerate various spatial operations, such
 * as the Barnes-Hut approximation for computing n-body forces, or collision
 * detection.
 *
 * @see pv.Force.charge
 * @see pv.Constraint.collision
 * @param {pv.Particle} particles the linked list of particles.
 */
pv.Quadtree = function(particles) {
  var p;

  /* Compute bounds. */
  var x1 = Number.POSITIVE_INFINITY, y1 = x1,
      x2 = Number.NEGATIVE_INFINITY, y2 = x2;
  for (p = particles; p; p = p.next) {
    if (p.x < x1) x1 = p.x;
    if (p.y < y1) y1 = p.y;
    if (p.x > x2) x2 = p.x;
    if (p.y > y2) y2 = p.y;
  }

  /* Squarify the bounds. */
  var dx = x2 - x1, dy = y2 - y1;
  if (dx > dy) y2 = y1 + dx;
  else x2 = x1 + dy;
  this.xMin = x1;
  this.yMin = y1;
  this.xMax = x2;
  this.yMax = y2;

  /**
   * @ignore Recursively inserts the specified particle <i>p</i> at the node
   * <i>n</i> or one of its descendants. The bounds are defined by [<i>x1</i>,
   * <i>x2</i>] and [<i>y1</i>, <i>y2</i>].
   */
  function insert(n, p, x1, y1, x2, y2) {
    if (isNaN(p.x) || isNaN(p.y)) return; // ignore invalid particles
    if (n.leaf) {
      if (n.p) {
        /*
         * If the particle at this leaf node is at the same position as the new
         * particle we are adding, we leave the particle associated with the
         * internal node while adding the new particle to a child node. This
         * avoids infinite recursion.
         */
        if ((Math.abs(n.p.x - p.x) + Math.abs(n.p.y - p.y)) < .01) {
          insertChild(n, p, x1, y1, x2, y2);
        } else {
          var v = n.p;
          n.p = null;
          insertChild(n, v, x1, y1, x2, y2);
          insertChild(n, p, x1, y1, x2, y2);
        }
      } else {
        n.p = p;
      }
    } else {
      insertChild(n, p, x1, y1, x2, y2);
    }
  }

  /**
   * @ignore Recursively inserts the specified particle <i>p</i> into a
   * descendant of node <i>n</i>. The bounds are defined by [<i>x1</i>,
   * <i>x2</i>] and [<i>y1</i>, <i>y2</i>].
   */
  function insertChild(n, p, x1, y1, x2, y2) {
    /* Compute the split point, and the quadrant in which to insert p. */
    var sx = (x1 + x2) * .5,
        sy = (y1 + y2) * .5,
        right = p.x >= sx,
        bottom = p.y >= sy;

    /* Recursively insert into the child node. */
    n.leaf = false;
    switch ((bottom << 1) + right) {
      case 0: n = n.c1 || (n.c1 = new pv.Quadtree.Node()); break;
      case 1: n = n.c2 || (n.c2 = new pv.Quadtree.Node()); break;
      case 2: n = n.c3 || (n.c3 = new pv.Quadtree.Node()); break;
      case 3: n = n.c4 || (n.c4 = new pv.Quadtree.Node()); break;
    }

    /* Update the bounds as we recurse. */
    if (right) x1 = sx; else x2 = sx;
    if (bottom) y1 = sy; else y2 = sy;
    insert(n, p, x1, y1, x2, y2);
  }

  /* Insert all particles. */
  this.root = new pv.Quadtree.Node();
  for (p = particles; p; p = p.next) insert(this.root, p, x1, y1, x2, y2);
};

/**
 * The root node of the quadtree.
 *
 * @type pv.Quadtree.Node
 * @name pv.Quadtree.prototype.root
 */

/**
 * The minimum x-coordinate value of all contained particles.
 *
 * @type number
 * @name pv.Quadtree.prototype.xMin
 */

/**
 * The maximum x-coordinate value of all contained particles.
 *
 * @type number
 * @name pv.Quadtree.prototype.xMax
 */

/**
 * The minimum y-coordinate value of all contained particles.
 *
 * @type number
 * @name pv.Quadtree.prototype.yMin
 */

/**
 * The maximum y-coordinate value of all contained particles.
 *
 * @type number
 * @name pv.Quadtree.prototype.yMax
 */

/**
 * Constructs a new node.
 *
 * @class A node in a quadtree.
 *
 * @see pv.Quadtree
 */
pv.Quadtree.Node = function() {
  /*
   * Prepopulating all attributes significantly increases performance! Also,
   * letting the language interpreter manage garbage collection was moderately
   * faster than creating a cache pool.
   */
  this.leaf = true;
  this.c1 = null;
  this.c2 = null;
  this.c3 = null;
  this.c4 = null;
  this.p = null;
};

/**
 * True if this node is a leaf node; i.e., it has no children. Note that both
 * leaf nodes and non-leaf (internal) nodes may have associated particles. If
 * this is a non-leaf node, then at least one of {@link #c1}, {@link #c2},
 * {@link #c3} or {@link #c4} is guaranteed to be non-null.
 *
 * @type boolean
 * @name pv.Quadtree.Node.prototype.leaf
 */

/**
 * The particle associated with this node, if any.
 *
 * @type pv.Particle
 * @name pv.Quadtree.Node.prototype.p
 */

/**
 * The child node for the second quadrant, if any.
 *
 * @type pv.Quadtree.Node
 * @name pv.Quadtree.Node.prototype.c2
 */

/**
 * The child node for the third quadrant, if any.
 *
 * @type pv.Quadtree.Node
 * @name pv.Quadtree.Node.prototype.c3
 */

/**
 * The child node for the fourth quadrant, if any.
 *
 * @type pv.Quadtree.Node
 * @name pv.Quadtree.Node.prototype.c4
 */
/**
 * Abstract; see an implementing class.
 *
 * @class Represents a force that acts on particles. Note that this interface
 * does not specify how to bind a force to specific particles; in general,
 * forces are applied globally to all particles. However, some forces may be
 * applied to specific particles or between particles, such as spring forces,
 * through additional specialization.
 *
 * @see pv.Simulation
 * @see pv.Particle
 * @see pv.Force.charge
 * @see pv.Force.drag
 * @see pv.Force.spring
 */
pv.Force = {};

/**
 * Applies this force to the specified particles.
 *
 * @function
 * @name pv.Force.prototype.apply
 * @param {pv.Particle} particles particles to which to apply this force.
 * @param {pv.Quadtree} q a quadtree for spatial acceleration.
 */
/**
 * Constructs a new charge force, with an optional charge constant. The charge
 * constant can be negative for repulsion (e.g., particles with electrical
 * charge of equal sign), or positive for attraction (e.g., massive particles
 * with mutual gravity). The default charge constant is -40.
 *
 * @class An n-body force, as defined by Coulomb's law or Newton's law of
 * gravitation, inversely proportional to the square of the distance between
 * particles. Note that the force is independent of the <i>mass</i> of the
 * associated particles, and that the particles do not have charges of varying
 * magnitude; instead, the attraction or repulsion of all particles is globally
 * specified as the charge {@link #constant}.
 *
 * <p>This particular implementation uses the Barnes-Hut algorithm. For details,
 * see <a
 * href="http://www.nature.com/nature/journal/v324/n6096/abs/324446a0.html">"A
 * hierarchical O(N log N) force-calculation algorithm"</a>, J. Barnes &amp;
 * P. Hut, <i>Nature</i> 1986.
 *
 * @name pv.Force.charge
 * @param {number} [k] the charge constant.
 */
pv.Force.charge = function(k) {
  var min = 2, // minimum distance at which to observe forces
      min1 = 1 / min,
      max = 500, // maximum distance at which to observe forces
      max1 = 1 / max,
      theta = .9, // Barnes-Hut theta approximation constant
      force = {};

  if (!arguments.length) k = -40; // default charge constant (repulsion)

  /**
   * Sets or gets the charge constant. If an argument is specified, it is the
   * new charge constant. The charge constant can be negative for repulsion
   * (e.g., particles with electrical charge of equal sign), or positive for
   * attraction (e.g., massive particles with mutual gravity). The default
   * charge constant is -40.
   *
   * @function
   * @name pv.Force.charge.prototype.constant
   * @param {number} x the charge constant.
   * @returns {pv.Force.charge} this.
   */
  force.constant = function(x) {
    if (arguments.length) {
      k = Number(x);
      return force;
    }
    return k;
  };

  /**
   * Sets or gets the domain; specifies the minimum and maximum domain within
   * which charge forces are applied. A minimum distance threshold avoids
   * applying forces that are two strong (due to granularity of the simulation's
   * numeric integration). A maximum distance threshold improves performance by
   * skipping force calculations for particles that are far apart.
   *
   * <p>The default domain is [2, 500].
   *
   * @function
   * @name pv.Force.charge.prototype.domain
   * @param {number} a
   * @param {number} b
   * @returns {pv.Force.charge} this.
   */
  force.domain = function(a, b) {
    if (arguments.length) {
      min = Number(a);
      min1 = 1 / min;
      max = Number(b);
      max1 = 1 / max;
      return force;
    }
    return [min, max];
  };

  /**
   * Sets or gets the Barnes-Hut approximation factor. The Barnes-Hut
   * approximation criterion is the ratio of the size of the quadtree node to
   * the distance from the point to the node's center of mass is beneath some
   * threshold.
   *
   * @function
   * @name pv.Force.charge.prototype.theta
   * @param {number} x the new Barnes-Hut approximation factor.
   * @returns {pv.Force.charge} this.
   */
  force.theta = function(x) {
    if (arguments.length) {
      theta = Number(x);
      return force;
    }
    return theta;
  };

  /**
   * @ignore Recursively computes the center of charge for each node in the
   * quadtree. This is equivalent to the center of mass, assuming that all
   * particles have unit weight.
   */
  function accumulate(n) {
    var cx = 0, cy = 0;
    n.cn = 0;
    function accumulateChild(c) {
      accumulate(c);
      n.cn += c.cn;
      cx += c.cn * c.cx;
      cy += c.cn * c.cy;
    }
    if (!n.leaf) {
      if (n.c1) accumulateChild(n.c1);
      if (n.c2) accumulateChild(n.c2);
      if (n.c3) accumulateChild(n.c3);
      if (n.c4) accumulateChild(n.c4);
    }
    if (n.p) {
      n.cn += k;
      cx += k * n.p.x;
      cy += k * n.p.y;
    }
    n.cx = cx / n.cn;
    n.cy = cy / n.cn;
  }

  /**
   * @ignore Recursively computes forces on the given particle using the given
   * quadtree node. The Barnes-Hut approximation criterion is the ratio of the
   * size of the quadtree node to the distance from the point to the node's
   * center of mass is beneath some threshold.
   */
  function forces(n, p, x1, y1, x2, y2) {
    var dx = n.cx - p.x,
        dy = n.cy - p.y,
        dn = 1 / Math.sqrt(dx * dx + dy * dy);

    /* Barnes-Hut criterion. */
    if ((n.leaf && (n.p != p)) || ((x2 - x1) * dn < theta)) {
      if (dn < max1) return;
      if (dn > min1) dn = min1;
      var kc = n.cn * dn * dn * dn,
          fx = dx * kc,
          fy = dy * kc;
      p.fx += fx;
      p.fy += fy;
    } else if (!n.leaf) {
      var sx = (x1 + x2) * .5, sy = (y1 + y2) * .5;
      if (n.c1) forces(n.c1, p, x1, y1, sx, sy);
      if (n.c2) forces(n.c2, p, sx, y1, x2, sy);
      if (n.c3) forces(n.c3, p, x1, sy, sx, y2);
      if (n.c4) forces(n.c4, p, sx, sy, x2, y2);
      if (dn < max1) return;
      if (dn > min1) dn = min1;
      if (n.p && (n.p != p)) {
        var kc = k * dn * dn * dn,
            fx = dx * kc,
            fy = dy * kc;
        p.fx += fx;
        p.fy += fy;
      }
    }
  }

  /**
   * Applies this force to the specified particles. The force is applied between
   * all pairs of particles within the domain, using the specified quadtree to
   * accelerate n-body force calculation using the Barnes-Hut approximation
   * criterion.
   *
   * @function
   * @name pv.Force.charge.prototype.apply
   * @param {pv.Particle} particles particles to which to apply this force.
   * @param {pv.Quadtree} q a quadtree for spatial acceleration.
   */
  force.apply = function(particles, q) {
    accumulate(q.root);
    for (var p = particles; p; p = p.next) {
      forces(q.root, p, q.xMin, q.yMin, q.xMax, q.yMax);
    }
  };

  return force;
};
/**
 * Constructs a new drag force with the specified constant.
 *
 * @class Implements a drag force, simulating friction. The drag force is
 * applied in the opposite direction of the particle's velocity. Since Position
 * Verlet integration does not track velocities explicitly, the error term with
 * this estimate of velocity is fairly high, so the drag force may be
 * inaccurate.
 *
 * @extends pv.Force
 * @param {number} k the drag constant.
 * @see #constant
 */
pv.Force.drag = function(k) {
  var force = {};

  if (!arguments.length) k = .1; // default drag constant

  /**
   * Sets or gets the drag constant, in the range [0,1]. The default drag
   * constant is 0.1. The drag forces scales linearly with the particle's
   * velocity based on the given drag constant.
   *
   * @function
   * @name pv.Force.drag.prototype.constant
   * @param {number} x the new drag constant.
   * @returns {pv.Force.drag} this, or the current drag constant.
   */
  force.constant = function(x) {
    if (arguments.length) { k = x; return force; }
    return k;
  };

  /**
   * Applies this force to the specified particles.
   *
   * @function
   * @name pv.Force.drag.prototype.apply
   * @param {pv.Particle} particles particles to which to apply this force.
   */
  force.apply = function(particles) {
    if (k) for (var p = particles; p; p = p.next) {
      p.fx -= k * p.vx;
      p.fy -= k * p.vy;
    }
  };

  return force;
};
/**
 * Constructs a new spring force with the specified constant. The links
 * associated with this spring force must be specified before the spring force
 * can be applied.
 *
 * @class Implements a spring force, per Hooke's law. The spring force can be
 * configured with a tension constant, rest length, and damping factor. The
 * tension and damping will automatically be normalized using the inverse square
 * root of the maximum link degree of attached nodes; this makes springs weaker
 * between nodes of high link degree.
 *
 * <p>Unlike other forces (such as charge and drag forces) which may be applied
 * globally, spring forces are only applied between linked particles. Therefore,
 * an array of links must be specified before this force can be applied; the
 * links should be an array of {@link pv.Layout.Network.Link}s. See also
 * {@link pv.Layout.Force} for an example of using spring and charge forces for
 * network layout.
 *
 * @extends pv.Force
 * @param {number} k the spring constant.
 * @see #constant
 * @see #links
 */
pv.Force.spring = function(k) {
  var d = .1, // default damping factor
      l = 20, // default rest length
      links, // links on which to apply spring forces
      kl, // per-spring normalization
      force = {};

  if (!arguments.length) k = .1; // default spring constant (tension)

  /**
   * Sets or gets the links associated with this spring force. Unlike other
   * forces (such as charge and drag forces) which may be applied globally,
   * spring forces are only applied between linked particles. Therefore, an
   * array of links must be specified before this force can be applied; the
   * links should be an array of {@link pv.Layout.Network.Link}s.
   *
   * @function
   * @name pv.Force.spring.prototype.links
   * @param {array} x the new array of links.
   * @returns {pv.Force.spring} this, or the current array of links.
   */
  force.links = function(x) {
    if (arguments.length) {
      links = x;
      kl = x.map(function(l) {
          return 1 / Math.sqrt(Math.max(
              l.sourceNode.linkDegree,
              l.targetNode.linkDegree));
        });
      return force;
    }
    return links;
  };

  /**
   * Sets or gets the spring constant. The default value is 0.1; greater values
   * will result in stronger tension. The spring tension is automatically
   * normalized using the inverse square root of the maximum link degree of
   * attached nodes.
   *
   * @function
   * @name pv.Force.spring.prototype.constant
   * @param {number} x the new spring constant.
   * @returns {pv.Force.spring} this, or the current spring constant.
   */
  force.constant = function(x) {
    if (arguments.length) {
      k = Number(x);
      return force;
    }
    return k;
  };

  /**
   * The spring damping factor, in the range [0,1]. Damping functions
   * identically to drag forces, damping spring bounciness by applying a force
   * in the opposite direction of attached nodes' velocities. The default value
   * is 0.1. The spring damping is automatically normalized using the inverse
   * square root of the maximum link degree of attached nodes.
   *
   * @function
   * @name pv.Force.spring.prototype.damping
   * @param {number} x the new spring damping factor.
   * @returns {pv.Force.spring} this, or the current spring damping factor.
   */
  force.damping = function(x) {
    if (arguments.length) {
      d = Number(x);
      return force;
    }
    return d;
  };

  /**
   * The spring rest length. The default value is 20 pixels.
   *
   * @function
   * @name pv.Force.spring.prototype.length
   * @param {number} x the new spring rest length.
   * @returns {pv.Force.spring} this, or the current spring rest length.
   */
  force.length = function(x) {
    if (arguments.length) {
      l = Number(x);
      return force;
    }
    return l;
  };

  /**
   * Applies this force to the specified particles.
   *
   * @function
   * @name pv.Force.spring.prototype.apply
   * @param {pv.Particle} particles particles to which to apply this force.
   */
  force.apply = function(particles) {
    for (var i = 0; i < links.length; i++) {
      var a = links[i].sourceNode,
          b = links[i].targetNode,
          dx = a.x - b.x,
          dy = a.y - b.y,
          dn = Math.sqrt(dx * dx + dy * dy),
          dd = dn ? (1 / dn) : 1,
          ks = k * kl[i], // normalized tension
          kd = d * kl[i], // normalized damping
          kk = (ks * (dn - l) + kd * (dx * (a.vx - b.vx) + dy * (a.vy - b.vy)) * dd) * dd,
          fx = -kk * (dn ? dx : (.01 * (.5 - Math.random()))),
          fy = -kk * (dn ? dy : (.01 * (.5 - Math.random())));
      a.fx += fx;
      a.fy += fy;
      b.fx -= fx;
      b.fy -= fy;
    }
  };

  return force;
};
/**
 * Abstract; see an implementing class.
 *
 * @class Represents a constraint that acts on particles. Note that this
 * interface does not specify how to bind a constraint to specific particles; in
 * general, constraints are applied globally to all particles. However, some
 * constraints may be applied to specific particles or between particles, such
 * as position constraints, through additional specialization.
 *
 * @see pv.Simulation
 * @see pv.Particle
 * @see pv.Constraint.bound
 * @see pv.Constraint.collision
 * @see pv.Constraint.position
 */
pv.Constraint = {};

/**
 * Applies this constraint to the specified particles.
 *
 * @function
 * @name pv.Constraint.prototype.apply
 * @param {pv.Particle} particles particles to which to apply this constraint.
 * @param {pv.Quadtree} q a quadtree for spatial acceleration.
 * @returns {pv.Constraint} this.
 */
/**
 * Constructs a new collision constraint. The default search radius is 10, and
 * the default repeat count is 1. A radius function must be specified to compute
 * the radius of particles.
 *
 * @class Constraints circles to avoid overlap. Each particle is treated as a
 * circle, with the radius of the particle computed using a specified function.
 * For example, if the particle has an <tt>r</tt> attribute storing the radius,
 * the radius <tt>function(d) d.r</tt> specifies a collision constraint using
 * this radius. The radius function is passed each {@link pv.Particle} as the
 * first argument.
 *
 * <p>To accelerate collision detection, this implementation uses a quadtree and
 * a search radius. The search radius is computed as the maximum radius of all
 * particles in the simulation.
 *
 * @see pv.Constraint
 * @param {function} radius the radius function.
 */
pv.Constraint.collision = function(radius) {
  var n = 1, // number of times to repeat the constraint
      r1,
      px1,
      py1,
      px2,
      py2,
      constraint = {};

  if (!arguments.length) r1 = 10; // default search radius

  /**
   * Sets or gets the repeat count. If the repeat count is greater than 1, the
   * constraint will be applied repeatedly; this is a form of the Gauss-Seidel
   * method for constraints relaxation. Repeating the collision constraint makes
   * the constraint have more of an effect when there is a potential for many
   * co-occurring collisions.
   *
   * @function
   * @name pv.Constraint.collision.prototype.repeat
   * @param {number} x the number of times to repeat this constraint.
   * @returns {pv.Constraint.collision} this.
   */
  constraint.repeat = function(x) {
    if (arguments.length) {
      n = Number(x);
      return constraint;
    }
    return n;
  };

  /** @private */
  function constrain(n, p, x1, y1, x2, y2) {
    if (!n.leaf) {
      var sx = (x1 + x2) * .5,
          sy = (y1 + y2) * .5,
          top = sy > py1,
          bottom = sy < py2,
          left = sx > px1,
          right = sx < px2;
      if (top) {
        if (n.c1 && left) constrain(n.c1, p, x1, y1, sx, sy);
        if (n.c2 && right) constrain(n.c2, p, sx, y1, x2, sy);
      }
      if (bottom) {
        if (n.c3 && left) constrain(n.c3, p, x1, sy, sx, y2);
        if (n.c4 && right) constrain(n.c4, p, sx, sy, x2, y2);
      }
    }
    if (n.p && (n.p != p)) {
      var dx = p.x - n.p.x,
          dy = p.y - n.p.y,
          l = Math.sqrt(dx * dx + dy * dy),
          d = r1 + radius(n.p);
      if (l < d) {
        var k = (l - d) / l * .5;
        dx *= k;
        dy *= k;
        p.x -= dx;
        p.y -= dy;
        n.p.x += dx;
        n.p.y += dy;
      }
    }
  }

  /**
   * Applies this constraint to the specified particles.
   *
   * @function
   * @name pv.Constraint.collision.prototype.apply
   * @param {pv.Particle} particles particles to which to apply this constraint.
   * @param {pv.Quadtree} q a quadtree for spatial acceleration.
   */
  constraint.apply = function(particles, q) {
    var p, r, max = -Infinity;
    for (p = particles; p; p = p.next) {
      r = radius(p);
      if (r > max) max = r;
    }
    for (var i = 0; i < n; i++) {
      for (p = particles; p; p = p.next) {
        r = (r1 = radius(p)) + max;
        px1 = p.x - r;
        px2 = p.x + r;
        py1 = p.y - r;
        py2 = p.y + r;
        constrain(q.root, p, q.xMin, q.yMin, q.xMax, q.yMax);
      }
    }
  };

  return constraint;
};
/**
 * Constructs a default position constraint using the <tt>fix</tt> attribute.
 * An optional position function can be specified to determine how the fixed
 * position per-particle is determined.
 *
 * @class Constraints particles to a fixed position. The fixed position per
 * particle is determined using a given position function, which defaults to
 * <tt>function(d) d.fix</tt>.
 *
 * <p>If the position function returns null, then no position constraint is
 * applied to the given particle. Otherwise, the particle's position is set to
 * the returned position, as expressed by a {@link pv.Vector}. (Note: the
 * position does not need to be an instance of <tt>pv.Vector</tt>, but simply an
 * object with <tt>x</tt> and <tt>y</tt> attributes.)
 *
 * <p>This constraint also supports a configurable alpha parameter, which
 * defaults to 1. If the alpha parameter is in the range [0,1], then rather than
 * setting the particle's new position directly to the position returned by the
 * supplied position function, the particle's position is interpolated towards
 * the fixed position. This results is a smooth (exponential) drift towards the
 * fixed position, which can increase the stability of the physics simulation.
 * In addition, the alpha parameter can be decayed over time, relaxing the
 * position constraint, which helps to stabilize on an optimal solution.
 *
 * @param {function} [f] the position function.
 */
pv.Constraint.position = function(f) {
  var a = 1, // default alpha
      constraint = {};

  if (!arguments.length) /** @ignore */ f = function(p) { return p.fix; };

  /**
   * Sets or gets the alpha parameter for position interpolation. If the alpha
   * parameter is in the range [0,1], then rather than setting the particle's
   * new position directly to the position returned by the supplied position
   * function, the particle's position is interpolated towards the fixed
   * position.
   *
   * @function
   * @name pv.Constraint.position.prototype.alpha
   * @param {number} x the new alpha parameter, in the range [0,1].
   * @returns {pv.Constraint.position} this.
   */
  constraint.alpha = function(x) {
    if (arguments.length) {
      a = Number(x);
      return constraint;
    }
    return a;
  };

  /**
   * Applies this constraint to the specified particles.
   *
   * @function
   * @name pv.Constraint.position.prototype.apply
   * @param {pv.Particle} particles particles to which to apply this constraint.
   */
  constraint.apply = function(particles) {
    for (var p = particles; p; p = p.next) {
      var v = f(p);
      if (v) {
        p.x += (v.x - p.x) * a;
        p.y += (v.y - p.y) * a;
        p.fx = p.fy = p.vx = p.vy = 0;
      }
    }
  };

  return constraint;
};
/**
 * Constructs a new bound constraint. Before the constraint can be used, the
 * {@link #x} and {@link #y} methods must be call to specify the bounds.
 *
 * @class Constrains particles to within fixed rectangular bounds. For example,
 * this constraint can be used to constrain particles in a physics simulation
 * within the bounds of an enclosing panel.
 *
 * <p>Note that the current implementation treats particles as points, with no
 * area. If the particles are rendered as dots, be sure to include some
 * additional padding to inset the bounds such that the edges of the dots do not
 * get clipped by the panel bounds. If the particles have different radii, this
 * constraint would need to be extended using a radius function, similar to
 * {@link pv.Constraint.collision}.
 *
 * @see pv.Layout.Force
 * @extends pv.Constraint
 */
pv.Constraint.bound = function() {
  var constraint = {},
      x,
      y;

  /**
   * Sets or gets the bounds on the x-coordinate.
   *
   * @function
   * @name pv.Constraint.bound.prototype.x
   * @param {number} min the minimum allowed x-coordinate.
   * @param {number} max the maximum allowed x-coordinate.
   * @returns {pv.Constraint.bound} this.
   */
  constraint.x = function(min, max) {
    if (arguments.length) {
      x = {min: Math.min(min, max), max: Math.max(min, max)};
      return this;
    }
    return x;
  };

  /**
   * Sets or gets the bounds on the y-coordinate.
   *
   * @function
   * @name pv.Constraint.bound.prototype.y
   * @param {number} min the minimum allowed y-coordinate.
   * @param {number} max the maximum allowed y-coordinate.
   * @returns {pv.Constraint.bound} this.
   */
  constraint.y = function(min, max) {
    if (arguments.length) {
      y = {min: Math.min(min, max), max: Math.max(min, max)};
      return this;
    }
    return y;
  };

  /**
   * Applies this constraint to the specified particles.
   *
   * @function
   * @name pv.Constraint.bound.prototype.apply
   * @param {pv.Particle} particles particles to which to apply this constraint.
   */
  constraint.apply = function(particles) {
    if (x) for (var p = particles; p; p = p.next) {
      p.x = p.x < x.min ? x.min : (p.x > x.max ? x.max : p.x);
    }
    if (y) for (var p = particles; p; p = p.next) {
      p.y = p.y < y.min ? y.min : (p.y > y.max ? y.max : p.y);
    }
  };

  return constraint;
};
/**
 * Constructs a new, empty layout with default properties. Layouts are not
 * typically constructed directly; instead, a concrete subclass is added to an
 * existing panel via {@link pv.Mark#add}.
 *
 * @class Represents an abstract layout, encapsulating a visualization technique
 * such as a streamgraph or treemap. Layouts are themselves containers,
 * extending from {@link pv.Panel}, and defining a set of mark prototypes as
 * children. These mark prototypes provide default properties that together
 * implement the given visualization technique.
 *
 * <p>Layouts do not initially contain any marks; any exported marks (such as a
 * network layout's <tt>link</tt> and <tt>node</tt>) are intended to be used as
 * prototypes. By adding a concrete mark, such as a {@link pv.Bar}, to the
 * appropriate mark prototype, the mark is added to the layout and inherits the
 * given properties. This approach allows further customization of the layout,
 * either by choosing a different mark type to add, or more simply by overriding
 * some of the layout's defined properties.
 *
 * <p>Each concrete layout, such as treemap or circle-packing, has different
 * behavior and may export different mark prototypes, depending on what marks
 * are typically needed to render the desired visualization. Therefore it is
 * important to understand how each layout is structured, such that the provided
 * mark prototypes are used appropriately.
 *
 * <p>In addition to the mark prototypes, layouts may define custom properties
 * that affect the overall behavior of the layout. For example, a treemap layout
 * might use a property to specify which layout algorithm to use. These
 * properties are just like other mark properties, and can be defined as
 * constants or as functions. As with panels, the data property can be used to
 * replicate layouts, and properties can be defined to in terms of layout data.
 *
 * @extends pv.Panel
 */
pv.Layout = function() {
  pv.Panel.call(this);
};

pv.Layout.prototype = pv.extend(pv.Panel);

/**
 * @private Defines a local property with the specified name and cast. Note that
 * although the property method is only defined locally, the cast function is
 * global, which is necessary since properties are inherited!
 *
 * @param {string} name the property name.
 * @param {function} [cast] the cast function for this property.
 */
pv.Layout.prototype.property = function(name, cast) {
  if (!this.hasOwnProperty("properties")) {
    this.properties = pv.extend(this.properties);
  }
  this.properties[name] = true;
  this.propertyMethod(name, false, pv.Mark.cast[name] = cast);
  return this;
};
/**
 * Constructs a new, empty network layout. Layouts are not typically constructed
 * directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Represents an abstract layout for network diagrams. This class
 * provides the basic structure for both node-link diagrams (such as
 * force-directed graph layout) and space-filling network diagrams (such as
 * sunbursts and treemaps). Note that "network" here is a general term that
 * includes hierarchical structures; a tree is represented using links from
 * child to parent.
 *
 * <p>Network layouts require the graph data structure to be defined using two
 * properties:<ul>
 *
 * <li><tt>nodes</tt> - an array of objects representing nodes. Objects in this
 * array must conform to the {@link pv.Layout.Network.Node} interface; which is
 * to say, be careful to avoid naming collisions with automatic attributes such
 * as <tt>index</tt> and <tt>linkDegree</tt>. If the nodes property is defined
 * as an array of primitives, such as numbers or strings, these primitives are
 * automatically wrapped in an object; the resulting object's <tt>nodeValue</tt>
 * attribute points to the original primitive value.
 *
 * <p><li><tt>links</tt> - an array of objects representing links. Objects in
 * this array must conform to the {@link pv.Layout.Network.Link} interface; at a
 * minimum, either <tt>source</tt> and <tt>target</tt> indexes or
 * <tt>sourceNode</tt> and <tt>targetNode</tt> references must be set. Note that
 * if the links property is defined after the nodes property, the links can be
 * defined in terms of <tt>this.nodes()</tt>.
 *
 * </ul>
 *
 * <p>Three standard mark prototypes are provided:<ul>
 *
 * <li><tt>node</tt> - for rendering nodes; typically a {@link pv.Dot}. The node
 * mark is added directly to the layout, with the data property defined via the
 * layout's <tt>nodes</tt> property. Properties such as <tt>strokeStyle</tt> and
 * <tt>fillStyle</tt> can be overridden to compute properties from node data
 * dynamically.
 *
 * <p><li><tt>link</tt> - for rendering links; typically a {@link pv.Line}. The
 * link mark is added to a child panel, whose data property is defined as
 * layout's <tt>links</tt> property. The link's data property is then a
 * two-element array of the source node and target node. Thus, poperties such as
 * <tt>strokeStyle</tt> and <tt>fillStyle</tt> can be overridden to compute
 * properties from either the node data (the first argument) or the link data
 * (the second argument; the parent panel data) dynamically.
 *
 * <p><li><tt>label</tt> - for rendering node labels; typically a
 * {@link pv.Label}. The label mark is added directly to the layout, with the
 * data property defined via the layout's <tt>nodes</tt> property. Properties
 * such as <tt>strokeStyle</tt> and <tt>fillStyle</tt> can be overridden to
 * compute properties from node data dynamically.
 *
 * </ul>Note that some network implementations may not support all three
 * standard mark prototypes; for example, space-filling hierarchical layouts
 * typically do not use a <tt>link</tt> prototype, as the parent-child links are
 * implied by the structure of the space-filling <tt>node</tt> marks.  Check the
 * specific network layout for implementation details.
 *
 * <p>Network layout properties, including <tt>nodes</tt> and <tt>links</tt>,
 * are typically cached rather than re-evaluated with every call to render. This
 * is a performance optimization, as network layout algorithms can be
 * expensive. If the network structure changes, call {@link #reset} to clear the
 * cache before rendering. Note that although the network layout properties are
 * cached, child mark properties, such as the marks used to render the nodes and
 * links, <i>are not</i>. Therefore, non-structural changes to the network
 * layout, such as changing the color of a mark on mouseover, do not need to
 * reset the layout.
 *
 * @see pv.Layout.Hierarchy
 * @see pv.Layout.Force
 * @see pv.Layout.Matrix
 * @see pv.Layout.Arc
 * @see pv.Layout.Rollup
 * @extends pv.Layout
 */
pv.Layout.Network = function() {
  pv.Layout.call(this);
  var that = this;

  /* @private Version tracking to cache layout state, improving performance. */
  this.$id = pv.id();

  /**
   * The node prototype. This prototype is intended to be used with a Dot mark
   * in conjunction with the link prototype.
   *
   * @type pv.Mark
   * @name pv.Layout.Network.prototype.node
   */
  (this.node = new pv.Mark()
      .data(function() { return that.nodes(); })
      .strokeStyle("#1f77b4")
      .fillStyle("#fff")
      .left(function(n) { return n.x; })
      .top(function(n) { return n.y; })).parent = this;

  /**
   * The link prototype, which renders edges between source nodes and target
   * nodes. This prototype is intended to be used with a Line mark in
   * conjunction with the node prototype.
   *
   * @type pv.Mark
   * @name pv.Layout.Network.prototype.link
   */
  this.link = new pv.Mark()
      .extend(this.node)
      .data(function(p) { return [p.sourceNode, p.targetNode]; })
      .fillStyle(null)
      .lineWidth(function(d, p) { return p.linkValue * 1.5; })
      .strokeStyle("rgba(0,0,0,.2)");

  this.link.add = function(type) {
    return that.add(pv.Panel)
        .data(function() { return that.links(); })
      .add(type)
        .extend(this);
  };

  /**
   * The node label prototype, which renders the node name adjacent to the node.
   * This prototype is provided as an alternative to using the anchor on the
   * node mark; it is primarily intended to be used with radial node-link
   * layouts, since it provides a convenient mechanism to set the text angle.
   *
   * @type pv.Mark
   * @name pv.Layout.Network.prototype.label
   */
  (this.label = new pv.Mark()
      .extend(this.node)
      .textMargin(7)
      .textBaseline("middle")
      .text(function(n) { return n.nodeName || n.nodeValue; })
      .textAngle(function(n) {
          var a = n.midAngle;
          return pv.Wedge.upright(a) ? a : (a + Math.PI);
        })
      .textAlign(function(n) {
          return pv.Wedge.upright(n.midAngle) ? "left" : "right";
        })).parent = this;
};

/**
 * @class Represents a node in a network layout. There is no explicit
 * constructor; this class merely serves to document the attributes that are
 * used on nodes in network layouts. (Note that hierarchical nodes place
 * additional requirements on node representation, vis {@link pv.Dom.Node}.)
 *
 * @see pv.Layout.Network
 * @name pv.Layout.Network.Node
 */

/**
 * The node index, zero-based. This attribute is populated automatically based
 * on the index in the array returned by the <tt>nodes</tt> property.
 *
 * @type number
 * @name pv.Layout.Network.Node.prototype.index
 */

/**
 * The link degree; the sum of link values for all incoming and outgoing links.
 * This attribute is populated automatically.
 *
 * @type number
 * @name pv.Layout.Network.Node.prototype.linkDegree
 */

/**
 * The node name; optional. If present, this attribute will be used to provide
 * the text for node labels. If not present, the label text will fallback to the
 * <tt>nodeValue</tt> attribute.
 *
 * @type string
 * @name pv.Layout.Network.Node.prototype.nodeName
 */

/**
 * The node value; optional. If present, and no <tt>nodeName</tt> attribute is
 * present, the node value will be used as the label text. This attribute is
 * also automatically populated if the nodes are specified as an array of
 * primitives, such as strings or numbers.
 *
 * @type object
 * @name pv.Layout.Network.Node.prototype.nodeValue
 */

/**
 * @class Represents a link in a network layout. There is no explicit
 * constructor; this class merely serves to document the attributes that are
 * used on links in network layouts. For hierarchical layouts, this class is
 * used to represent the parent-child links.
 *
 * @see pv.Layout.Network
 * @name pv.Layout.Network.Link
 */

/**
 * The link value, or weight; optional. If not specified (or not a number), the
 * default value of 1 is used.
 *
 * @type number
 * @name pv.Layout.Network.Link.prototype.linkValue
 */

/**
 * The link's source node. If not set, this value will be derived from the
 * <tt>source</tt> attribute index.
 *
 * @type pv.Layout.Network.Node
 * @name pv.Layout.Network.Link.prototype.sourceNode
 */

/**
 * The link's target node. If not set, this value will be derived from the
 * <tt>target</tt> attribute index.
 *
 * @type pv.Layout.Network.Node
 * @name pv.Layout.Network.Link.prototype.targetNode
 */

/**
 * Alias for <tt>sourceNode</tt>, as expressed by the index of the source node.
 * This attribute is not populated automatically, but may be used as a more
 * convenient identification of the link's source, for example in a static JSON
 * representation.
 *
 * @type number
 * @name pv.Layout.Network.Link.prototype.source
 */

/**
 * Alias for <tt>targetNode</tt>, as expressed by the index of the target node.
 * This attribute is not populated automatically, but may be used as a more
 * convenient identification of the link's target, for example in a static JSON
 * representation.
 *
 * @type number
 * @name pv.Layout.Network.Link.prototype.target
 */

/**
 * Alias for <tt>linkValue</tt>. This attribute is not populated automatically,
 * but may be used instead of the <tt>linkValue</tt> attribute when specifying
 * links.
 *
 * @type number
 * @name pv.Layout.Network.Link.prototype.value
 */

/** @private Transform nodes and links on cast. */
pv.Layout.Network.prototype = pv.extend(pv.Layout)
    .property("nodes", function(v) {
        return v.map(function(d, i) {
            if (typeof d != "object") d = {nodeValue: d};
            d.index = i;
            d.linkDegree = 0;
            return d;
          });
      })
    .property("links", function(v) {
        return v.map(function(d) {
            if (isNaN(d.linkValue)) d.linkValue = isNaN(d.value) ? 1 : d.value;
            return d;
          });
      });

/**
 * Resets the cache, such that changes to layout property definitions will be
 * visible on subsequent render. Unlike normal marks (and normal layouts),
 * properties associated with network layouts are not automatically re-evaluated
 * on render; the properties are cached, and any expensive layout algorithms are
 * only run after the layout is explicitly reset.
 *
 * @returns {pv.Layout.Network} this.
 */
pv.Layout.Network.prototype.reset = function() {
  this.$id = pv.id();
  return this;
};

/** @private Skip evaluating properties if cached. */
pv.Layout.Network.prototype.buildProperties = function(s, properties) {
  if ((s.$id || 0) < this.$id) {
    pv.Layout.prototype.buildProperties.call(this, s, properties);
  }
};

/** @private Compute link degrees; map source and target indexes to nodes. */
pv.Layout.Network.prototype.buildImplied = function(s) {
  pv.Layout.prototype.buildImplied.call(this, s);
  if (s.$id >= this.$id) return true;
  s.$id = this.$id;
  s.links.forEach(function(d) {
      var v = d.linkValue;
      (d.sourceNode || (d.sourceNode = s.nodes[d.source])).linkDegree += v;
      (d.targetNode || (d.targetNode = s.nodes[d.target])).linkDegree += v;
    });
};
/**
 * Constructs a new, empty hierarchy layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Represents an abstract layout for hierarchy diagrams. This class is a
 * specialization of {@link pv.Layout.Network}, providing the basic structure
 * for both hierarchical node-link diagrams (such as Reingold-Tilford trees) and
 * space-filling hierarchy diagrams (such as sunbursts and treemaps).
 *
 * <p>Unlike general network layouts, the <tt>links</tt> property need not be
 * defined explicitly. Instead, the links are computed implicitly from the
 * <tt>parentNode</tt> attribute of the node objects, as defined by the
 * <tt>nodes</tt> property. This implementation is also available as
 * {@link #links}, for reuse with non-hierarchical layouts; for example, to
 * render a tree using force-directed layout.
 *
 * <p>Correspondingly, the <tt>nodes</tt> property is represented as a union of
 * {@link pv.Layout.Network.Node} and {@link pv.Dom.Node}. To construct a node
 * hierarchy from a simple JSON map, use the {@link pv.Dom} operator; this
 * operator also provides an easy way to sort nodes before passing them to the
 * layout.
 *
 * <p>For more details on how to use this layout, see
 * {@link pv.Layout.Network}.
 *
 * @see pv.Layout.Cluster
 * @see pv.Layout.Partition
 * @see pv.Layout.Tree
 * @see pv.Layout.Treemap
 * @see pv.Layout.Indent
 * @see pv.Layout.Pack
 * @extends pv.Layout.Network
 */
pv.Layout.Hierarchy = function() {
  pv.Layout.Network.call(this);
  this.link.strokeStyle("#ccc");
};

pv.Layout.Hierarchy.prototype = pv.extend(pv.Layout.Network);

/** @private Compute the implied links. (Links are null by default.) */
pv.Layout.Hierarchy.prototype.buildImplied = function(s) {
  if (!s.links) s.links = pv.Layout.Hierarchy.links.call(this);
  pv.Layout.Network.prototype.buildImplied.call(this, s);
};

/** The implied links; computes links using the <tt>parentNode</tt> attribute. */
pv.Layout.Hierarchy.links = function() {
  return this.nodes()
      .filter(function(n) { return n.parentNode; })
      .map(function(n) {
          return {
              sourceNode: n,
              targetNode: n.parentNode,
              linkValue: 1
            };
      });
};

/** @private Provides standard node-link layout based on breadth & depth. */
pv.Layout.Hierarchy.NodeLink = {

  /** @private */
  buildImplied: function(s) {
    var nodes = s.nodes,
        orient = s.orient,
        horizontal = /^(top|bottom)$/.test(orient),
        w = s.width,
        h = s.height;

    /* Compute default inner and outer radius. */
    if (orient == "radial") {
      var ir = s.innerRadius, or = s.outerRadius;
      if (ir == null) ir = 0;
      if (or == null) or = Math.min(w, h) / 2;
    }

    /** @private Returns the radius of the given node. */
    function radius(n) {
      return n.parentNode ? (n.depth * (or - ir) + ir) : 0;
    }

    /** @private Returns the angle of the given node. */
    function midAngle(n) {
      return (n.parentNode ? (n.breadth - .25) * 2 * Math.PI : 0);
    }

    /** @private */
    function x(n) {
      switch (orient) {
        case "left": return n.depth * w;
        case "right": return w - n.depth * w;
        case "top": return n.breadth * w;
        case "bottom": return w - n.breadth * w;
        case "radial": return w / 2 + radius(n) * Math.cos(n.midAngle);
      }
    }

    /** @private */
    function y(n) {
      switch (orient) {
        case "left": return n.breadth * h;
        case "right": return h - n.breadth * h;
        case "top": return n.depth * h;
        case "bottom": return h - n.depth * h;
        case "radial": return h / 2 + radius(n) * Math.sin(n.midAngle);
      }
    }

    for (var i = 0; i < nodes.length; i++) {
      var n = nodes[i];
      n.midAngle = orient == "radial" ? midAngle(n)
          : horizontal ? Math.PI / 2 : 0;
      n.x = x(n);
      n.y = y(n);
      if (n.firstChild) n.midAngle += Math.PI;
    }
  }
};

/** @private Provides standard space-filling layout based on breadth & depth. */
pv.Layout.Hierarchy.Fill = {

  /** @private */
  constructor: function() {
    this.node
        .strokeStyle("#fff")
        .fillStyle("#ccc")
        .width(function(n) { return n.dx; })
        .height(function(n) { return n.dy; })
        .innerRadius(function(n) { return n.innerRadius; })
        .outerRadius(function(n) { return n.outerRadius; })
        .startAngle(function(n) { return n.startAngle; })
        .angle(function(n) { return n.angle; });

    this.label
        .textAlign("center")
        .left(function(n) { return n.x + (n.dx / 2); })
        .top(function(n) { return n.y + (n.dy / 2); });

    /* Hide unsupported link. */
    delete this.link;
  },

  /** @private */
  buildImplied: function(s) {
    var nodes = s.nodes,
        orient = s.orient,
        horizontal = /^(top|bottom)$/.test(orient),
        w = s.width,
        h = s.height,
        depth = -nodes[0].minDepth;

    /* Compute default inner and outer radius. */
    if (orient == "radial") {
      var ir = s.innerRadius, or = s.outerRadius;
      if (ir == null) ir = 0;
      if (ir) depth *= 2; // use full depth step for root
      if (or == null) or = Math.min(w, h) / 2;
    }

    /** @private Scales the specified depth for a space-filling layout. */
    function scale(d, depth) {
      return (d + depth) / (1 + depth);
    }

    /** @private */
    function x(n) {
      switch (orient) {
        case "left": return scale(n.minDepth, depth) * w;
        case "right": return (1 - scale(n.maxDepth, depth)) * w;
        case "top": return n.minBreadth * w;
        case "bottom": return (1 - n.maxBreadth) * w;
        case "radial": return w / 2;
      }
    }

    /** @private */
    function y(n) {
      switch (orient) {
        case "left": return n.minBreadth * h;
        case "right": return (1 - n.maxBreadth) * h;
        case "top": return scale(n.minDepth, depth) * h;
        case "bottom": return (1 - scale(n.maxDepth, depth)) * h;
        case "radial": return h / 2;
      }
    }

    /** @private */
    function dx(n) {
      switch (orient) {
        case "left":
        case "right": return (n.maxDepth - n.minDepth) / (1 + depth) * w;
        case "top":
        case "bottom": return (n.maxBreadth - n.minBreadth) * w;
        case "radial": return n.parentNode ? (n.innerRadius + n.outerRadius) * Math.cos(n.midAngle) : 0;
      }
    }

    /** @private */
    function dy(n) {
      switch (orient) {
        case "left":
        case "right": return (n.maxBreadth - n.minBreadth) * h;
        case "top":
        case "bottom": return (n.maxDepth - n.minDepth) / (1 + depth) * h;
        case "radial": return n.parentNode ? (n.innerRadius + n.outerRadius) * Math.sin(n.midAngle) : 0;
      }
    }

    /** @private */
    function innerRadius(n) {
      return Math.max(0, scale(n.minDepth, depth / 2)) * (or - ir) + ir;
    }

    /** @private */
    function outerRadius(n) {
      return scale(n.maxDepth, depth / 2) * (or - ir) + ir;
    }

    /** @private */
    function startAngle(n) {
      return (n.parentNode ? n.minBreadth - .25 : 0) * 2 * Math.PI;
    }

    /** @private */
    function angle(n) {
      return (n.parentNode ? n.maxBreadth - n.minBreadth : 1) * 2 * Math.PI;
    }

    for (var i = 0; i < nodes.length; i++) {
      var n = nodes[i];
      n.x = x(n);
      n.y = y(n);
      if (orient == "radial") {
        n.innerRadius = innerRadius(n);
        n.outerRadius = outerRadius(n);
        n.startAngle = startAngle(n);
        n.angle = angle(n);
        n.midAngle = n.startAngle + n.angle / 2;
      } else {
        n.midAngle = horizontal ? -Math.PI / 2 : 0;
      }
      n.dx = dx(n);
      n.dy = dy(n);
    }
  }
};
/**
 * Constructs a new, empty grid layout. Layouts are not typically constructed
 * directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a grid layout with regularly-sized rows and columns. The
 * number of rows and columns are determined from their respective
 * properties. For example, the 2&times;3 array:
 *
 * <pre>1 2 3
 * 4 5 6</pre>
 *
 * can be represented using the <tt>rows</tt> property as:
 *
 * <pre>[[1, 2, 3], [4, 5, 6]]</pre>
 *
 * If your data is in column-major order, you can equivalently use the
 * <tt>columns</tt> property. If the <tt>rows</tt> property is an array, it
 * takes priority over the <tt>columns</tt> property. The data is implicitly
 * transposed, as if the {@link pv.transpose} operator were applied.
 *
 * <p>This layout exports a single <tt>cell</tt> mark prototype, which is
 * intended to be used with a bar, panel, layout, or subclass thereof. The data
 * property of the cell prototype is defined as the elements in the array. For
 * example, if the array is a two-dimensional array of values in the range
 * [0,1], a simple heatmap can be generated as:
 *
 * <pre>vis.add(pv.Layout.Grid)
 *     .rows(arrays)
 *   .cell.add(pv.Bar)
 *     .fillStyle(pv.ramp("white", "black"))</pre>
 *
 * The grid subdivides the full width and height of the parent panel into equal
 * rectangles. Note, however, that for large, interactive, or animated heatmaps,
 * you may see significantly better performance through dynamic {@link pv.Image}
 * generation.
 *
 * <p>For irregular grids using value-based spatial partitioning, see {@link
 * pv.Layout.Treemap}.
 *
 * @extends pv.Layout
 */
pv.Layout.Grid = function() {
  pv.Layout.call(this);
  var that = this;

  /**
   * The cell prototype. This prototype is intended to be used with a bar,
   * panel, or layout (or subclass thereof) to render the grid cells.
   *
   * @type pv.Mark
   * @name pv.Layout.Grid.prototype.cell
   */
  (this.cell = new pv.Mark()
      .data(function() {
          return that.scene[that.index].$grid;
        })
      .width(function() {
          return that.width() / that.cols();
        })
      .height(function() {
          return that.height() / that.rows();
        })
      .left(function() {
          return this.width() * (this.index % that.cols());
        })
      .top(function() {
          return this.height() * Math.floor(this.index / that.cols());
        })).parent = this;
};

pv.Layout.Grid.prototype = pv.extend(pv.Layout)
    .property("rows")
    .property("cols");

/**
 * Default properties for grid layouts. By default, there is one row and one
 * column, and the data is the propagated to the child cell.
 *
 * @type pv.Layout.Grid
 */
pv.Layout.Grid.prototype.defaults = new pv.Layout.Grid()
    .extend(pv.Layout.prototype.defaults)
    .rows(1)
    .cols(1);

/** @private */
pv.Layout.Grid.prototype.buildImplied = function(s) {
  pv.Layout.prototype.buildImplied.call(this, s);
  var r = s.rows, c = s.cols;
  if (typeof c == "object") r = pv.transpose(c);
  if (typeof r == "object") {
    s.$grid = pv.blend(r);
    s.rows = r.length;
    s.cols = r[0] ? r[0].length : 0;
  } else {
    s.$grid = pv.repeat([s.data], r * c);
  }
};

/**
 * The number of rows. This property can also be specified as the data in
 * row-major order; in this case, the rows property is implicitly set to the
 * length of the array, and the cols property is set to the length of the first
 * element in the array.
 *
 * @type number
 * @name pv.Layout.Grid.prototype.rows
 */

/**
 * The number of columns. This property can also be specified as the data in
 * column-major order; in this case, the cols property is implicitly set to the
 * length of the array, and the rows property is set to the length of the first
 * element in the array.
 *
 * @type number
 * @name pv.Layout.Grid.prototype.cols
 */
/**
 * Constructs a new, empty stack layout. Layouts are not typically constructed
 * directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a layout for stacked visualizations, ranging from simple
 * stacked bar charts to more elaborate "streamgraphs" composed of stacked
 * areas. Stack layouts uses length as a visual encoding, as opposed to
 * position, as the layers do not share an aligned axis.
 *
 * <p>Marks can be stacked vertically or horizontally. For example,
 *
 * <pre>vis.add(pv.Layout.Stack)
 *     .layers([[1, 1.2, 1.7, 1.5, 1.7],
 *              [.5, 1, .8, 1.1, 1.3],
 *              [.2, .5, .8, .9, 1]])
 *     .x(function() this.index * 35)
 *     .y(function(d) d * 40)
 *   .layer.add(pv.Area);</pre>
 *
 * specifies a vertically-stacked area chart, using the default "bottom-left"
 * orientation with "zero" offset. This visualization can be easily changed into
 * a streamgraph using the "wiggle" offset, which attempts to minimize change in
 * slope weighted by layer thickness. See the {@link #offset} property for more
 * supported streamgraph algorithms.
 *
 * <p>In the simplest case, the layer data can be specified as a two-dimensional
 * array of numbers. The <tt>x</tt> and <tt>y</tt> psuedo-properties are used to
 * define the thickness of each layer at the given position, respectively; in
 * the above example of the "bottom-left" orientation, the <tt>x</tt> and
 * <tt>y</tt> psuedo-properties are equivalent to the <tt>left</tt> and
 * <tt>height</tt> properties that you might use if you implemented a stacked
 * area by hand.
 *
 * <p>The advantage of using the stack layout is that the baseline, i.e., the
 * <tt>bottom</tt> property is computed automatically using the specified offset
 * algorithm. In addition, the order of layers can be computed using a built-in
 * algorithm via the <tt>order</tt> property.
 *
 * <p>With the exception of the "expand" <tt>offset</tt>, the stack layout does
 * not perform any automatic scaling of data; the values returned from
 * <tt>x</tt> and <tt>y</tt> specify pixel sizes. To simplify scaling math, use
 * this layout in conjunction with {@link pv.Scale.linear} or similar.
 *
 * <p>In other cases, the <tt>values</tt> psuedo-property can be used to define
 * the data more flexibly. As with a typical panel &amp; area, the
 * <tt>layers</tt> property corresponds to the data in the enclosing panel,
 * while the <tt>values</tt> psuedo-property corresponds to the data for the
 * area within the panel. For example, given an array of data values:
 *
 * <pre>var crimea = [
 *  { date: "4/1854", wounds: 0, other: 110, disease: 110 },
 *  { date: "5/1854", wounds: 0, other: 95, disease: 105 },
 *  { date: "6/1854", wounds: 0, other: 40, disease: 95 },
 *  ...</pre>
 *
 * and a corresponding array of series names:
 *
 * <pre>var causes = ["wounds", "other", "disease"];</pre>
 *
 * Separate layers can be defined for each cause like so:
 *
 * <pre>vis.add(pv.Layout.Stack)
 *     .layers(causes)
 *     .values(crimea)
 *     .x(function(d) x(d.date))
 *     .y(function(d, p) y(d[p]))
 *   .layer.add(pv.Area)
 *     ...</pre>
 *
 * As with the panel &amp; area case, the datum that is passed to the
 * psuedo-properties <tt>x</tt> and <tt>y</tt> are the values (an element in
 * <tt>crimea</tt>); the second argument is the layer data (a string in
 * <tt>causes</tt>). Additional arguments specify the data of enclosing panels,
 * if any.
 *
 * @extends pv.Layout
 */
pv.Layout.Stack = function() {
  pv.Layout.call(this);
  var that = this,
      /** @ignore */ none = function() { return null; },
      prop = {t: none, l: none, r: none, b: none, w: none, h: none},
      values,
      buildImplied = that.buildImplied;

  /** @private Proxy the given property on the layer. */
  function proxy(name) {
    return function() {
        return prop[name](this.parent.index, this.index);
      };
  }

  /** @private Compute the layout! */
  this.buildImplied = function(s) {
    buildImplied.call(this, s);

    var data = s.layers,
        n = data.length,
        m,
        orient = s.orient,
        horizontal = /^(top|bottom)\b/.test(orient),
        h = this.parent[horizontal ? "height" : "width"](),
        x = [],
        y = [],
        dy = [];

    /*
     * Iterate over the data, evaluating the values, x and y functions. The
     * context in which the x and y psuedo-properties are evaluated is a
     * pseudo-mark that is a grandchild of this layout.
     */
    var stack = pv.Mark.stack, o = {parent: {parent: this}};
    stack.unshift(null);
    values = [];
    for (var i = 0; i < n; i++) {
      dy[i] = [];
      y[i] = [];
      o.parent.index = i;
      stack[0] = data[i];
      values[i] = this.$values.apply(o.parent, stack);
      if (!i) m = values[i].length;
      stack.unshift(null);
      for (var j = 0; j < m; j++) {
        stack[0] = values[i][j];
        o.index = j;
        if (!i) x[j] = this.$x.apply(o, stack);
        dy[i][j] = this.$y.apply(o, stack);
      }
      stack.shift();
    }
    stack.shift();

    /* order */
    var index;
    switch (s.order) {
      case "inside-out": {
        var max = dy.map(function(v) { return pv.max.index(v); }),
            map = pv.range(n).sort(function(a, b) { return max[a] - max[b]; }),
            sums = dy.map(function(v) { return pv.sum(v); }),
            top = 0,
            bottom = 0,
            tops = [],
            bottoms = [];
        for (var i = 0; i < n; i++) {
          var j = map[i];
          if (top < bottom) {
            top += sums[j];
            tops.push(j);
          } else {
            bottom += sums[j];
            bottoms.push(j);
          }
        }
        index = bottoms.reverse().concat(tops);
        break;
      }
      case "reverse": index = pv.range(n - 1, -1, -1); break;
      default: index = pv.range(n); break;
    }

    /* offset */
    switch (s.offset) {
      case "silohouette": {
        for (var j = 0; j < m; j++) {
          var o = 0;
          for (var i = 0; i < n; i++) o += dy[i][j];
          y[index[0]][j] = (h - o) / 2;
        }
        break;
      }
      case "wiggle": {
        var o = 0;
        for (var i = 0; i < n; i++) o += dy[i][0];
        y[index[0]][0] = o = (h - o) / 2;
        for (var j = 1; j < m; j++) {
          var s1 = 0, s2 = 0, dx = x[j] - x[j - 1];
          for (var i = 0; i < n; i++) s1 += dy[i][j];
          for (var i = 0; i < n; i++) {
            var s3 = (dy[index[i]][j] - dy[index[i]][j - 1]) / (2 * dx);
            for (var k = 0; k < i; k++) {
              s3 += (dy[index[k]][j] - dy[index[k]][j - 1]) / dx;
            }
            s2 += s3 * dy[index[i]][j];
          }
          y[index[0]][j] = o -= s1 ? s2 / s1 * dx : 0;
        }
        break;
      }
      case "expand": {
        for (var j = 0; j < m; j++) {
          y[index[0]][j] = 0;
          var k = 0;
          for (var i = 0; i < n; i++) k += dy[i][j];
          if (k) {
            k = h / k;
            for (var i = 0; i < n; i++) dy[i][j] *= k;
          } else {
            k = h / n;
            for (var i = 0; i < n; i++) dy[i][j] = k;
          }
        }
        break;
      }
      default: {
        for (var j = 0; j < m; j++) y[index[0]][j] = 0;
        break;
      }
    }

    /* Propagate the offset to the other series. */
    for (var j = 0; j < m; j++) {
      var o = y[index[0]][j];
      for (var i = 1; i < n; i++) {
        o += dy[index[i - 1]][j];
        y[index[i]][j] = o;
      }
    }

    /* Find the property definitions for dynamic substitution. */
    var i = orient.indexOf("-"),
        pdy = horizontal ? "h" : "w",
        px = i < 0 ? (horizontal ? "l" : "b") : orient.charAt(i + 1),
        py = orient.charAt(0);
    for (var p in prop) prop[p] = none;
    prop[px] = function(i, j) { return x[j]; };
    prop[py] = function(i, j) { return y[i][j]; };
    prop[pdy] = function(i, j) { return dy[i][j]; };
  };

  /**
   * The layer prototype. This prototype is intended to be used with an area,
   * bar or panel mark (or subclass thereof). Other mark types may be possible,
   * though note that the stack layout is not currently designed to support
   * radial stacked visualizations using wedges.
   *
   * <p>The layer is not a direct child of the stack layout; a hidden panel is
   * used to replicate layers.
   *
   * @type pv.Mark
   * @name pv.Layout.Stack.prototype.layer
   */
  this.layer = new pv.Mark()
      .data(function() { return values[this.parent.index]; })
      .top(proxy("t"))
      .left(proxy("l"))
      .right(proxy("r"))
      .bottom(proxy("b"))
      .width(proxy("w"))
      .height(proxy("h"));

  this.layer.add = function(type) {
    return that.add(pv.Panel)
        .data(function() { return that.layers(); })
      .add(type)
        .extend(this);
  };
};

pv.Layout.Stack.prototype = pv.extend(pv.Layout)
    .property("orient", String)
    .property("offset", String)
    .property("order", String)
    .property("layers");

/**
 * Default properties for stack layouts. The default orientation is
 * "bottom-left", the default offset is "zero", and the default layers is
 * <tt>[[]]</tt>.
 *
 * @type pv.Layout.Stack
 */
pv.Layout.Stack.prototype.defaults = new pv.Layout.Stack()
    .extend(pv.Layout.prototype.defaults)
    .orient("bottom-left")
    .offset("zero")
    .layers([[]]);

/** @private */
pv.Layout.Stack.prototype.$x
    = /** @private */ pv.Layout.Stack.prototype.$y
    = function() { return 0; };

/**
 * The x psuedo-property; determines the position of the value within the layer.
 * This typically corresponds to the independent variable. For example, with the
 * default "bottom-left" orientation, this function defines the "left" property.
 *
 * @param {function} f the x function.
 * @returns {pv.Layout.Stack} this.
 */
pv.Layout.Stack.prototype.x = function(f) {
  /** @private */ this.$x = pv.functor(f);
  return this;
};

/**
 * The y psuedo-property; determines the thickness of the layer at the given
 * value.  This typically corresponds to the dependent variable. For example,
 * with the default "bottom-left" orientation, this function defines the
 * "height" property.
 *
 * @param {function} f the y function.
 * @returns {pv.Layout.Stack} this.
 */
pv.Layout.Stack.prototype.y = function(f) {
  /** @private */ this.$y = pv.functor(f);
  return this;
};

/** @private The default value function; identity. */
pv.Layout.Stack.prototype.$values = pv.identity;

/**
 * The values function; determines the values for a given layer. The default
 * value is the identity function, which assumes that the layers property is
 * specified as a two-dimensional (i.e., nested) array.
 *
 * @param {function} f the values function.
 * @returns {pv.Layout.Stack} this.
 */
pv.Layout.Stack.prototype.values = function(f) {
  this.$values = pv.functor(f);
  return this;
};

/**
 * The layer data in row-major order. The value of this property is typically a
 * two-dimensional (i.e., nested) array, but any array can be used, provided the
 * values psuedo-property is defined accordingly.
 *
 * @type array[]
 * @name pv.Layout.Stack.prototype.layers
 */

/**
 * The layer orientation. The following values are supported:<ul>
 *
 * <li>bottom-left == bottom
 * <li>bottom-right
 * <li>top-left == top
 * <li>top-right
 * <li>left-top
 * <li>left-bottom == left
 * <li>right-top
 * <li>right-bottom == right
 *
 * </ul>. The default value is "bottom-left", which means that the layers will
 * be built from the bottom-up, and the values within layers will be laid out
 * from left-to-right.
 *
 * <p>Note that with non-zero baselines, some orientations may give similar
 * results. For example, offset("silohouette") centers the layers, resulting in
 * a streamgraph. Thus, the orientations "bottom-left" and "top-left" will
 * produce similar results, differing only in the layer order.
 *
 * @type string
 * @name pv.Layout.Stack.prototype.orient
 */

/**
 * The layer order. The following values are supported:<ul>
 *
 * <li><i>null</i> - use given layer order.
 * <li>inside-out - sort by maximum value, with balanced order.
 * <li>reverse - use reverse of given layer order.
 *
 * </ul>For details on the inside-out order algorithm, refer to "Stacked Graphs
 * -- Geometry &amp; Aesthetics" by L. Byron and M. Wattenberg, IEEE TVCG
 * November/December 2008.
 *
 * @type string
 * @name pv.Layout.Stack.prototype.order
 */

/**
 * The layer offset; the y-position of the bottom of the lowest layer. The
 * following values are supported:<ul>
 *
 * <li>zero - use a zero baseline, i.e., the y-axis.
 * <li>silohouette - center the stream, i.e., ThemeRiver.
 * <li>wiggle - minimize weighted change in slope.
 * <li>expand - expand layers to fill the enclosing layout dimensions.
 *
 * </ul>For details on these offset algorithms, refer to "Stacked Graphs --
 * Geometry &amp; Aesthetics" by L. Byron and M. Wattenberg, IEEE TVCG
 * November/December 2008.
 *
 * @type string
 * @name pv.Layout.Stack.prototype.offset
 */
/**
 * Constructs a new, empty treemap layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a space-filling rectangular layout, with the hierarchy
 * represented via containment. Treemaps represent nodes as boxes, with child
 * nodes placed within parent boxes. The size of each box is proportional to the
 * size of the node in the tree. This particular algorithm is taken from Bruls,
 * D.M., C. Huizing, and J.J. van Wijk, <a
 * href="http://www.win.tue.nl/~vanwijk/stm.pdf">"Squarified Treemaps"</a> in
 * <i>Data Visualization 2000, Proceedings of the Joint Eurographics and IEEE
 * TCVG Sumposium on Visualization</i>, 2000, pp. 33-42.
 *
 * <p>The meaning of the exported mark prototypes changes slightly in the
 * space-filling implementation:<ul>
 *
 * <li><tt>node</tt> - for rendering nodes; typically a {@link pv.Bar}. The node
 * data is populated with <tt>dx</tt> and <tt>dy</tt> attributes, in addition to
 * the standard <tt>x</tt> and <tt>y</tt> position attributes.
 *
 * <p><li><tt>leaf</tt> - for rendering leaf nodes only, with no fill or stroke
 * style by default; typically a {@link pv.Panel} or another layout!
 *
 * <p><li><tt>link</tt> - unsupported; undefined. Links are encoded implicitly
 * in the arrangement of the space-filling nodes.
 *
 * <p><li><tt>label</tt> - for rendering node labels; typically a
 * {@link pv.Label}.
 *
 * </ul>For more details on how to use this layout, see
 * {@link pv.Layout.Hierarchy}.
 *
 * @extends pv.Layout.Hierarchy
 */
pv.Layout.Treemap = function() {
  pv.Layout.Hierarchy.call(this);

  this.node
      .strokeStyle("#fff")
      .fillStyle("rgba(31, 119, 180, .25)")
      .width(function(n) { return n.dx; })
      .height(function(n) { return n.dy; });

  this.label
      .visible(function(n) { return !n.firstChild; })
      .left(function(n) { return n.x + (n.dx / 2); })
      .top(function(n) { return n.y + (n.dy / 2); })
      .textAlign("center")
      .textAngle(function(n) { return n.dx > n.dy ? 0 : -Math.PI / 2; });

  (this.leaf = new pv.Mark()
      .extend(this.node)
      .fillStyle(null)
      .strokeStyle(null)
      .visible(function(n) { return !n.firstChild; })).parent = this;

  /* Hide unsupported link. */
  delete this.link;
};

pv.Layout.Treemap.prototype = pv.extend(pv.Layout.Hierarchy)
    .property("round", Boolean)
    .property("paddingLeft", Number)
    .property("paddingRight", Number)
    .property("paddingTop", Number)
    .property("paddingBottom", Number)
    .property("mode", String)
    .property("order", String);

/**
 * Default propertiess for treemap layouts. The default mode is "squarify" and
 * the default order is "ascending".
 *
 * @type pv.Layout.Treemap
 */
pv.Layout.Treemap.prototype.defaults = new pv.Layout.Treemap()
    .extend(pv.Layout.Hierarchy.prototype.defaults)
    .mode("squarify") // squarify, slice-and-dice, slice, dice
    .order("ascending"); // ascending, descending, reverse, null

/**
 * Whether node sizes should be rounded to integer values. This has a similar
 * effect to setting <tt>antialias(false)</tt> for node values, but allows the
 * treemap algorithm to accumulate error related to pixel rounding.
 *
 * @type boolean
 * @name pv.Layout.Treemap.prototype.round
 */

/**
 * The left inset between parent add child in pixels. Defaults to 0.
 *
 * @type number
 * @name pv.Layout.Treemap.prototype.paddingLeft
 * @see #padding
 */

/**
 * The right inset between parent add child in pixels. Defaults to 0.
 *
 * @type number
 * @name pv.Layout.Treemap.prototype.paddingRight
 * @see #padding
 */

/**
 * The top inset between parent and child in pixels. Defaults to 0.
 *
 * @type number
 * @name pv.Layout.Treemap.prototype.paddingTop
 * @see #padding
 */

/**
 * The bottom inset between parent and child in pixels. Defaults to 0.
 *
 * @type number
 * @name pv.Layout.Treemap.prototype.paddingBottom
 * @see #padding
 */

/**
 * The treemap algorithm. The default value is "squarify". The "slice-and-dice"
 * algorithm may also be used, which alternates between horizontal and vertical
 * slices for different depths. In addition, the "slice" and "dice" algorithms
 * may be specified explicitly to control whether horizontal or vertical slices
 * are used, which may be useful for nested treemap layouts.
 *
 * @type string
 * @name pv.Layout.Treemap.prototype.mode
 * @see <a
 * href="ftp://ftp.cs.umd.edu/pub/hcil/Reports-Abstracts-Bibliography/2001-06html/2001-06.pdf"
 * >"Ordered Treemap Layouts"</a> by B. Shneiderman &amp; M. Wattenberg, IEEE
 * InfoVis 2001.
 */

/**
 * The sibling node order. A <tt>null</tt> value means to use the sibling order
 * specified by the nodes property as-is; "reverse" will reverse the given
 * order. The default value "ascending" will sort siblings in ascending order of
 * size, while "descending" will do the reverse. For sorting based on data
 * attributes other than size, use the default <tt>null</tt> for the order
 * property, and sort the nodes beforehand using the {@link pv.Dom} operator.
 *
 * @type string
 * @name pv.Layout.Treemap.prototype.order
 */

/**
 * Alias for setting the left, right, top and bottom padding properties
 * simultaneously.
 *
 * @see #paddingLeft
 * @see #paddingRight
 * @see #paddingTop
 * @see #paddingBottom
 * @returns {pv.Layout.Treemap} this.
 */
pv.Layout.Treemap.prototype.padding = function(n) {
  return this.paddingLeft(n).paddingRight(n).paddingTop(n).paddingBottom(n);
};

/** @private The default size function. */
pv.Layout.Treemap.prototype.$size = function(d) {
  return Number(d.nodeValue);
};

/**
 * Specifies the sizing function. By default, the size function uses the
 * <tt>nodeValue</tt> attribute of nodes as a numeric value: <tt>function(d)
 * Number(d.nodeValue)</tt>.
 *
 * <p>The sizing function is invoked for each leaf node in the tree, per the
 * <tt>nodes</tt> property. For example, if the tree data structure represents a
 * file system, with files as leaf nodes, and each file has a <tt>bytes</tt>
 * attribute, you can specify a size function as:
 *
 * <pre>    .size(function(d) d.bytes)</pre>
 *
 * @param {function} f the new sizing function.
 * @returns {pv.Layout.Treemap} this.
 */
pv.Layout.Treemap.prototype.size = function(f) {
  this.$size = pv.functor(f);
  return this;
};

/** @private */
pv.Layout.Treemap.prototype.buildImplied = function(s) {
  if (pv.Layout.Hierarchy.prototype.buildImplied.call(this, s)) return;

  var that = this,
      nodes = s.nodes,
      root = nodes[0],
      stack = pv.Mark.stack,
      left = s.paddingLeft,
      right = s.paddingRight,
      top = s.paddingTop,
      bottom = s.paddingBottom,
      /** @ignore */ size = function(n) { return n.size; },
      round = s.round ? Math.round : Number,
      mode = s.mode;

  /** @private */
  function slice(row, sum, horizontal, x, y, w, h) {
    for (var i = 0, d = 0; i < row.length; i++) {
      var n = row[i];
      if (horizontal) {
        n.x = x + d;
        n.y = y;
        d += n.dx = round(w * n.size / sum);
        n.dy = h;
      } else {
        n.x = x;
        n.y = y + d;
        n.dx = w;
        d += n.dy = round(h * n.size / sum);
      }
    }
    if (n) { // correct on-axis rounding error
      if (horizontal) {
        n.dx += w - d;
      } else {
        n.dy += h - d;
      }
    }
  }

  /** @private */
  function ratio(row, l) {
    var rmax = -Infinity, rmin = Infinity, s = 0;
    for (var i = 0; i < row.length; i++) {
      var r = row[i].size;
      if (r < rmin) rmin = r;
      if (r > rmax) rmax = r;
      s += r;
    }
    s = s * s;
    l = l * l;
    return Math.max(l * rmax / s, s / (l * rmin));
  }

  /** @private */
  function layout(n, i) {
    var x = n.x + left,
        y = n.y + top,
        w = n.dx - left - right,
        h = n.dy - top - bottom;

    /* Assume squarify by default. */
    if (mode != "squarify") {
      slice(n.childNodes, n.size,
          mode == "slice" ? true
          : mode == "dice" ? false
          : i & 1, x, y, w, h);
      return;
    }

    var row = [],
        mink = Infinity,
        l = Math.min(w, h),
        k = w * h / n.size;

    /* Abort if the size is nonpositive. */
    if (n.size <= 0) return;

    /* Scale the sizes to fill the current subregion. */
    n.visitBefore(function(n) { n.size *= k; });

    /** @private Position the specified nodes along one dimension. */
    function position(row) {
      var horizontal = w == l,
          sum = pv.sum(row, size),
          r = l ? round(sum / l) : 0;
      slice(row, sum, horizontal, x, y, horizontal ? w : r, horizontal ? r : h);
      if (horizontal) {
        y += r;
        h -= r;
      } else {
        x += r;
        w -= r;
      }
      l = Math.min(w, h);
      return horizontal;
    }

    var children = n.childNodes.slice(); // copy
    while (children.length) {
      var child = children[children.length - 1];
      if (!child.size) {
        children.pop();
        continue;
      }
      row.push(child);

      var k = ratio(row, l);
      if (k <= mink) {
        children.pop();
        mink = k;
      } else {
        row.pop();
        position(row);
        row.length = 0;
        mink = Infinity;
      }
    }

    /* correct off-axis rounding error */
    if (position(row)) for (var i = 0; i < row.length; i++) {
      row[i].dy += h;
    } else for (var i = 0; i < row.length; i++) {
      row[i].dx += w;
    }
  }

  /* Recursively compute the node depth and size. */
  stack.unshift(null);
  root.visitAfter(function(n, i) {
      n.depth = i;
      n.x = n.y = n.dx = n.dy = 0;
      n.size = n.firstChild
          ? pv.sum(n.childNodes, function(n) { return n.size; })
          : that.$size.apply(that, (stack[0] = n, stack));
    });
  stack.shift();

  /* Sort. */
  switch (s.order) {
    case "ascending": {
      root.sort(function(a, b) { return a.size - b.size; });
      break;
    }
    case "descending": {
      root.sort(function(a, b) { return b.size - a.size; });
      break;
    }
    case "reverse": root.reverse(); break;
  }

  /* Recursively compute the layout. */
  root.x = 0;
  root.y = 0;
  root.dx = s.width;
  root.dy = s.height;
  root.visitBefore(layout);
};
/**
 * Constructs a new, empty tree layout. Layouts are not typically constructed
 * directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a node-link tree diagram using the Reingold-Tilford "tidy"
 * tree layout algorithm. The specific algorithm used by this layout is based on
 * <a href="http://citeseer.ist.psu.edu/buchheim02improving.html">"Improving
 * Walker's Algorithm to Run in Linear Time"</A> by C. Buchheim, M. J&uuml;nger
 * &amp; S. Leipert, Graph Drawing 2002. This layout supports both cartesian and
 * radial orientations orientations for node-link diagrams.
 *
 * <p>The tree layout supports a "group" property, which if true causes siblings
 * to be positioned closer together than unrelated nodes at the same depth. The
 * layout can be configured using the <tt>depth</tt> and <tt>breadth</tt>
 * properties, which control the increments in pixel space between nodes in both
 * dimensions, similar to the indent layout.
 *
 * <p>For more details on how to use this layout, see
 * {@link pv.Layout.Hierarchy}.
 *
 * @extends pv.Layout.Hierarchy
 */
pv.Layout.Tree = function() {
  pv.Layout.Hierarchy.call(this);
};

pv.Layout.Tree.prototype = pv.extend(pv.Layout.Hierarchy)
    .property("group", Number)
    .property("breadth", Number)
    .property("depth", Number)
    .property("orient", String);

/**
 * Default properties for tree layouts. The default orientation is "top", the
 * default group parameter is 1, and the default breadth and depth offsets are
 * 15 and 60 respectively.
 *
 * @type pv.Layout.Tree
 */
pv.Layout.Tree.prototype.defaults = new pv.Layout.Tree()
    .extend(pv.Layout.Hierarchy.prototype.defaults)
    .group(1)
    .breadth(15)
    .depth(60)
    .orient("top");

/** @private */
pv.Layout.Tree.prototype.buildImplied = function(s) {
  if (pv.Layout.Hierarchy.prototype.buildImplied.call(this, s)) return;

  var nodes = s.nodes,
      orient = s.orient,
      depth = s.depth,
      breadth = s.breadth,
      group = s.group,
      w = s.width,
      h = s.height;

  /** @private */
  function firstWalk(v) {
    var l, r, a;
    if (!v.firstChild) {
      if (l = v.previousSibling) {
        v.prelim = l.prelim + distance(v.depth, true);
      }
    } else {
      l = v.firstChild;
      r = v.lastChild;
      a = l; // default ancestor
      for (var c = l; c; c = c.nextSibling) {
        firstWalk(c);
        a = apportion(c, a);
      }
      executeShifts(v);
      var midpoint = .5 * (l.prelim + r.prelim);
      if (l = v.previousSibling) {
        v.prelim = l.prelim + distance(v.depth, true);
        v.mod = v.prelim - midpoint;
      } else {
        v.prelim = midpoint;
      }
    }
  }

  /** @private */
  function secondWalk(v, m, depth) {
    v.breadth = v.prelim + m;
    m += v.mod;
    for (var c = v.firstChild; c; c = c.nextSibling) {
      secondWalk(c, m, depth);
    }
  }

  /** @private */
  function apportion(v, a) {
    var w = v.previousSibling;
    if (w) {
      var vip = v,
          vop = v,
          vim = w,
          vom = v.parentNode.firstChild,
          sip = vip.mod,
          sop = vop.mod,
          sim = vim.mod,
          som = vom.mod,
          nr = nextRight(vim),
          nl = nextLeft(vip);
      while (nr && nl) {
        vim = nr;
        vip = nl;
        vom = nextLeft(vom);
        vop = nextRight(vop);
        vop.ancestor = v;
        var shift = (vim.prelim + sim) - (vip.prelim + sip) + distance(vim.depth, false);
        if (shift > 0) {
          moveSubtree(ancestor(vim, v, a), v, shift);
          sip += shift;
          sop += shift;
        }
        sim += vim.mod;
        sip += vip.mod;
        som += vom.mod;
        sop += vop.mod;
        nr = nextRight(vim);
        nl = nextLeft(vip);
      }
      if (nr && !nextRight(vop)) {
        vop.thread = nr;
        vop.mod += sim - sop;
      }
      if (nl && !nextLeft(vom)) {
        vom.thread = nl;
        vom.mod += sip - som;
        a = v;
      }
    }
    return a;
  }

  /** @private */
  function nextLeft(v) {
    return v.firstChild || v.thread;
  }

  /** @private */
  function nextRight(v) {
    return v.lastChild || v.thread;
  }

  /** @private */
  function moveSubtree(wm, wp, shift) {
    var subtrees = wp.number - wm.number;
    wp.change -= shift / subtrees;
    wp.shift += shift;
    wm.change += shift / subtrees;
    wp.prelim += shift;
    wp.mod += shift;
  }

  /** @private */
  function executeShifts(v) {
    var shift = 0, change = 0;
    for (var c = v.lastChild; c; c = c.previousSibling) {
      c.prelim += shift;
      c.mod += shift;
      change += c.change;
      shift += c.shift + change;
    }
  }

  /** @private */
  function ancestor(vim, v, a) {
    return (vim.ancestor.parentNode == v.parentNode) ? vim.ancestor : a;
  }

  /** @private */
  function distance(depth, siblings) {
    return (siblings ? 1 : (group + 1)) / ((orient == "radial") ? depth : 1);
  }

  /* Initialize temporary layout variables. TODO: store separately. */
  var root = nodes[0];
  root.visitAfter(function(v, i) {
      v.ancestor = v;
      v.prelim = 0;
      v.mod = 0;
      v.change = 0;
      v.shift = 0;
      v.number = v.previousSibling ? (v.previousSibling.number + 1) : 0;
      v.depth = i;
    });

  /* Compute the layout using Buchheim et al.'s algorithm. */
  firstWalk(root);
  secondWalk(root, -root.prelim, 0);

  /** @private Returns the angle of the given node. */
  function midAngle(n) {
    return (orient == "radial") ? n.breadth / depth : 0;
  }

  /** @private */
  function x(n) {
    switch (orient) {
      case "left": return n.depth;
      case "right": return w - n.depth;
      case "top":
      case "bottom": return n.breadth + w / 2;
      case "radial": return w / 2 + n.depth * Math.cos(midAngle(n));
    }
  }

  /** @private */
  function y(n) {
    switch (orient) {
      case "left":
      case "right": return n.breadth + h / 2;
      case "top": return n.depth;
      case "bottom": return h - n.depth;
      case "radial": return h / 2 + n.depth * Math.sin(midAngle(n));
    }
  }

  /* Clear temporary layout variables; transform depth and breadth. */
  root.visitAfter(function(v) {
      v.breadth *= breadth;
      v.depth *= depth;
      v.midAngle = midAngle(v);
      v.x = x(v);
      v.y = y(v);
      if (v.firstChild) v.midAngle += Math.PI;
      delete v.breadth;
      delete v.depth;
      delete v.ancestor;
      delete v.prelim;
      delete v.mod;
      delete v.change;
      delete v.shift;
      delete v.number;
      delete v.thread;
    });
};

/**
 * The offset between siblings nodes; defaults to 15.
 *
 * @type number
 * @name pv.Layout.Tree.prototype.breadth
 */

/**
 * The offset between parent and child nodes; defaults to 60.
 *
 * @type number
 * @name pv.Layout.Tree.prototype.depth
 */

/**
 * The orientation. The default orientation is "top", which means that the root
 * node is placed on the top edge, leaf nodes appear at the bottom, and internal
 * nodes are in-between. The following orientations are supported:<ul>
 *
 * <li>left - left-to-right.
 * <li>right - right-to-left.
 * <li>top - top-to-bottom.
 * <li>bottom - bottom-to-top.
 * <li>radial - radially, with the root at the center.</ul>
 *
 * @type string
 * @name pv.Layout.Tree.prototype.orient
 */

/**
 * The sibling grouping, i.e., whether differentiating space is placed between
 * sibling groups. The default is 1 (or true), causing sibling leaves to be
 * separated by one breadth offset. Setting this to false (or 0) causes
 * non-siblings to be adjacent.
 *
 * @type number
 * @name pv.Layout.Tree.prototype.group
 */
/**
 * Constructs a new, empty indent layout. Layouts are not typically constructed
 * directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a hierarchical layout using the indent algorithm. This
 * layout implements a node-link diagram where the nodes are presented in
 * preorder traversal, and nodes are indented based on their depth from the
 * root. This technique is used ubiquitously by operating systems to represent
 * file directories; although it requires much vertical space, indented trees
 * allow efficient <i>interactive</i> exploration of trees to find a specific
 * node. In addition they allow rapid scanning of node labels, and multivariate
 * data such as file sizes can be displayed adjacent to the hierarchy.
 *
 * <p>The indent layout can be configured using the <tt>depth</tt> and
 * <tt>breadth</tt> properties, which control the increments in pixel space for
 * each indent and row in the layout. This layout does not support multiple
 * orientations; the root node is rendered in the top-left, while
 * <tt>breadth</tt> is a vertical offset from the top, and <tt>depth</tt> is a
 * horizontal offset from the left.
 *
 * <p>For more details on how to use this layout, see
 * {@link pv.Layout.Hierarchy}.
 *
 * @extends pv.Layout.Hierarchy
 */
pv.Layout.Indent = function() {
  pv.Layout.Hierarchy.call(this);
  this.link.interpolate("step-after");
};

pv.Layout.Indent.prototype = pv.extend(pv.Layout.Hierarchy)
    .property("depth", Number)
    .property("breadth", Number);

/**
 * The horizontal offset between different levels of the tree; defaults to 15.
 *
 * @type number
 * @name pv.Layout.Indent.prototype.depth
 */

/**
 * The vertical offset between nodes; defaults to 15.
 *
 * @type number
 * @name pv.Layout.Indent.prototype.breadth
 */

/**
 * Default properties for indent layouts. By default the depth and breadth
 * offsets are 15 pixels.
 *
 * @type pv.Layout.Indent
 */
pv.Layout.Indent.prototype.defaults = new pv.Layout.Indent()
    .extend(pv.Layout.Hierarchy.prototype.defaults)
    .depth(15)
    .breadth(15);

/** @private */
pv.Layout.Indent.prototype.buildImplied = function(s) {
  if (pv.Layout.Hierarchy.prototype.buildImplied.call(this, s)) return;

  var nodes = s.nodes,
      bspace = s.breadth,
      dspace = s.depth,
      ax = 0,
      ay = 0;

  /** @private */
  function position(n, breadth, depth) {
    n.x = ax + depth++ * dspace;
    n.y = ay + breadth++ * bspace;
    n.midAngle = 0;
    for (var c = n.firstChild; c; c = c.nextSibling) {
      breadth = position(c, breadth, depth);
    }
    return breadth;
  }

  position(nodes[0], 1, 1);
};
/**
 * Constructs a new, empty circle-packing layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a hierarchical layout using circle-packing. The meaning of
 * the exported mark prototypes changes slightly in the space-filling
 * implementation:<ul>
 *
 * <li><tt>node</tt> - for rendering nodes; typically a {@link pv.Dot}.
 *
 * <p><li><tt>link</tt> - unsupported; undefined. Links are encoded implicitly
 * in the arrangement of the space-filling nodes.
 *
 * <p><li><tt>label</tt> - for rendering node labels; typically a
 * {@link pv.Label}.
 *
 * </ul>The pack layout support dynamic sizing for leaf nodes, if a
 * {@link #size} psuedo-property is specified. The default size function returns
 * 1, causing all leaf nodes to be sized equally, and all internal nodes to be
 * sized by the number of leaf nodes they have as descendants.
 *
 * <p>The size function can be used in conjunction with the order property,
 * which allows the nodes to the sorted by the computed size. Note: for sorting
 * based on other data attributes, simply use the default <tt>null</tt> for the
 * order property, and sort the nodes beforehand using the {@link pv.Dom}
 * operator.
 *
 * <p>For more details on how to use this layout, see
 * {@link pv.Layout.Hierarchy}.
 *
 * @extends pv.Layout.Hierarchy
 * @see <a href="http://portal.acm.org/citation.cfm?id=1124772.1124851"
 * >"Visualization of large hierarchical data by circle packing"</a> by W. Wang,
 * H. Wang, G. Dai, and H. Wang, ACM CHI 2006.
 */
pv.Layout.Pack = function() {
  pv.Layout.Hierarchy.call(this);

  this.node
      .radius(function(n) { return n.radius; })
      .strokeStyle("rgb(31, 119, 180)")
      .fillStyle("rgba(31, 119, 180, .25)");

  this.label
      .textAlign("center");

  /* Hide unsupported link. */
  delete this.link;
};

pv.Layout.Pack.prototype = pv.extend(pv.Layout.Hierarchy)
    .property("spacing", Number)
    .property("order", String); // ascending, descending, reverse, null

/**
 * Default properties for circle-packing layouts. The default spacing parameter
 * is 1 and the default order is "ascending".
 *
 * @type pv.Layout.Pack
 */
pv.Layout.Pack.prototype.defaults = new pv.Layout.Pack()
    .extend(pv.Layout.Hierarchy.prototype.defaults)
    .spacing(1)
    .order("ascending");

/**
 * The spacing parameter; defaults to 1, which provides a little bit of padding
 * between sibling nodes and the enclosing circle. Larger values increase the
 * spacing, by making the sibling nodes smaller; a value of zero makes the leaf
 * nodes as large as possible, with no padding on enclosing circles.
 *
 * @type number
 * @name pv.Layout.Pack.prototype.spacing
 */

/**
 * The sibling node order. The default order is <tt>null</tt>, which means to
 * use the sibling order specified by the nodes property as-is. A value of
 * "ascending" will sort siblings in ascending order of size, while "descending"
 * will do the reverse. For sorting based on data attributes other than size,
 * use the default <tt>null</tt> for the order property, and sort the nodes
 * beforehand using the {@link pv.Dom} operator.
 *
 * @see pv.Dom.Node#sort
 * @type string
 * @name pv.Layout.Pack.prototype.order
 */

/** @private The default size function. */
pv.Layout.Pack.prototype.$radius = function() { return 1; };

// TODO is it possible for spacing to operate in pixel space?
// Right now it appears to be multiples of the smallest radius.

/**
 * Specifies the sizing function. By default, a sizing function is disabled and
 * all nodes are given constant size. The sizing function is invoked for each
 * leaf node in the tree (passed to the constructor).
 *
 * <p>For example, if the tree data structure represents a file system, with
 * files as leaf nodes, and each file has a <tt>bytes</tt> attribute, you can
 * specify a size function as:
 *
 * <pre>    .size(function(d) d.bytes)</pre>
 *
 * As with other properties, a size function may specify additional arguments to
 * access the data associated with the layout and any enclosing panels.
 *
 * @param {function} f the new sizing function.
 * @returns {pv.Layout.Pack} this.
 */
pv.Layout.Pack.prototype.size = function(f) {
  this.$radius = typeof f == "function"
      ? function() { return Math.sqrt(f.apply(this, arguments)); }
      : (f = Math.sqrt(f), function() { return f; });
  return this;
};

/** @private */
pv.Layout.Pack.prototype.buildImplied = function(s) {
  if (pv.Layout.Hierarchy.prototype.buildImplied.call(this, s)) return;

  var that = this,
      nodes = s.nodes,
      root = nodes[0];

  /** @private Compute the radii of the leaf nodes. */
  function radii(nodes) {
    var stack = pv.Mark.stack;
    stack.unshift(null);
    for (var i = 0, n = nodes.length; i < n; i++) {
      var c = nodes[i];
      if (!c.firstChild) {
        c.radius = that.$radius.apply(that, (stack[0] = c, stack));
      }
    }
    stack.shift();
  }

  /** @private */
  function packTree(n) {
    var nodes = [];
    for (var c = n.firstChild; c; c = c.nextSibling) {
      if (c.firstChild) c.radius = packTree(c);
      c.n = c.p = c;
      nodes.push(c);
    }

    /* Sort. */
    switch (s.order) {
      case "ascending": {
        nodes.sort(function(a, b) { return a.radius - b.radius; });
        break;
      }
      case "descending": {
        nodes.sort(function(a, b) { return b.radius - a.radius; });
        break;
      }
      case "reverse": nodes.reverse(); break;
    }

    return packCircle(nodes);
  }

  /** @private */
  function packCircle(nodes) {
    var xMin = Infinity,
        xMax = -Infinity,
        yMin = Infinity,
        yMax = -Infinity,
        a, b, c, j, k;

    /** @private */
    function bound(n) {
      xMin = Math.min(n.x - n.radius, xMin);
      xMax = Math.max(n.x + n.radius, xMax);
      yMin = Math.min(n.y - n.radius, yMin);
      yMax = Math.max(n.y + n.radius, yMax);
    }

    /** @private */
    function insert(a, b) {
      var c = a.n;
      a.n = b;
      b.p = a;
      b.n = c;
      c.p = b;
    }

    /** @private */
    function splice(a, b) {
      a.n = b;
      b.p = a;
    }

    /** @private */
    function intersects(a, b) {
      var dx = b.x - a.x,
          dy = b.y - a.y,
          dr = a.radius + b.radius;
      return (dr * dr - dx * dx - dy * dy) > .001; // within epsilon
    }

    /* Create first node. */
    a = nodes[0];
    a.x = -a.radius;
    a.y = 0;
    bound(a);

    /* Create second node. */
    if (nodes.length > 1) {
      b = nodes[1];
      b.x = b.radius;
      b.y = 0;
      bound(b);

      /* Create third node and build chain. */
      if (nodes.length > 2) {
        c = nodes[2];
        place(a, b, c);
        bound(c);
        insert(a, c);
        a.p = c;
        insert(c, b);
        b = a.n;

        /* Now iterate through the rest. */
        for (var i = 3; i < nodes.length; i++) {
          place(a, b, c = nodes[i]);

          /* Search for the closest intersection. */
          var isect = 0, s1 = 1, s2 = 1;
          for (j = b.n; j != b; j = j.n, s1++) {
            if (intersects(j, c)) {
              isect = 1;
              break;
            }
          }
          if (isect == 1) {
            for (k = a.p; k != j.p; k = k.p, s2++) {
              if (intersects(k, c)) {
                if (s2 < s1) {
                  isect = -1;
                  j = k;
                }
                break;
              }
            }
          }

          /* Update node chain. */
          if (isect == 0) {
            insert(a, c);
            b = c;
            bound(c);
          } else if (isect > 0) {
            splice(a, j);
            b = j;
            i--;
          } else if (isect < 0) {
            splice(j, b);
            a = j;
            i--;
          }
        }
      }
    }

    /* Re-center the circles and return the encompassing radius. */
    var cx = (xMin + xMax) / 2,
        cy = (yMin + yMax) / 2,
        cr = 0;
    for (var i = 0; i < nodes.length; i++) {
      var n = nodes[i];
      n.x -= cx;
      n.y -= cy;
      cr = Math.max(cr, n.radius + Math.sqrt(n.x * n.x + n.y * n.y));
    }
    return cr + s.spacing;
  }

  /** @private */
  function place(a, b, c) {
    var da = b.radius + c.radius,
        db = a.radius + c.radius,
        dx = b.x - a.x,
        dy = b.y - a.y,
        dc = Math.sqrt(dx * dx + dy * dy),
        cos = (db * db + dc * dc - da * da) / (2 * db * dc),
        theta = Math.acos(cos),
        x = cos * db,
        h = Math.sin(theta) * db;
    dx /= dc;
    dy /= dc;
    c.x = a.x + x * dx + h * dy;
    c.y = a.y + x * dy - h * dx;
  }

  /** @private */
  function transform(n, x, y, k) {
    for (var c = n.firstChild; c; c = c.nextSibling) {
      c.x += n.x;
      c.y += n.y;
      transform(c, x, y, k);
    }
    n.x = x + k * n.x;
    n.y = y + k * n.y;
    n.radius *= k;
  }

  radii(nodes);

  /* Recursively compute the layout. */
  root.x = 0;
  root.y = 0;
  root.radius = packTree(root);

  var w = this.width(),
      h = this.height(),
      k = 1 / Math.max(2 * root.radius / w, 2 * root.radius / h);
  transform(root, w / 2, h / 2, k);
};
/**
 * Constructs a new, empty force-directed layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements force-directed network layout as a node-link diagram. This
 * layout uses the Fruchterman-Reingold algorithm, which applies an attractive
 * spring force between neighboring nodes, and a repulsive electrical charge
 * force between all nodes. An additional drag force improves stability of the
 * simulation. See {@link pv.Force.spring}, {@link pv.Force.drag} and {@link
 * pv.Force.charge} for more details; note that the n-body charge force is
 * approximated using the Barnes-Hut algorithm.
 *
 * <p>This layout is implemented on top of {@link pv.Simulation}, which can be
 * used directly for more control over simulation parameters. The simulation
 * uses Position Verlet integration, which does not compute velocities
 * explicitly, but allows for easy geometric constraints, such as bounding the
 * nodes within the layout panel. Many of the configuration properties supported
 * by this layout are simply passed through to the underlying forces and
 * constraints of the simulation.
 *
 * <p>Force layouts are typically interactive. The gradual movement of the nodes
 * as they stabilize to a local stress minimum can help reveal the structure of
 * the network, as can {@link pv.Behavior.drag}, which allows the user to pick
 * up nodes and reposition them while the physics simulation continues. This
 * layout can also be used with pan &amp; zoom behaviors for interaction.
 *
 * <p>To facilitate interaction, this layout by default automatically re-renders
 * using a <tt>setInterval</tt> every 42 milliseconds. This can be disabled via
 * the <tt>iterations</tt> property, which if non-null specifies the number of
 * simulation iterations to run before the force-directed layout is finalized.
 * Be careful not to use too high an iteration count, as this can lead to an
 * annoying delay on page load.
 *
 * <p>As with other network layouts, the network data can be updated
 * dynamically, provided the property cache is reset. See
 * {@link pv.Layout.Network} for details. New nodes are initialized with random
 * positions near the center. Alternatively, positions can be specified manually
 * by setting the <tt>x</tt> and <tt>y</tt> attributes on nodes.
 *
 * @extends pv.Layout.Network
 * @see <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.13.8444&rep=rep1&type=pdf"
 * >"Graph Drawing by Force-directed Placement"</a> by T. Fruchterman &amp;
 * E. Reingold, Software--Practice &amp; Experience, November 1991.
 */
pv.Layout.Force = function() {
  pv.Layout.Network.call(this);

  /* Force-directed graphs can be messy, so reduce the link width. */
  this.link.lineWidth(function(d, p) { return Math.sqrt(p.linkValue) * 1.5; });
  this.label.textAlign("center");
};

pv.Layout.Force.prototype = pv.extend(pv.Layout.Network)
    .property("bound", Boolean)
    .property("iterations", Number)
    .property("dragConstant", Number)
    .property("chargeConstant", Number)
    .property("chargeMinDistance", Number)
    .property("chargeMaxDistance", Number)
    .property("chargeTheta", Number)
    .property("springConstant", Number)
    .property("springDamping", Number)
    .property("springLength", Number);

/**
 * The bound parameter; true if nodes should be constrained within the layout
 * panel. Bounding is disabled by default. Currently the layout does not observe
 * the radius of the nodes; strictly speaking, only the center of the node is
 * constrained to be within the panel, with an additional 6-pixel offset for
 * padding. A future enhancement could extend the bound constraint to observe
 * the node's radius, which would also support bounding for variable-size nodes.
 *
 * <p>Note that if this layout is used in conjunction with pan &amp; zoom
 * behaviors, those behaviors should have their bound parameter set to the same
 * value.
 *
 * @type boolean
 * @name pv.Layout.Force.prototype.bound
 */

/**
 * The number of simulation iterations to run, or null if this layout is
 * interactive. Force-directed layouts are interactive by default, using a
 * <tt>setInterval</tt> to advance the physics simulation and re-render
 * automatically.
 *
 * @type number
 * @name pv.Layout.Force.prototype.iterations
 */

/**
 * The drag constant, in the range [0,1]. A value of 0 means no drag (a
 * perfectly frictionless environment), while a value of 1 means friction
 * immediately cancels all momentum. The default value is 0.1, which provides a
 * minimum amount of drag that helps stabilize bouncy springs; lower values may
 * result in excessive bounciness, while higher values cause the simulation to
 * take longer to converge.
 *
 * @type number
 * @name pv.Layout.Force.prototype.dragConstant
 * @see pv.Force.drag#constant
 */

/**
 * The charge constant, which should be a negative number. The default value is
 * -40; more negative values will result in a stronger repulsive force, which
 * may lead to faster convergence at the risk of instability. Too strong
 * repulsive charge forces can cause comparatively weak springs to be stretched
 * well beyond their rest length, emphasizing global structure over local
 * structure. A nonnegative value will break the Fruchterman-Reingold algorithm,
 * and is for entertainment purposes only.
 *
 * @type number
 * @name pv.Layout.Force.prototype.chargeConstant
 * @see pv.Force.charge#constant
 */

/**
 * The minimum distance at which charge forces are applied. The default minimum
 * distance of 2 avoids applying forces that are two strong; because the physics
 * simulation is run at discrete time intervals, it is possible for two same-
 * charged particles to become very close or even a singularity! Since the
 * charge force is inversely proportional to the square of the distance, very
 * small distances can break the simulation.
 *
 * <p>In rare cases, two particles can become stuck on top of each other, as a
 * minimum distance threshold will prevent the charge force from repelling them.
 * However, this occurs very rarely because other forces and momentum typically
 * cause the particles to become separated again, at which point the repulsive
 * charge force kicks in.
 *
 * @type number
 * @name pv.Layout.Force.prototype.chargeMinDistance
 * @see pv.Force.charge#domain
 */

/**
 * The maximum distance at which charge forces are applied. This improves
 * performance by ignoring weak charge forces at great distances. Note that this
 * parameter is partly redundant, as the Barnes-Hut algorithm for n-body forces
 * already improves performance for far-away particles through approximation.
 *
 * @type number
 * @name pv.Layout.Force.prototype.chargeMaxDistance
 * @see pv.Force.charge#domain
 */

/**
 * The Barnes-Hut approximation factor. The Barnes-Hut approximation criterion
 * is the ratio of the size of the quadtree node to the distance from the point
 * to the node's center of mass is beneath some threshold. The default value is
 * 0.9.
 *
 * @type number
 * @name pv.Layout.Force.prototype.chargeTheta
 * @see pv.Force.charge#theta
 */

/**
 * The spring constant, which should be a positive number. The default value is
 * 0.1; greater values will result in a stronger attractive force, which may
 * lead to faster convergence at the risk of instability. Too strong spring
 * forces can cause comparatively weak charge forces to be ignored, emphasizing
 * local structure over global structure. A nonpositive value will break the
 * Fruchterman-Reingold algorithm, and is for entertainment purposes only.
 *
 * <p>The spring tension is automatically normalized using the inverse square
 * root of the maximum link degree of attached nodes.
 *
 * @type number
 * @name pv.Layout.Force.prototype.springConstant
 * @see pv.Force.spring#constant
 */

/**
 * The spring damping factor, in the range [0,1]. Damping functions identically
 * to drag forces, damping spring bounciness by applying a force in the opposite
 * direction of attached nodes' velocities. The default value is 0.3.
 *
 * <p>The spring damping is automatically normalized using the inverse square
 * root of the maximum link degree of attached nodes.
 *
 * @type number
 * @name pv.Layout.Force.prototype.springDamping
 * @see pv.Force.spring#damping
 */

/**
 * The spring rest length. The default value is 20 pixels. Larger values may be
 * appropriate if the layout panel is larger, or if the nodes are rendered
 * larger than the default dot size of 20.
 *
 * @type number
 * @name pv.Layout.Force.prototype.springLength
 * @see pv.Force.spring#length
 */

/**
 * Default properties for force-directed layouts. The default drag constant is
 * 0.1, the default charge constant is -40 (with a domain of [2, 500] and theta
 * of 0.9), and the default spring constant is 0.1 (with a damping of 0.3 and a
 * rest length of 20).
 *
 * @type pv.Layout.Force
 */
pv.Layout.Force.prototype.defaults = new pv.Layout.Force()
    .extend(pv.Layout.Network.prototype.defaults)
    .dragConstant(.1)
    .chargeConstant(-40)
    .chargeMinDistance(2)
    .chargeMaxDistance(500)
    .chargeTheta(.9)
    .springConstant(.1)
    .springDamping(.3)
    .springLength(20);

/** @private Initialize the physics simulation. */
pv.Layout.Force.prototype.buildImplied = function(s) {

  /* Any cached interactive layouts need to be rebound for the timer. */
  if (pv.Layout.Network.prototype.buildImplied.call(this, s)) {
    var f = s.$force;
    if (f) {
      f.next = this.binds.$force;
      this.binds.$force = f;
    }
    return;
  }

  var that = this,
      nodes = s.nodes,
      links = s.links,
      k = s.iterations,
      w = s.width,
      h = s.height;

  /* Initialize positions randomly near the center. */
  for (var i = 0, n; i < nodes.length; i++) {
    n = nodes[i];
    if (isNaN(n.x)) n.x = w / 2 + 40 * Math.random() - 20;
    if (isNaN(n.y)) n.y = h / 2 + 40 * Math.random() - 20;
  }

  /* Initialize the simulation. */
  var sim = pv.simulation(nodes);

  /* Drag force. */
  sim.force(pv.Force.drag(s.dragConstant));

  /* Charge (repelling) force. */
  sim.force(pv.Force.charge(s.chargeConstant)
      .domain(s.chargeMinDistance, s.chargeMaxDistance)
      .theta(s.chargeTheta));

  /* Spring (attracting) force. */
  sim.force(pv.Force.spring(s.springConstant)
      .damping(s.springDamping)
      .length(s.springLength)
      .links(links));

  /* Position constraint (for interactive dragging). */
  sim.constraint(pv.Constraint.position());

  /* Optionally add bound constraint. TODO: better padding. */
  if (s.bound) {
    sim.constraint(pv.Constraint.bound().x(6, w - 6).y(6, h - 6));
  }

  /** @private Returns the speed of the given node, to determine cooling. */
  function speed(n) {
    return n.fix ? 1 : n.vx * n.vx + n.vy * n.vy;
  }

  /*
   * If the iterations property is null (the default), the layout is
   * interactive. The simulation is run until the fastest particle drops below
   * an arbitrary minimum speed. Although the timer keeps firing, this speed
   * calculation is fast so there is minimal CPU overhead. Note: if a particle
   * is fixed for interactivity, treat this as a high speed and resume
   * simulation.
   */
  if (k == null) {
    sim.step(); // compute initial previous velocities
    sim.step(); // compute initial velocities

    /* Add the simulation state to the bound list. */
    var force = s.$force = this.binds.$force = {
      next: this.binds.$force,
      nodes: nodes,
      min: 1e-4 * (links.length + 1),
      sim: sim
    };

    /* Start the timer, if not already started. */
    if (!this.$timer) this.$timer = setInterval(function() {
      var render = false;
      for (var f = that.binds.$force; f; f = f.next) {
        if (pv.max(f.nodes, speed) > f.min) {
          f.sim.step();
          render = true;
        }
      }
      if (render) that.render();
    }, 42);
  } else for (var i = 0; i < k; i++) {
    sim.step();
  }
};
/**
 * Constructs a new, empty cluster layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a hierarchical layout using the cluster (or dendrogram)
 * algorithm. This layout provides both node-link and space-filling
 * implementations of cluster diagrams. In many ways it is similar to
 * {@link pv.Layout.Partition}, except that leaf nodes are positioned at maximum
 * depth, and the depth of internal nodes is based on their distance from their
 * deepest descendant, rather than their distance from the root.
 *
 * <p>The cluster layout supports a "group" property, which if true causes
 * siblings to be positioned closer together than unrelated nodes at the same
 * depth. Unlike the partition layout, this layout does not support dynamic
 * sizing for leaf nodes; all leaf nodes are the same size.
 *
 * <p>For more details on how to use this layout, see
 * {@link pv.Layout.Hierarchy}.
 *
 * @see pv.Layout.Cluster.Fill
 * @extends pv.Layout.Hierarchy
 */
pv.Layout.Cluster = function() {
  pv.Layout.Hierarchy.call(this);
  var interpolate, // cached interpolate
      buildImplied = this.buildImplied;

  /** @private Cache layout state to optimize properties. */
  this.buildImplied = function(s) {
    buildImplied.call(this, s);
    interpolate
        = /^(top|bottom)$/.test(s.orient) ? "step-before"
        : /^(left|right)$/.test(s.orient) ? "step-after"
        : "linear";
  };

  this.link.interpolate(function() { return interpolate; });
};

pv.Layout.Cluster.prototype = pv.extend(pv.Layout.Hierarchy)
    .property("group", Number)
    .property("orient", String)
    .property("innerRadius", Number)
    .property("outerRadius", Number);

/**
 * The group parameter; defaults to 0, disabling grouping of siblings. If this
 * parameter is set to a positive number (or true, which is equivalent to 1),
 * then additional space will be allotted between sibling groups. In other
 * words, siblings (nodes that share the same parent) will be positioned more
 * closely than nodes at the same depth that do not share a parent.
 *
 * @type number
 * @name pv.Layout.Cluster.prototype.group
 */

/**
 * The orientation. The default orientation is "top", which means that the root
 * node is placed on the top edge, leaf nodes appear on the bottom edge, and
 * internal nodes are in-between. The following orientations are supported:<ul>
 *
 * <li>left - left-to-right.
 * <li>right - right-to-left.
 * <li>top - top-to-bottom.
 * <li>bottom - bottom-to-top.
 * <li>radial - radially, with the root at the center.</ul>
 *
 * @type string
 * @name pv.Layout.Cluster.prototype.orient
 */

/**
 * The inner radius; defaults to 0. This property applies only to radial
 * orientations, and can be used to compress the layout radially. Note that for
 * the node-link implementation, the root node is always at the center,
 * regardless of the value of this property; this property only affects internal
 * and leaf nodes. For the space-filling implementation, a non-zero value of
 * this property will result in the root node represented as a ring rather than
 * a circle.
 *
 * @type number
 * @name pv.Layout.Cluster.prototype.innerRadius
 */

/**
 * The outer radius; defaults to fill the containing panel, based on the height
 * and width of the layout. If the layout has no height and width specified, it
 * will extend to fill the enclosing panel.
 *
 * @type number
 * @name pv.Layout.Cluster.prototype.outerRadius
 */

/**
 * Defaults for cluster layouts. The default group parameter is 0 and the
 * default orientation is "top".
 *
 * @type pv.Layout.Cluster
 */
pv.Layout.Cluster.prototype.defaults = new pv.Layout.Cluster()
    .extend(pv.Layout.Hierarchy.prototype.defaults)
    .group(0)
    .orient("top");

/** @private */
pv.Layout.Cluster.prototype.buildImplied = function(s) {
  if (pv.Layout.Hierarchy.prototype.buildImplied.call(this, s)) return;

  var root = s.nodes[0],
      group = s.group,
      breadth,
      depth,
      leafCount = 0,
      leafIndex = .5 - group / 2;

  /* Count the leaf nodes and compute the depth of descendants. */
  var p = undefined;
  root.visitAfter(function(n) {
      if (n.firstChild) {
        n.depth = 1 + pv.max(n.childNodes, function(n) { return n.depth; });
      } else {
        if (group && (p != n.parentNode)) {
          p = n.parentNode;
          leafCount += group;
        }
        leafCount++;
        n.depth = 0;
      }
    });
  breadth = 1 / leafCount;
  depth = 1 / root.depth;

  /* Compute the unit breadth and depth of each node. */
  var p = undefined;
  root.visitAfter(function(n) {
      if (n.firstChild) {
        n.breadth = pv.mean(n.childNodes, function(n) { return n.breadth; });
      } else {
        if (group && (p != n.parentNode)) {
          p = n.parentNode;
          leafIndex += group;
        }
        n.breadth = breadth * leafIndex++;
      }
      n.depth = 1 - n.depth * depth;
    });

  /* Compute breadth and depth ranges for space-filling layouts. */
  root.visitAfter(function(n) {
      n.minBreadth = n.firstChild
          ? n.firstChild.minBreadth
          : (n.breadth - breadth / 2);
      n.maxBreadth = n.firstChild
          ? n.lastChild.maxBreadth
          : (n.breadth + breadth / 2);
    });
  root.visitBefore(function(n) {
      n.minDepth = n.parentNode
          ? n.parentNode.maxDepth
          : 0;
      n.maxDepth = n.parentNode
          ? (n.depth + root.depth)
          : (n.minDepth + 2 * root.depth);
    });
  root.minDepth = -depth;

  pv.Layout.Hierarchy.NodeLink.buildImplied.call(this, s);
};

/**
 * Constructs a new, empty space-filling cluster layout. Layouts are not
 * typically constructed directly; instead, they are added to an existing panel
 * via {@link pv.Mark#add}.
 *
 * @class A variant of cluster layout that is space-filling. The meaning of the
 * exported mark prototypes changes slightly in the space-filling
 * implementation:<ul>
 *
 * <li><tt>node</tt> - for rendering nodes; typically a {@link pv.Bar} for
 * non-radial orientations, and a {@link pv.Wedge} for radial orientations.
 *
 * <p><li><tt>link</tt> - unsupported; undefined. Links are encoded implicitly
 * in the arrangement of the space-filling nodes.
 *
 * <p><li><tt>label</tt> - for rendering node labels; typically a
 * {@link pv.Label}.
 *
 * </ul>For more details on how to use this layout, see
 * {@link pv.Layout.Cluster}.
 *
 * @extends pv.Layout.Cluster
 */
pv.Layout.Cluster.Fill = function() {
  pv.Layout.Cluster.call(this);
  pv.Layout.Hierarchy.Fill.constructor.call(this);
};

pv.Layout.Cluster.Fill.prototype = pv.extend(pv.Layout.Cluster);

/** @private */
pv.Layout.Cluster.Fill.prototype.buildImplied = function(s) {
  if (pv.Layout.Cluster.prototype.buildImplied.call(this, s)) return;
  pv.Layout.Hierarchy.Fill.buildImplied.call(this, s);
};
/**
 * Constructs a new, empty partition layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implemeents a hierarchical layout using the partition (or sunburst,
 * icicle) algorithm. This layout provides both node-link and space-filling
 * implementations of partition diagrams. In many ways it is similar to
 * {@link pv.Layout.Cluster}, except that leaf nodes are positioned based on
 * their distance from the root.
 *
 * <p>The partition layout support dynamic sizing for leaf nodes, if a
 * {@link #size} psuedo-property is specified. The default size function returns
 * 1, causing all leaf nodes to be sized equally, and all internal nodes to be
 * sized by the number of leaf nodes they have as descendants.
 *
 * <p>The size function can be used in conjunction with the order property,
 * which allows the nodes to the sorted by the computed size. Note: for sorting
 * based on other data attributes, simply use the default <tt>null</tt> for the
 * order property, and sort the nodes beforehand using the {@link pv.Dom}
 * operator.
 *
 * <p>For more details on how to use this layout, see
 * {@link pv.Layout.Hierarchy}.
 *
 * @see pv.Layout.Partition.Fill
 * @extends pv.Layout.Hierarchy
 */
pv.Layout.Partition = function() {
  pv.Layout.Hierarchy.call(this);
};

pv.Layout.Partition.prototype = pv.extend(pv.Layout.Hierarchy)
    .property("order", String) // null, ascending, descending?
    .property("orient", String) // top, left, right, bottom, radial
    .property("innerRadius", Number)
    .property("outerRadius", Number);

/**
 * The sibling node order. The default order is <tt>null</tt>, which means to
 * use the sibling order specified by the nodes property as-is. A value of
 * "ascending" will sort siblings in ascending order of size, while "descending"
 * will do the reverse. For sorting based on data attributes other than size,
 * use the default <tt>null</tt> for the order property, and sort the nodes
 * beforehand using the {@link pv.Dom} operator.
 *
 * @see pv.Dom.Node#sort
 * @type string
 * @name pv.Layout.Partition.prototype.order
 */

/**
 * The orientation. The default orientation is "top", which means that the root
 * node is placed on the top edge, leaf nodes appear at the bottom, and internal
 * nodes are in-between. The following orientations are supported:<ul>
 *
 * <li>left - left-to-right.
 * <li>right - right-to-left.
 * <li>top - top-to-bottom.
 * <li>bottom - bottom-to-top.
 * <li>radial - radially, with the root at the center.</ul>
 *
 * @type string
 * @name pv.Layout.Partition.prototype.orient
 */

/**
 * The inner radius; defaults to 0. This property applies only to radial
 * orientations, and can be used to compress the layout radially. Note that for
 * the node-link implementation, the root node is always at the center,
 * regardless of the value of this property; this property only affects internal
 * and leaf nodes. For the space-filling implementation, a non-zero value of
 * this property will result in the root node represented as a ring rather than
 * a circle.
 *
 * @type number
 * @name pv.Layout.Partition.prototype.innerRadius
 */

/**
 * The outer radius; defaults to fill the containing panel, based on the height
 * and width of the layout. If the layout has no height and width specified, it
 * will extend to fill the enclosing panel.
 *
 * @type number
 * @name pv.Layout.Partition.prototype.outerRadius
 */

/**
 * Default properties for partition layouts. The default orientation is "top".
 *
 * @type pv.Layout.Partition
 */
pv.Layout.Partition.prototype.defaults = new pv.Layout.Partition()
    .extend(pv.Layout.Hierarchy.prototype.defaults)
    .orient("top");

/** @private */
pv.Layout.Partition.prototype.$size = function() { return 1; };

/**
 * Specifies the sizing function. By default, a sizing function is disabled and
 * all nodes are given constant size. The sizing function is invoked for each
 * leaf node in the tree (passed to the constructor).
 *
 * <p>For example, if the tree data structure represents a file system, with
 * files as leaf nodes, and each file has a <tt>bytes</tt> attribute, you can
 * specify a size function as:
 *
 * <pre>    .size(function(d) d.bytes)</pre>
 *
 * As with other properties, a size function may specify additional arguments to
 * access the data associated with the layout and any enclosing panels.
 *
 * @param {function} f the new sizing function.
 * @returns {pv.Layout.Partition} this.
 */
pv.Layout.Partition.prototype.size = function(f) {
  this.$size = f;
  return this;
};

/** @private */
pv.Layout.Partition.prototype.buildImplied = function(s) {
  if (pv.Layout.Hierarchy.prototype.buildImplied.call(this, s)) return;

  var that = this,
      root = s.nodes[0],
      stack = pv.Mark.stack,
      maxDepth = 0;

  /* Recursively compute the tree depth and node size. */
  stack.unshift(null);
  root.visitAfter(function(n, i) {
      if (i > maxDepth) maxDepth = i;
      n.size = n.firstChild
          ? pv.sum(n.childNodes, function(n) { return n.size; })
          : that.$size.apply(that, (stack[0] = n, stack));
    });
  stack.shift();

  /* Order */
  switch (s.order) {
    case "ascending": root.sort(function(a, b) { return a.size - b.size; }); break;
    case "descending": root.sort(function(b, a) { return a.size - b.size; }); break;
  }

  /* Compute the unit breadth and depth of each node. */
  var ds = 1 / maxDepth;
  root.minBreadth = 0;
  root.breadth = .5;
  root.maxBreadth = 1;
  root.visitBefore(function(n) {
    var b = n.minBreadth, s = n.maxBreadth - b;
      for (var c = n.firstChild; c; c = c.nextSibling) {
        c.minBreadth = b;
        c.maxBreadth = b += (c.size / n.size) * s;
        c.breadth = (b + c.minBreadth) / 2;
      }
    });
  root.visitAfter(function(n, i) {
      n.minDepth = (i - 1) * ds;
      n.maxDepth = n.depth = i * ds;
    });

  pv.Layout.Hierarchy.NodeLink.buildImplied.call(this, s);
};

/**
 * Constructs a new, empty space-filling partition layout. Layouts are not
 * typically constructed directly; instead, they are added to an existing panel
 * via {@link pv.Mark#add}.
 *
 * @class A variant of partition layout that is space-filling. The meaning of
 * the exported mark prototypes changes slightly in the space-filling
 * implementation:<ul>
 *
 * <li><tt>node</tt> - for rendering nodes; typically a {@link pv.Bar} for
 * non-radial orientations, and a {@link pv.Wedge} for radial orientations.
 *
 * <p><li><tt>link</tt> - unsupported; undefined. Links are encoded implicitly
 * in the arrangement of the space-filling nodes.
 *
 * <p><li><tt>label</tt> - for rendering node labels; typically a
 * {@link pv.Label}.
 *
 * </ul>For more details on how to use this layout, see
 * {@link pv.Layout.Partition}.
 *
 * @extends pv.Layout.Partition
 */
pv.Layout.Partition.Fill = function() {
  pv.Layout.Partition.call(this);
  pv.Layout.Hierarchy.Fill.constructor.call(this);
};

pv.Layout.Partition.Fill.prototype = pv.extend(pv.Layout.Partition);

/** @private */
pv.Layout.Partition.Fill.prototype.buildImplied = function(s) {
  if (pv.Layout.Partition.prototype.buildImplied.call(this, s)) return;
  pv.Layout.Hierarchy.Fill.buildImplied.call(this, s);
};
/**
 * Constructs a new, empty arc layout. Layouts are not typically constructed
 * directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a layout for arc diagrams. An arc diagram is a network
 * visualization with a one-dimensional layout of nodes, using circular arcs to
 * render links between nodes. For undirected networks, arcs are rendering on a
 * single side; this makes arc diagrams useful as annotations to other
 * two-dimensional network layouts, such as rollup, matrix or table layouts. For
 * directed networks, links in opposite directions can be rendered on opposite
 * sides using <tt>directed(true)</tt>.
 *
 * <p>Arc layouts are particularly sensitive to node ordering; for best results,
 * order the nodes such that related nodes are close to each other. A poor
 * (e.g., random) order may result in large arcs with crossovers that impede
 * visual processing. A future improvement to this layout may include automatic
 * reordering using, e.g., spectral graph layout or simulated annealing.
 *
 * <p>This visualization technique is related to that developed by
 * M. Wattenberg, <a
 * href="http://www.research.ibm.com/visual/papers/arc-diagrams.pdf">"Arc
 * Diagrams: Visualizing Structure in Strings"</a> in <i>IEEE InfoVis</i>, 2002.
 * However, this implementation is limited to simple node-link networks, as
 * opposed to structures with hierarchical self-similarity (such as strings).
 *
 * <p>As with other network layouts, three mark prototypes are provided:<ul>
 *
 * <li><tt>node</tt> - for rendering nodes; typically a {@link pv.Dot}.
 * <li><tt>link</tt> - for rendering links; typically a {@link pv.Line}.
 * <li><tt>label</tt> - for rendering node labels; typically a {@link pv.Label}.
 *
 * </ul>For more details on how this layout is structured and can be customized,
 * see {@link pv.Layout.Network}.
 *
 * @extends pv.Layout.Network
 **/
pv.Layout.Arc = function() {
  pv.Layout.Network.call(this);
  var interpolate, // cached interpolate
      directed, // cached directed
      reverse, // cached reverse
      buildImplied = this.buildImplied;

  /** @private Cache layout state to optimize properties. */
  this.buildImplied = function(s) {
    buildImplied.call(this, s);
    directed = s.directed;
    interpolate = s.orient == "radial" ? "linear" : "polar";
    reverse = s.orient == "right" || s.orient == "top";
  };

  /* Override link properties to handle directedness and orientation. */
  this.link
      .data(function(p) {
          var s = p.sourceNode, t = p.targetNode;
          return reverse != (directed || (s.breadth < t.breadth)) ? [s, t] : [t, s];
        })
      .interpolate(function() { return interpolate; });
};

pv.Layout.Arc.prototype = pv.extend(pv.Layout.Network)
    .property("orient", String)
    .property("directed", Boolean);

/**
 * Default properties for arc layouts. By default, the orientation is "bottom".
 *
 * @type pv.Layout.Arc
 */
pv.Layout.Arc.prototype.defaults = new pv.Layout.Arc()
    .extend(pv.Layout.Network.prototype.defaults)
    .orient("bottom");

/**
 * Specifies an optional sort function. The sort function follows the same
 * comparator contract required by {@link pv.Dom.Node#sort}. Specifying a sort
 * function provides an alternative to sort the nodes as they are specified by
 * the <tt>nodes</tt> property; the main advantage of doing this is that the
 * comparator function can access implicit fields populated by the network
 * layout, such as the <tt>linkDegree</tt>.
 *
 * <p>Note that arc diagrams are particularly sensitive to order. This is
 * referred to as the seriation problem, and many different techniques exist to
 * find good node orders that emphasize clusters, such as spectral layout and
 * simulated annealing.
 *
 * @param {function} f comparator function for nodes.
 * @returns {pv.Layout.Arc} this.
 */
pv.Layout.Arc.prototype.sort = function(f) {
  this.$sort = f;
  return this;
};

/** @private Populates the x, y and angle attributes on the nodes. */
pv.Layout.Arc.prototype.buildImplied = function(s) {
  if (pv.Layout.Network.prototype.buildImplied.call(this, s)) return;

  var nodes = s.nodes,
      orient = s.orient,
      sort = this.$sort,
      index = pv.range(nodes.length),
      w = s.width,
      h = s.height,
      r = Math.min(w, h) / 2;

  /* Sort the nodes. */
  if (sort) index.sort(function(a, b) { return sort(nodes[a], nodes[b]); });

  /** @private Returns the mid-angle, given the breadth. */
  function midAngle(b) {
    switch (orient) {
      case "top": return -Math.PI / 2;
      case "bottom": return Math.PI / 2;
      case "left": return Math.PI;
      case "right": return 0;
      case "radial": return (b - .25) * 2 * Math.PI;
    }
  }

  /** @private Returns the x-position, given the breadth. */
  function x(b) {
    switch (orient) {
      case "top":
      case "bottom": return b * w;
      case "left": return 0;
      case "right": return w;
      case "radial": return w / 2 + r * Math.cos(midAngle(b));
    }
  }

  /** @private Returns the y-position, given the breadth. */
  function y(b) {
    switch (orient) {
      case "top": return 0;
      case "bottom": return h;
      case "left":
      case "right": return b * h;
      case "radial": return h / 2 + r * Math.sin(midAngle(b));
    }
  }

  /* Populate the x, y and mid-angle attributes. */
  for (var i = 0; i < nodes.length; i++) {
    var n = nodes[index[i]], b = n.breadth = (i + .5) / nodes.length;
    n.x = x(b);
    n.y = y(b);
    n.midAngle = midAngle(b);
  }
};

/**
 * The orientation. The default orientation is "left", which means that nodes
 * will be positioned from left-to-right in the order they are specified in the
 * <tt>nodes</tt> property. The following orientations are supported:<ul>
 *
 * <li>left - left-to-right.
 * <li>right - right-to-left.
 * <li>top - top-to-bottom.
 * <li>bottom - bottom-to-top.
 * <li>radial - radially, starting at 12 o'clock and proceeding clockwise.</ul>
 *
 * @type string
 * @name pv.Layout.Arc.prototype.orient
 */

/**
 * Whether this arc digram is directed (bidirectional); only applies to
 * non-radial orientations. By default, arc digrams are undirected, such that
 * all arcs appear on one side. If the arc digram is directed, then forward
 * links are drawn on the conventional side (the same as as undirected
 * links--right, left, bottom and top for left, right, top and bottom,
 * respectively), while reverse links are drawn on the opposite side.
 *
 * @type boolean
 * @name pv.Layout.Arc.prototype.directed
 */
/**
 * Constructs a new, empty horizon layout. Layouts are not typically constructed
 * directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a horizon layout, which is a variation of a single-series
 * area chart where the area is folded into multiple bands. Color is used to
 * encode band, allowing the size of the chart to be reduced significantly
 * without impeding readability. This layout algorithm is based on the work of
 * J. Heer, N. Kong and M. Agrawala in <a
 * href="http://hci.stanford.edu/publications/2009/heer-horizon-chi09.pdf">"Sizing
 * the Horizon: The Effects of Chart Size and Layering on the Graphical
 * Perception of Time Series Visualizations"</a>, CHI 2009.
 *
 * <p>This layout exports a single <tt>band</tt> mark prototype, which is
 * intended to be used with an area mark. The band mark is contained in a panel
 * which is replicated per band (and for negative/positive bands). For example,
 * to create a simple horizon graph given an array of numbers:
 *
 * <pre>vis.add(pv.Layout.Horizon)
 *     .bands(n)
 *   .band.add(pv.Area)
 *     .data(data)
 *     .left(function() this.index * 35)
 *     .height(function(d) d * 40);</pre>
 *
 * The layout can be further customized by changing the number of bands, and
 * toggling whether the negative bands are mirrored or offset. (See the
 * above-referenced paper for guidance.)
 *
 * <p>The <tt>fillStyle</tt> of the area can be overridden, though typically it
 * is easier to customize the layout's behavior through the custom
 * <tt>backgroundStyle</tt>, <tt>positiveStyle</tt> and <tt>negativeStyle</tt>
 * properties. By default, the background is white, positive bands are blue, and
 * negative bands are red. For the most accurate presentation, use fully-opaque
 * colors of equal intensity for the negative and positive bands.
 *
 * @extends pv.Layout
 */
pv.Layout.Horizon = function() {
  pv.Layout.call(this);
  var that = this,
      bands, // cached bands
      mode, // cached mode
      size, // cached height
      fill, // cached background style
      red, // cached negative color (ramp)
      blue, // cached positive color (ramp)
      buildImplied = this.buildImplied;

  /** @private Cache the layout state to optimize properties. */
  this.buildImplied = function(s) {
    buildImplied.call(this, s);
    bands = s.bands;
    mode = s.mode;
    size = Math.round((mode == "color" ? .5 : 1) * s.height);
    fill = s.backgroundStyle;
    red = pv.ramp(fill, s.negativeStyle).domain(0, bands);
    blue = pv.ramp(fill, s.positiveStyle).domain(0, bands);
  };

  var bands = new pv.Panel()
      .data(function() { return pv.range(bands * 2); })
      .overflow("hidden")
      .height(function() { return size; })
      .top(function(i) { return mode == "color" ? (i & 1) * size : 0; })
      .fillStyle(function(i) { return i ? null : fill; });

  /**
   * The band prototype. This prototype is intended to be used with an Area
   * mark to render the horizon bands.
   *
   * @type pv.Mark
   * @name pv.Layout.Horizon.prototype.band
   */
  this.band = new pv.Mark()
      .top(function(d, i) {
          return mode == "mirror" && i & 1
              ? (i + 1 >> 1) * size
              : null;
        })
      .bottom(function(d, i) {
          return mode == "mirror"
              ? (i & 1 ? null : (i + 1 >> 1) * -size)
              : ((i & 1 || -1) * (i + 1 >> 1) * size);
        })
      .fillStyle(function(d, i) {
          return (i & 1 ? red : blue)((i >> 1) + 1);
        });

  this.band.add = function(type) {
    return that.add(pv.Panel).extend(bands).add(type).extend(this);
  };
};

pv.Layout.Horizon.prototype = pv.extend(pv.Layout)
    .property("bands", Number)
    .property("mode", String)
    .property("backgroundStyle", pv.color)
    .property("positiveStyle", pv.color)
    .property("negativeStyle", pv.color);

/**
 * Default properties for horizon layouts. By default, there are two bands, the
 * mode is "offset", the background style is "white", the positive style is
 * blue, negative style is red.
 *
 * @type pv.Layout.Horizon
 */
pv.Layout.Horizon.prototype.defaults = new pv.Layout.Horizon()
    .extend(pv.Layout.prototype.defaults)
    .bands(2)
    .mode("offset")
    .backgroundStyle("white")
    .positiveStyle("#1f77b4")
    .negativeStyle("#d62728");

/**
 * The horizon mode: offset, mirror, or color. The default is "offset".
 *
 * @type string
 * @name pv.Layout.Horizon.prototype.mode
 */

/**
 * The number of bands. Must be at least one. The default value is two.
 *
 * @type number
 * @name pv.Layout.Horizon.prototype.bands
 */

/**
 * The positive band color; if non-null, the interior of positive bands are
 * filled with the specified color. The default value of this property is blue.
 * For accurate blending, this color should be fully opaque.
 *
 * @type pv.Color
 * @name pv.Layout.Horizon.prototype.positiveStyle
 */

/**
 * The negative band color; if non-null, the interior of negative bands are
 * filled with the specified color. The default value of this property is red.
 * For accurate blending, this color should be fully opaque.
 *
 * @type pv.Color
 * @name pv.Layout.Horizon.prototype.negativeStyle
 */

/**
 * The background color. The panel background is filled with the specified
 * color, and the negative and positive bands are filled with an interpolated
 * color between this color and the respective band color. The default value of
 * this property is white. For accurate blending, this color should be fully
 * opaque.
 *
 * @type pv.Color
 * @name pv.Layout.Horizon.prototype.backgroundStyle
 */
/**
 * Constructs a new, empty rollup network layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a network visualization using a node-link diagram where
 * nodes are rolled up along two dimensions. This implementation is based on the
 * "PivotGraph" designed by Martin Wattenberg:
 *
 * <blockquote>The method is designed for graphs that are "multivariate", i.e.,
 * where each node is associated with several attributes. Unlike visualizations
 * which emphasize global graph topology, PivotGraph uses a simple grid-based
 * approach to focus on the relationship between node attributes &amp;
 * connections.</blockquote>
 *
 * This layout requires two psuedo-properties to be specified, which assign node
 * positions along the two dimensions {@link #x} and {@link #y}, corresponding
 * to the left and top properties, respectively. Typically, these functions are
 * specified using an {@link pv.Scale.ordinal}. Nodes that share the same
 * position in <i>x</i> and <i>y</i> are "rolled up" into a meta-node, and
 * similarly links are aggregated between meta-nodes. For example, to construct
 * a rollup to analyze links by gender and affiliation, first define two ordinal
 * scales:
 *
 * <pre>var x = pv.Scale.ordinal(nodes, function(d) d.gender).split(0, w),
 *     y = pv.Scale.ordinal(nodes, function(d) d.aff).split(0, h);</pre>
 *
 * Next, define the position psuedo-properties:
 *
 * <pre>    .x(function(d) x(d.gender))
 *     .y(function(d) y(d.aff))</pre>
 *
 * Linear and other quantitative scales can alternatively be used to position
 * the nodes along either dimension. Note, however, that the rollup requires
 * that the positions match exactly, and thus ordinal scales are recommended to
 * avoid precision errors.
 *
 * <p>Note that because this layout provides a visualization of the rolled up
 * graph, the data properties for the mark prototypes (<tt>node</tt>,
 * <tt>link</tt> and <tt>label</tt>) are different from most other network
 * layouts: they reference the rolled-up nodes and links, rather than the nodes
 * and links of the full network. The underlying nodes and links for each
 * rolled-up node and link can be accessed via the <tt>nodes</tt> and
 * <tt>links</tt> attributes, respectively. The aggregated link values for
 * rolled-up links can similarly be accessed via the <tt>linkValue</tt>
 * attribute.
 *
 * <p>For undirected networks, links are duplicated in both directions. For
 * directed networks, use <tt>directed(true)</tt>. The graph is assumed to be
 * undirected by default.
 *
 * @extends pv.Layout.Network
 * @see <a href="http://www.research.ibm.com/visual/papers/pivotgraph.pdf"
 * >"Visual Exploration of Multivariate Graphs"</a> by M. Wattenberg, CHI 2006.
 */
pv.Layout.Rollup = function() {
  pv.Layout.Network.call(this);
  var that = this,
      nodes, // cached rollup nodes
      links, // cached rollup links
      buildImplied = that.buildImplied;

  /** @private Cache layout state to optimize properties. */
  this.buildImplied = function(s) {
    buildImplied.call(this, s);
    nodes = s.$rollup.nodes;
    links = s.$rollup.links;
  };

  /* Render rollup nodes. */
  this.node
      .data(function() { return nodes; })
      .size(function(d) { return d.nodes.length * 20; });

  /* Render rollup links. */
  this.link
      .interpolate("polar")
      .eccentricity(.8);

  this.link.add = function(type) {
    return that.add(pv.Panel)
        .data(function() { return links; })
      .add(type)
        .extend(this);
  };
};

pv.Layout.Rollup.prototype = pv.extend(pv.Layout.Network)
    .property("directed", Boolean);

/**
 * Whether the underlying network is directed. By default, the graph is assumed
 * to be undirected, and links are rendered in both directions. If the network
 * is directed, then forward links are drawn above the diagonal, while reverse
 * links are drawn below.
 *
 * @type boolean
 * @name pv.Layout.Rollup.prototype.directed
 */

/**
 * Specifies the <i>x</i>-position function used to rollup nodes. The rolled up
 * nodes are positioned horizontally using the return values from the given
 * function. Typically the function is specified as an ordinal scale. For
 * single-dimension rollups, a constant value can be specified.
 *
 * @param {function} f the <i>x</i>-position function.
 * @returns {pv.Layout.Rollup} this.
 * @see pv.Scale.ordinal
 */
pv.Layout.Rollup.prototype.x = function(f) {
  this.$x = pv.functor(f);
  return this;
};

/**
 * Specifies the <i>y</i>-position function used to rollup nodes. The rolled up
 * nodes are positioned vertically using the return values from the given
 * function. Typically the function is specified as an ordinal scale. For
 * single-dimension rollups, a constant value can be specified.
 *
 * @param {function} f the <i>y</i>-position function.
 * @returns {pv.Layout.Rollup} this.
 * @see pv.Scale.ordinal
 */
pv.Layout.Rollup.prototype.y = function(f) {
  this.$y = pv.functor(f);
  return this;
};

/** @private */
pv.Layout.Rollup.prototype.buildImplied = function(s) {
  if (pv.Layout.Network.prototype.buildImplied.call(this, s)) return;

  var nodes = s.nodes,
      links = s.links,
      directed = s.directed,
      n = nodes.length,
      x = [],
      y = [],
      rnindex = 0,
      rnodes = {},
      rlinks = {};

  /** @private */
  function id(i) {
    return x[i] + "," + y[i];
  }

  /* Iterate over the data, evaluating the x and y functions. */
  var stack = pv.Mark.stack, o = {parent: this};
  stack.unshift(null);
  for (var i = 0; i < n; i++) {
    o.index = i;
    stack[0] = nodes[i];
    x[i] = this.$x.apply(o, stack);
    y[i] = this.$y.apply(o, stack);
  }
  stack.shift();

  /* Compute rollup nodes. */
  for (var i = 0; i < nodes.length; i++) {
    var nodeId = id(i),
        rn = rnodes[nodeId];
    if (!rn) {
      rn = rnodes[nodeId] = pv.extend(nodes[i]);
      rn.index = rnindex++;
      rn.x = x[i];
      rn.y = y[i];
      rn.nodes = [];
    }
    rn.nodes.push(nodes[i]);
  }

  /* Compute rollup links. */
  for (var i = 0; i < links.length; i++) {
    var source = links[i].sourceNode,
        target = links[i].targetNode,
        rsource = rnodes[id(source.index)],
        rtarget = rnodes[id(target.index)],
        reverse = !directed && rsource.index > rtarget.index,
        linkId = reverse
            ? rtarget.index + "," + rsource.index
            : rsource.index + "," + rtarget.index,
        rl = rlinks[linkId];
    if (!rl) {
      rl = rlinks[linkId] = {
        sourceNode: rsource,
        targetNode: rtarget,
        linkValue: 0,
        links: []
      };
    }
    rl.links.push(links[i]);
    rl.linkValue += links[i].linkValue;
  }

  /* Export the rolled up nodes and links to the scene. */
  s.$rollup = {
    nodes: pv.values(rnodes),
    links: pv.values(rlinks)
  };
};
/**
 * Constructs a new, empty matrix network layout. Layouts are not typically
 * constructed directly; instead, they are added to an existing panel via
 * {@link pv.Mark#add}.
 *
 * @class Implements a network visualization using a matrix view. This is, in
 * effect, a visualization of the graph's <i>adjacency matrix</i>: the cell at
 * row <i>i</i>, column <i>j</i>, corresponds to the link from node <i>i</i> to
 * node <i>j</i>. The fill color of each cell is binary by default, and
 * corresponds to whether a link exists between the two nodes. If the underlying
 * graph has links with variable values, the <tt>fillStyle</tt> property can be
 * substited to use an appropriate color function, such as {@link pv.ramp}.
 *
 * <p>For undirected networks, the matrix is symmetric around the diagonal. For
 * directed networks, links in opposite directions can be rendered on opposite
 * sides of the diagonal using <tt>directed(true)</tt>. The graph is assumed to
 * be undirected by default.
 *
 * <p>The mark prototypes for this network layout are slightly different than
 * other implementations:<ul>
 *
 * <li><tt>node</tt> - unsupported; undefined. No mark is needed to visualize
 * nodes directly, as the nodes are implicit in the location (rows and columns)
 * of the links.
 *
 * <p><li><tt>link</tt> - for rendering links; typically a {@link pv.Bar}. The
 * link mark is added directly to the layout, with the data property defined as
 * all possible pairs of nodes. Each pair is represented as a
 * {@link pv.Network.Layout.Link}, though the <tt>linkValue</tt> attribute may
 * be 0 if no link exists in the graph.
 *
 * <p><li><tt>label</tt> - for rendering node labels; typically a
 * {@link pv.Label}. The label mark is added directly to the layout, with the
 * data property defined via the layout's <tt>nodes</tt> property; note,
 * however, that the nodes are duplicated so as to provide a label across the
 * top and down the side. Properties such as <tt>strokeStyle</tt> and
 * <tt>fillStyle</tt> can be overridden to compute properties from node data
 * dynamically.
 *
 * </ul>For more details on how to use this layout, see
 * {@link pv.Layout.Network}.
 *
 * @extends pv.Layout.Network
 */
pv.Layout.Matrix = function() {
  pv.Layout.Network.call(this);
  var that = this,
      n, // cached matrix size
      dx, // cached cell width
      dy, // cached cell height
      labels, // cached labels (array of strings)
      pairs, // cached pairs (array of links)
      buildImplied = that.buildImplied;

  /** @private Cache layout state to optimize properties. */
  this.buildImplied = function(s) {
    buildImplied.call(this, s);
    n = s.nodes.length;
    dx = s.width / n;
    dy = s.height / n;
    labels = s.$matrix.labels;
    pairs = s.$matrix.pairs;
  };

  /* Links are all pairs of nodes. */
  this.link
      .data(function() { return pairs; })
      .left(function() { return dx * (this.index % n); })
      .top(function() { return dy * Math.floor(this.index / n); })
      .width(function() { return dx; })
      .height(function() { return dy; })
      .lineWidth(1.5)
      .strokeStyle("#fff")
      .fillStyle(function(l) { return l.linkValue ? "#555" : "#eee"; })
      .parent = this;

  /* No special add for links! */
  delete this.link.add;

  /* Labels are duplicated for top & left. */
  this.label
      .data(function() { return labels; })
      .left(function() { return this.index & 1 ? dx * ((this.index >> 1) + .5) : null; })
      .top(function() { return this.index & 1 ? null : dy * ((this.index >> 1) + .5); })
      .textMargin(4)
      .textAlign(function() { return this.index & 1 ? "left" : "right"; })
      .textAngle(function() { return this.index & 1 ? -Math.PI / 2 : 0; });

  /* The node mark is unused. */
  delete this.node;
};

pv.Layout.Matrix.prototype = pv.extend(pv.Layout.Network)
    .property("directed", Boolean);

/**
 * Whether this matrix visualization is directed (bidirectional). By default,
 * the graph is assumed to be undirected, such that the visualization is
 * symmetric across the matrix diagonal. If the network is directed, then
 * forward links are drawn above the diagonal, while reverse links are drawn
 * below.
 *
 * @type boolean
 * @name pv.Layout.Matrix.prototype.directed
 */

/**
 * Specifies an optional sort function. The sort function follows the same
 * comparator contract required by {@link pv.Dom.Node#sort}. Specifying a sort
 * function provides an alternative to sort the nodes as they are specified by
 * the <tt>nodes</tt> property; the main advantage of doing this is that the
 * comparator function can access implicit fields populated by the network
 * layout, such as the <tt>linkDegree</tt>.
 *
 * <p>Note that matrix visualizations are particularly sensitive to order. This
 * is referred to as the seriation problem, and many different techniques exist
 * to find good node orders that emphasize clusters, such as spectral layout and
 * simulated annealing.
 *
 * @param {function} f comparator function for nodes.
 * @returns {pv.Layout.Matrix} this.
 */
pv.Layout.Matrix.prototype.sort = function(f) {
  this.$sort = f;
  return this;
};

/** @private */
pv.Layout.Matrix.prototype.buildImplied = function(s) {
  if (pv.Layout.Network.prototype.buildImplied.call(this, s)) return;

  var nodes = s.nodes,
      links = s.links,
      sort = this.$sort,
      n = nodes.length,
      index = pv.range(n),
      labels = [],
      pairs = [],
      map = {};

  s.$matrix = {labels: labels, pairs: pairs};

  /* Sort the nodes. */
  if (sort) index.sort(function(a, b) { return sort(nodes[a], nodes[b]); });

  /* Create pairs. */
  for (var i = 0; i < n; i++) {
    for (var j = 0; j < n; j++) {
      var a = index[i],
          b = index[j],
          p = {
            row: i,
            col: j,
            sourceNode: nodes[a],
            targetNode: nodes[b],
            linkValue: 0
          };
      pairs.push(map[a + "." + b] = p);
    }
  }

  /* Create labels. */
  for (var i = 0; i < n; i++) {
    var a = index[i];
    labels.push(nodes[a], nodes[a]);
  }

  /* Accumulate link values. */
  for (var i = 0; i < links.length; i++) {
    var l = links[i],
        source = l.sourceNode.index,
        target = l.targetNode.index,
        value = l.linkValue;
    map[source + "." + target].linkValue += value;
    if (!s.directed) map[target + "." + source].linkValue += value;
  }
};
// ranges (bad, satisfactory, good)
// measures (actual, forecast)
// markers (previous, goal)

/*
 * Chart design based on the recommendations of Stephen Few. Implementation
 * based on the work of Clint Ivy, Jamie Love, and Jason Davies.
 * http://projects.instantcognition.com/protovis/bulletchart/
 */

pv.Layout.Bullet = function() {
  pv.Layout.call(this);
  var that = this,
      buildImplied = that.buildImplied,
      scale = that.x = pv.Scale.linear(),
      orient,
      horizontal,
      rangeColor,
      measureColor,
      x;

  /** @private Cache layout state to optimize properties. */
  this.buildImplied = function(s) {
    buildImplied.call(this, x = s);
    orient = s.orient;
    horizontal = /^left|right$/.test(orient);
    rangeColor = pv.ramp("#bbb", "#eee")
        .domain(0, Math.max(1, x.ranges.length - 1));
    measureColor = pv.ramp("steelblue", "lightsteelblue")
        .domain(0, Math.max(1, x.measures.length - 1));
  };

  (this.range = new pv.Mark())
      .data(function() { return x.ranges; })
      .reverse(true)
      .left(function() { return orient == "left" ? 0 : null; })
      .top(function() { return orient == "top" ? 0 : null; })
      .right(function() { return orient == "right" ? 0 : null; })
      .bottom(function() { return orient == "bottom" ? 0 : null; })
      .width(function(d) { return horizontal ? scale(d) : null; })
      .height(function(d) { return horizontal ? null : scale(d); })
      .fillStyle(function() { return rangeColor(this.index); })
      .antialias(false)
      .parent = that;

  (this.measure = new pv.Mark())
      .extend(this.range)
      .data(function() { return x.measures; })
      .left(function() { return orient == "left" ? 0 : horizontal ? null : this.parent.width() / 3.25; })
      .top(function() { return orient == "top" ? 0 : horizontal ? this.parent.height() / 3.25 : null; })
      .right(function() { return orient == "right" ? 0 : horizontal ? null : this.parent.width() / 3.25; })
      .bottom(function() { return orient == "bottom" ? 0 : horizontal ? this.parent.height() / 3.25 : null; })
      .fillStyle(function() { return measureColor(this.index); })
      .parent = that;

  (this.marker = new pv.Mark())
      .data(function() { return x.markers; })
      .left(function(d) { return orient == "left" ? scale(d) : horizontal ? null : this.parent.width() / 2; })
      .top(function(d) { return orient == "top" ? scale(d) : horizontal ? this.parent.height() / 2 : null; })
      .right(function(d) { return orient == "right" ? scale(d) : null; })
      .bottom(function(d) { return orient == "bottom" ? scale(d) : null; })
      .strokeStyle("black")
      .shape("bar")
      .angle(function() { return horizontal ? 0 : Math.PI / 2; })
      .parent = that;

  (this.tick = new pv.Mark())
      .data(function() { return scale.ticks(7); })
      .left(function(d) { return orient == "left" ? scale(d) : null; })
      .top(function(d) { return orient == "top" ? scale(d) : null; })
      .right(function(d) { return orient == "right" ? scale(d) : horizontal ? null : -6; })
      .bottom(function(d) { return orient == "bottom" ? scale(d) : horizontal ? -8 : null; })
      .height(function() { return horizontal ? 6 : null; })
      .width(function() { return horizontal ? null : 6; })
      .parent = that;
};

pv.Layout.Bullet.prototype = pv.extend(pv.Layout)
    .property("orient", String) // left, right, top, bottom
    .property("ranges")
    .property("markers")
    .property("measures")
    .property("maximum", Number);

pv.Layout.Bullet.prototype.defaults = new pv.Layout.Bullet()
    .extend(pv.Layout.prototype.defaults)
    .orient("left")
    .ranges([])
    .markers([])
    .measures([]);

/** @private */
pv.Layout.Bullet.prototype.buildImplied = function(s) {
  pv.Layout.prototype.buildImplied.call(this, s);
  var size = this.parent[/^left|right$/.test(s.orient) ? "width" : "height"]();
  s.maximum = s.maximum || pv.max([].concat(s.ranges, s.markers, s.measures));
  this.x.domain(0, s.maximum).range(0, size);
};
/**
 * Abstract; see an implementing class for details.
 *
 * @class Represents a reusable interaction; applies an interactive behavior to
 * a given mark. Behaviors are themselves functions designed to be used as event
 * handlers. For example, to add pan and zoom support to any panel, say:
 *
 * <pre>    .event("mousedown", pv.Behavior.pan())
 *     .event("mousewheel", pv.Behavior.zoom())</pre>
 *
 * The behavior should be registered on the event that triggers the start of the
 * behavior. Typically, the behavior will take care of registering for any
 * additional events that are necessary. For example, dragging starts on
 * mousedown, while the drag behavior automatically listens for mousemove and
 * mouseup events on the window. By listening to the window, the behavior can
 * continue to receive mouse events even if the mouse briefly leaves the mark
 * being dragged, or even the root panel.
 *
 * <p>Each behavior implementation has specific requirements as to which events
 * it supports, and how it should be used. For example, the drag behavior
 * requires that the data associated with the mark be an object with <tt>x</tt>
 * and <tt>y</tt> attributes, such as a {@link pv.Vector}, storing the mark's
 * position. See an implementing class for details.
 *
 * @see pv.Behavior.drag
 * @see pv.Behavior.pan
 * @see pv.Behavior.point
 * @see pv.Behavior.select
 * @see pv.Behavior.zoom
 * @extends function
 */
pv.Behavior = {};
/**
 * Returns a new drag behavior to be registered on mousedown events.
 *
 * @class Implements interactive dragging starting with mousedown events.
 * Register this behavior on marks that should be draggable by the user, such as
 * the selected region for brushing and linking. This behavior can be used in
 * tandom with {@link pv.Behavior.select} to allow the selected region to be
 * dragged interactively.
 *
 * <p>After the initial mousedown event is triggered, this behavior listens for
 * mousemove and mouseup events on the window. This allows dragging to continue
 * even if the mouse temporarily leaves the mark that is being dragged, or even
 * the root panel.
 *
 * <p>This behavior requires that the data associated with the mark being
 * dragged have <tt>x</tt> and <tt>y</tt> attributes that correspond to the
 * mark's location in pixels. The mark's positional properties are not set
 * directly by this behavior; instead, the positional properties should be
 * defined as:
 *
 * <pre>    .left(function(d) d.x)
 *     .top(function(d) d.y)</pre>
 *
 * Thus, the behavior does not move the mark directly, but instead updates the
 * mark position by updating the underlying data. Note that if the positional
 * properties are defined with bottom and right (rather than top and left), the
 * drag behavior will be inverted, which will confuse users!
 *
 * <p>The drag behavior is bounded by the parent panel; the <tt>x</tt> and
 * <tt>y</tt> attributes are clamped such that the mark being dragged does not
 * extend outside the enclosing panel's bounds. To facilitate this, the drag
 * behavior also queries for <tt>dx</tt> and <tt>dy</tt> attributes on the
 * underlying data, to determine the dimensions of the bar being dragged. For
 * non-rectangular marks, the drag behavior simply treats the mark as a point,
 * which means that only the mark's center is bounded.
 *
 * <p>The mark being dragged is automatically re-rendered for each mouse event
 * as part of the drag operation. In addition, a <tt>fix</tt> attribute is
 * populated on the mark, which allows visual feedback for dragging. For
 * example, to change the mark fill color while dragging:
 *
 * <pre>    .fillStyle(function(d) d.fix ? "#ff7f0e" : "#aec7e8")</pre>
 *
 * In some cases, such as with network layouts, dragging the mark may cause
 * related marks to change, in which case additional marks may also need to be
 * rendered. This can be accomplished by listening for the drag
 * psuedo-events:<ul>
 *
 * <li>dragstart (on mousedown)
 * <li>drag (on mousemove)
 * <li>dragend (on mouseup)
 *
 * </ul>For example, to render the parent panel while dragging, thus
 * re-rendering all sibling marks:
 *
 * <pre>    .event("mousedown", pv.Behavior.drag())
 *     .event("drag", function() this.parent)</pre>
 *
 * This behavior may be enhanced in the future to allow more flexible
 * configuration of drag behavior.
 *
 * @extends pv.Behavior
 * @see pv.Behavior
 * @see pv.Behavior.select
 * @see pv.Layout.force
 */
pv.Behavior.drag = function() {
  var scene, // scene context
      index, // scene context
      p, // particle being dragged
      v1, // initial mouse-particle offset
      max;

  /** @private */
  function mousedown(d) {
    index = this.index;
    scene = this.scene;
    var m = this.mouse();
    v1 = ((p = d).fix = pv.vector(d.x, d.y)).minus(m);
    max = {
      x: this.parent.width() - (d.dx || 0),
      y: this.parent.height() - (d.dy || 0)
    };
    scene.mark.context(scene, index, function() { this.render(); });
    pv.Mark.dispatch("dragstart", scene, index);
  }

  /** @private */
  function mousemove() {
    if (!scene) return;
    scene.mark.context(scene, index, function() {
        var m = this.mouse();
        p.x = p.fix.x = Math.max(0, Math.min(v1.x + m.x, max.x));
        p.y = p.fix.y = Math.max(0, Math.min(v1.y + m.y, max.y));
        this.render();
      });
    pv.Mark.dispatch("drag", scene, index);
  }

  /** @private */
  function mouseup() {
    if (!scene) return;
    p.fix = null;
    scene.mark.context(scene, index, function() { this.render(); });
    pv.Mark.dispatch("dragend", scene, index);
    scene = null;
  }

  pv.listen(window, "mousemove", mousemove);
  pv.listen(window, "mouseup", mouseup);
  return mousedown;
};
/**
 * Returns a new point behavior to be registered on mousemove events.
 *
 * @class Implements interactive fuzzy pointing, identifying marks that are in
 * close proximity to the mouse cursor. This behavior is an alternative to the
 * native mouseover and mouseout events, improving usability. Rather than
 * requiring the user to mouseover a mark exactly, the mouse simply needs to
 * move near the given mark and a "point" event is triggered. In addition, if
 * multiple marks overlap, the point behavior can be used to identify the mark
 * instance closest to the cursor, as opposed to the one that is rendered on
 * top.
 *
 * <p>The point behavior can also identify the closest mark instance for marks
 * that produce a continuous graphic primitive. The point behavior can thus be
 * used to provide details-on-demand for both discrete marks (such as dots and
 * bars), as well as continuous marks (such as lines and areas).
 *
 * <p>This behavior is implemented by finding the closest mark instance to the
 * mouse cursor on every mousemove event. If this closest mark is within the
 * given radius threshold, which defaults to 30 pixels, a "point" psuedo-event
 * is dispatched to the given mark instance. If any mark were previously
 * pointed, it would receive a corresponding "unpoint" event. These two
 * psuedo-event types correspond to the native "mouseover" and "mouseout"
 * events, respectively. To increase the radius at which the point behavior can
 * be applied, specify an appropriate threshold to the constructor, up to
 * <tt>Infinity</tt>.
 *
 * <p>By default, the standard Cartesian distance is computed. However, with
 * some visualizations it is desirable to consider only a single dimension, such
 * as the <i>x</i>-dimension for an independent variable. In this case, the
 * collapse parameter can be set to collapse the <i>y</i> dimension:
 *
 * <pre>    .event("mousemove", pv.Behavior.point(Infinity).collapse("y"))</pre>
 *
 * <p>This behavior only listens to mousemove events on the assigned panel,
 * which is typically the root panel. The behavior will search recursively for
 * descendant marks to point. If the mouse leaves the assigned panel, the
 * behavior no longer receives mousemove events; an unpoint psuedo-event is
 * automatically dispatched to unpoint any pointed mark. Marks may be re-pointed
 * when the mouse reenters the panel.
 *
 * <p>Panels have transparent fill styles by default; this means that panels may
 * not receive the initial mousemove event to start pointing. To fix this
 * problem, either given the panel a visible fill style (such as "white"), or
 * set the <tt>events</tt> property to "all" such that the panel receives events
 * despite its transparent fill.
 *
 * <p>Note: this behavior does not currently wedge marks.
 *
 * @extends pv.Behavior
 *
 * @param {number} [r] the fuzzy radius threshold in pixels
 * @see <a href="http://www.tovigrossman.com/papers/chi2005bubblecursor.pdf"
 * >"The Bubble Cursor: Enhancing Target Acquisition by Dynamic Resizing of the
 * Cursor's Activation Area"</a> by T. Grossman &amp; R. Balakrishnan, CHI 2005.
 */
pv.Behavior.point = function(r) {
  var unpoint, // the current pointer target
      collapse = null, // dimensions to collapse
      kx = 1, // x-dimension cost scale
      ky = 1, // y-dimension cost scale
      r2 = arguments.length ? r * r : 900; // fuzzy radius

  /** @private Search for the mark closest to the mouse. */
  function search(scene, index) {
    var s = scene[index],
        point = {cost: Infinity};
    for (var i = 0, n = s.visible && s.children.length; i < n; i++) {
      var child = s.children[i], mark = child.mark, p;
      if (mark.type == "panel") {
        mark.scene = child;
        for (var j = 0, m = child.length; j < m; j++) {
          mark.index = j;
          p = search(child, j);
          if (p.cost < point.cost) point = p;
        }
        delete mark.scene;
        delete mark.index;
      } else if (mark.$handlers.point) {
        var v = mark.mouse();
        for (var j = 0, m = child.length; j < m; j++) {
          var c = child[j],
              dx = v.x - c.left - (c.width || 0) / 2,
              dy = v.y - c.top - (c.height || 0) / 2,
              dd = kx * dx * dx + ky * dy * dy;
          if (dd < point.cost) {
            point.distance = dx * dx + dy * dy;
            point.cost = dd;
            point.scene = child;
            point.index = j;
          }
        }
      }
    }
    return point;
  }

  /** @private */
  function mousemove() {
    /* If the closest mark is far away, clear the current target. */
    var point = search(this.scene, this.index);
    if ((point.cost == Infinity) || (point.distance > r2)) point = null;

    /* Unpoint the old target, if it's not the new target. */
    if (unpoint) {
      if (point
          && (unpoint.scene == point.scene)
          && (unpoint.index == point.index)) return;
      pv.Mark.dispatch("unpoint", unpoint.scene, unpoint.index);
    }

    /* Point the new target, if there is one. */
    if (unpoint = point) {
      pv.Mark.dispatch("point", point.scene, point.index);

      /* Unpoint when the mouse leaves the root panel. */
      pv.listen(this.root.canvas(), "mouseout", mouseout);
    }
  }

  /** @private */
  function mouseout(e) {
    if (unpoint && !pv.ancestor(this, e.relatedTarget)) {
      pv.Mark.dispatch("unpoint", unpoint.scene, unpoint.index);
      unpoint = null;
    }
  }

  /**
   * Sets or gets the collapse parameter. By default, the standard Cartesian
   * distance is computed. However, with some visualizations it is desirable to
   * consider only a single dimension, such as the <i>x</i>-dimension for an
   * independent variable. In this case, the collapse parameter can be set to
   * collapse the <i>y</i> dimension:
   *
   * <pre>    .event("mousemove", pv.Behavior.point(Infinity).collapse("y"))</pre>
   *
   * @function
   * @returns {pv.Behavior.point} this, or the current collapse parameter.
   * @name pv.Behavior.point.prototype.collapse
   * @param {string} [x] the new collapse parameter
   */
  mousemove.collapse = function(x) {
    if (arguments.length) {
      collapse = String(x);
      switch (collapse) {
        case "y": kx = 1; ky = 0; break;
        case "x": kx = 0; ky = 1; break;
        default: kx = 1; ky = 1; break;
      }
      return mousemove;
    }
    return collapse;
  };

  return mousemove;
};
/**
 * Returns a new select behavior to be registered on mousedown events.
 *
 * @class Implements interactive selecting starting with mousedown events.
 * Register this behavior on panels that should be selectable by the user, such
 * for brushing and linking. This behavior can be used in tandom with
 * {@link pv.Behavior.drag} to allow the selected region to be dragged
 * interactively.
 *
 * <p>After the initial mousedown event is triggered, this behavior listens for
 * mousemove and mouseup events on the window. This allows selecting to continue
 * even if the mouse temporarily leaves the assigned panel, or even the root
 * panel.
 *
 * <p>This behavior requires that the data associated with the mark being
 * dragged have <tt>x</tt>, <tt>y</tt>, <tt>dx</tt> and <tt>dy</tt> attributes
 * that correspond to the mark's location and dimensions in pixels. The mark's
 * positional properties are not set directly by this behavior; instead, the
 * positional properties should be defined as:
 *
 * <pre>    .left(function(d) d.x)
 *     .top(function(d) d.y)
 *     .width(function(d) d.dx)
 *     .height(function(d) d.dy)</pre>
 *
 * Thus, the behavior does not resize the mark directly, but instead updates the
 * selection by updating the assigned panel's underlying data. Note that if the
 * positional properties are defined with bottom and right (rather than top and
 * left), the drag behavior will be inverted, which will confuse users!
 *
 * <p>The select behavior is bounded by the assigned panel; the positional
 * attributes are clamped such that the selection does not extend outside the
 * panel's bounds.
 *
 * <p>The panel being selected is automatically re-rendered for each mouse event
 * as part of the drag operation. This behavior may be enhanced in the future to
 * allow more flexible configuration of select behavior. In some cases, such as
 * with parallel coordinates, making a selection may cause related marks to
 * change, in which case additional marks may also need to be rendered. This can
 * be accomplished by listening for the select psuedo-events:<ul>
 *
 * <li>selectstart (on mousedown)
 * <li>select (on mousemove)
 * <li>selectend (on mouseup)
 *
 * </ul>For example, to render the parent panel while selecting, thus
 * re-rendering all sibling marks:
 *
 * <pre>    .event("mousedown", pv.Behavior.drag())
 *     .event("select", function() this.parent)</pre>
 *
 * This behavior may be enhanced in the future to allow more flexible
 * configuration of the selection behavior.
 *
 * @extends pv.Behavior
 * @see pv.Behavior.drag
 */
pv.Behavior.select = function() {
  var scene, // scene context
      index, // scene context
      r, // region being selected
      m1; // initial mouse position

  /** @private */
  function mousedown(d) {
    index = this.index;
    scene = this.scene;
    m1 = this.mouse();
    r = d;
    r.x = m1.x;
    r.y = m1.y;
    r.dx = r.dy = 0;
    pv.Mark.dispatch("selectstart", scene, index);
  }

  /** @private */
  function mousemove() {
    if (!scene) return;
    scene.mark.context(scene, index, function() {
        var m2 = this.mouse();
        r.x = Math.max(0, Math.min(m1.x, m2.x));
        r.y = Math.max(0, Math.min(m1.y, m2.y));
        r.dx = Math.min(this.width(), Math.max(m2.x, m1.x)) - r.x;
        r.dy = Math.min(this.height(), Math.max(m2.y, m1.y)) - r.y;
        this.render();
      });
    pv.Mark.dispatch("select", scene, index);
  }

  /** @private */
  function mouseup() {
    if (!scene) return;
    pv.Mark.dispatch("selectend", scene, index);
    scene = null;
  }

  pv.listen(window, "mousemove", mousemove);
  pv.listen(window, "mouseup", mouseup);
  return mousedown;
};
/**
 * Returns a new resize behavior to be registered on mousedown events.
 *
 * @class Implements interactive resizing of a selection starting with mousedown
 * events. Register this behavior on selection handles that should be resizeable
 * by the user, such for brushing and linking. This behavior can be used in
 * tandom with {@link pv.Behavior.select} and {@link pv.Behavior.drag} to allow
 * the selected region to be selected and dragged interactively.
 *
 * <p>After the initial mousedown event is triggered, this behavior listens for
 * mousemove and mouseup events on the window. This allows resizing to continue
 * even if the mouse temporarily leaves the assigned panel, or even the root
 * panel.
 *
 * <p>This behavior requires that the data associated with the mark being
 * resized have <tt>x</tt>, <tt>y</tt>, <tt>dx</tt> and <tt>dy</tt> attributes
 * that correspond to the mark's location and dimensions in pixels. The mark's
 * positional properties are not set directly by this behavior; instead, the
 * positional properties should be defined as:
 *
 * <pre>    .left(function(d) d.x)
 *     .top(function(d) d.y)
 *     .width(function(d) d.dx)
 *     .height(function(d) d.dy)</pre>
 *
 * Thus, the behavior does not resize the mark directly, but instead updates the
 * size by updating the assigned panel's underlying data. Note that if the
 * positional properties are defined with bottom and right (rather than top and
 * left), the resize behavior will be inverted, which will confuse users!
 *
 * <p>The resize behavior is bounded by the assigned mark's enclosing panel; the
 * positional attributes are clamped such that the selection does not extend
 * outside the panel's bounds.
 *
 * <p>The mark being resized is automatically re-rendered for each mouse event
 * as part of the resize operation. This behavior may be enhanced in the future
 * to allow more flexible configuration. In some cases, such as with parallel
 * coordinates, resizing the selection may cause related marks to change, in
 * which case additional marks may also need to be rendered. This can be
 * accomplished by listening for the select psuedo-events:<ul>
 *
 * <li>resizestart (on mousedown)
 * <li>resize (on mousemove)
 * <li>resizeend (on mouseup)
 *
 * </ul>For example, to render the parent panel while resizing, thus
 * re-rendering all sibling marks:
 *
 * <pre>    .event("mousedown", pv.Behavior.resize("left"))
 *     .event("resize", function() this.parent)</pre>
 *
 * This behavior may be enhanced in the future to allow more flexible
 * configuration of the selection behavior.
 *
 * @extends pv.Behavior
 * @see pv.Behavior.select
 * @see pv.Behavior.drag
 */
pv.Behavior.resize = function(side) {
  var scene, // scene context
      index, // scene context
      r, // region being selected
      m1; // initial mouse position

  /** @private */
  function mousedown(d) {
    index = this.index;
    scene = this.scene;
    m1 = this.mouse();
    r = d;
    switch (side) {
      case "left": m1.x = r.x + r.dx; break;
      case "right": m1.x = r.x; break;
      case "top": m1.y = r.y + r.dy; break;
      case "bottom": m1.y = r.y; break;
    }
    pv.Mark.dispatch("resizestart", scene, index);
  }

  /** @private */
  function mousemove() {
    if (!scene) return;
    scene.mark.context(scene, index, function() {
        var m2 = this.mouse();
        r.x = Math.max(0, Math.min(m1.x, m2.x));
        r.y = Math.max(0, Math.min(m1.y, m2.y));
        r.dx = Math.min(this.parent.width(), Math.max(m2.x, m1.x)) - r.x;
        r.dy = Math.min(this.parent.height(), Math.max(m2.y, m1.y)) - r.y;
        this.render();
      });
    pv.Mark.dispatch("resize", scene, index);
  }

  /** @private */
  function mouseup() {
    if (!scene) return;
    pv.Mark.dispatch("resizeend", scene, index);
    scene = null;
  }

  pv.listen(window, "mousemove", mousemove);
  pv.listen(window, "mouseup", mouseup);
  return mousedown;
};
/**
 * Returns a new pan behavior to be registered on mousedown events.
 *
 * @class Implements interactive panning starting with mousedown events.
 * Register this behavior on panels to allow panning. This behavior can be used
 * in tandem with {@link pv.Behavior.zoom} to allow both panning and zooming:
 *
 * <pre>    .event("mousedown", pv.Behavior.pan())
 *     .event("mousewheel", pv.Behavior.zoom())</pre>
 *
 * The pan behavior currently supports only mouse events; support for keyboard
 * shortcuts to improve accessibility may be added in the future.
 *
 * <p>After the initial mousedown event is triggered, this behavior listens for
 * mousemove and mouseup events on the window. This allows panning to continue
 * even if the mouse temporarily leaves the panel that is being panned, or even
 * the root panel.
 *
 * <p>The implementation of this behavior relies on the panel's
 * <tt>transform</tt> property, which specifies a matrix transformation that is
 * applied to child marks. Note that the transform property only affects the
 * panel's children, but not the panel itself; therefore the panel's fill and
 * stroke will not change when the contents are panned.
 *
 * <p>Panels have transparent fill styles by default; this means that panels may
 * not receive the initial mousedown event to start panning. To fix this
 * problem, either given the panel a visible fill style (such as "white"), or
 * set the <tt>events</tt> property to "all" such that the panel receives events
 * despite its transparent fill.
 *
 * <p>The pan behavior has optional support for bounding. If enabled, the user
 * will not be able to pan the panel outside of the initial bounds. This feature
 * is designed to work in conjunction with the zoom behavior; otherwise,
 * bounding the panel effectively disables all panning.
 *
 * @extends pv.Behavior
 * @see pv.Behavior.zoom
 * @see pv.Panel#transform
 */
pv.Behavior.pan = function() {
  var scene, // scene context
      index, // scene context
      m1, // transformation matrix at the start of panning
      v1, // mouse location at the start of panning
      k, // inverse scale
      bound; // whether to bound to the panel

  /** @private */
  function mousedown() {
    index = this.index;
    scene = this.scene;
    v1 = pv.vector(pv.event.pageX, pv.event.pageY);
    m1 = this.transform();
    k = 1 / (m1.k * this.scale);
    if (bound) {
      bound = {
        x: (1 - m1.k) * this.width(),
        y: (1 - m1.k) * this.height()
      };
    }
  }

  /** @private */
  function mousemove() {
    if (!scene) return;
    scene.mark.context(scene, index, function() {
        var x = (pv.event.pageX - v1.x) * k,
            y = (pv.event.pageY - v1.y) * k,
            m = m1.translate(x, y);
        if (bound) {
          m.x = Math.max(bound.x, Math.min(0, m.x));
          m.y = Math.max(bound.y, Math.min(0, m.y));
        }
        this.transform(m).render();
      });
    pv.Mark.dispatch("pan", scene, index);
  }

  /** @private */
  function mouseup() {
    scene = null;
  }

  /**
   * Sets or gets the bound parameter. If bounding is enabled, the user will not
   * be able to pan outside the initial panel bounds; this typically applies
   * only when the pan behavior is used in tandem with the zoom behavior.
   * Bounding is not enabled by default.
   *
   * <p>Note: enabling bounding after panning has already occurred will not
   * immediately reset the transform. Bounding should be enabled before the
   * panning behavior is applied.
   *
   * @function
   * @returns {pv.Behavior.pan} this, or the current bound parameter.
   * @name pv.Behavior.pan.prototype.bound
   * @param {boolean} [x] the new bound parameter.
   */
  mousedown.bound = function(x) {
    if (arguments.length) {
      bound = Boolean(x);
      return this;
    }
    return Boolean(bound);
  };

  pv.listen(window, "mousemove", mousemove);
  pv.listen(window, "mouseup", mouseup);
  return mousedown;
};
/**
 * Returns a new zoom behavior to be registered on mousewheel events.
 *
 * @class Implements interactive zooming using mousewheel events. Register this
 * behavior on panels to allow zooming. This behavior can be used in tandem with
 * {@link pv.Behavior.pan} to allow both panning and zooming:
 *
 * <pre>    .event("mousedown", pv.Behavior.pan())
 *     .event("mousewheel", pv.Behavior.zoom())</pre>
 *
 * The zoom behavior currently supports only mousewheel events; support for
 * keyboard shortcuts and gesture events to improve accessibility may be added
 * in the future.
 *
 * <p>The implementation of this behavior relies on the panel's
 * <tt>transform</tt> property, which specifies a matrix transformation that is
 * applied to child marks. Note that the transform property only affects the
 * panel's children, but not the panel itself; therefore the panel's fill and
 * stroke will not change when the contents are zoomed. The built-in support for
 * transforms only supports uniform scaling and translates, which is sufficient
 * for panning and zooming.  Note that this is not a strict geometric
 * transformation, as the <tt>lineWidth</tt> property is scale-aware: strokes
 * are drawn at constant size independent of scale.
 *
 * <p>Panels have transparent fill styles by default; this means that panels may
 * not receive mousewheel events to zoom. To fix this problem, either given the
 * panel a visible fill style (such as "white"), or set the <tt>events</tt>
 * property to "all" such that the panel receives events despite its transparent
 * fill.
 *
 * <p>The zoom behavior has optional support for bounding. If enabled, the user
 * will not be able to zoom out farther than the initial bounds. This feature is
 * designed to work in conjunction with the pan behavior.
 *
 * @extends pv.Behavior
 * @see pv.Panel#transform
 * @see pv.Mark#scale
 * @param {number} speed
 */
pv.Behavior.zoom = function(speed) {
  var bound; // whether to bound to the panel

  if (!arguments.length) speed = 1 / 48;

  /** @private */
  function mousewheel() {
    var v = this.mouse(),
        k = pv.event.wheel * speed,
        m = this.transform().translate(v.x, v.y)
            .scale((k < 0) ? (1e3 / (1e3 - k)) : ((1e3 + k) / 1e3))
            .translate(-v.x, -v.y);
    if (bound) {
      m.k = Math.max(1, m.k);
      m.x = Math.max((1 - m.k) * this.width(), Math.min(0, m.x));
      m.y = Math.max((1 - m.k) * this.height(), Math.min(0, m.y));
    }
    this.transform(m).render();
    pv.Mark.dispatch("zoom", this.scene, this.index);
  }

  /**
   * Sets or gets the bound parameter. If bounding is enabled, the user will not
   * be able to zoom out farther than the initial panel bounds. Bounding is not
   * enabled by default. If this behavior is used in tandem with the pan
   * behavior, both should use the same bound parameter.
   *
   * <p>Note: enabling bounding after zooming has already occurred will not
   * immediately reset the transform. Bounding should be enabled before the zoom
   * behavior is applied.
   *
   * @function
   * @returns {pv.Behavior.zoom} this, or the current bound parameter.
   * @name pv.Behavior.zoom.prototype.bound
   * @param {boolean} [x] the new bound parameter.
   */
  mousewheel.bound = function(x) {
    if (arguments.length) {
      bound = Boolean(x);
      return this;
    }
    return Boolean(bound);
  };

  return mousewheel;
};
/**
 * @ignore
 * @namespace
 */
pv.Geo = function() {};
/**
 * Abstract; not implemented. There is no explicit constructor; this class
 * merely serves to document the representation used by {@link pv.Geo.scale}.
 *
 * @class Represents a pair of geographic coordinates.
 *
 * @name pv.Geo.LatLng
 * @see pv.Geo.scale
 */

/**
 * The <i>latitude</i> coordinate in degrees; positive is North.
 *
 * @type number
 * @name pv.Geo.LatLng.prototype.lat
 */

/**
 * The <i>longitude</i> coordinate in degrees; positive is East.
 *
 * @type number
 * @name pv.Geo.LatLng.prototype.lng
 */
/**
 * Abstract; not implemented. There is no explicit constructor; this class
 * merely serves to document the representation used by {@link pv.Geo.scale}.
 *
 * @class Represents a geographic projection. This class provides the core
 * implementation for {@link pv.Geo.scale}s, mapping between geographic
 * coordinates (latitude and longitude) and normalized screen space in the range
 * [-1,1]. The remaining mapping between normalized screen space and actual
 * pixels is performed by <tt>pv.Geo.scale</tt>.
 *
 * <p>Many geographic projections have a point around which the projection is
 * centered. Rather than have each implementation add support for a
 * user-specified center point, the <tt>pv.Geo.scale</tt> translates the
 * geographic coordinates relative to the center point for both the forward and
 * inverse projection.
 *
 * <p>In general, this class should not be used directly, unless the desire is
 * to implement a new geographic projection. Instead, use <tt>pv.Geo.scale</tt>.
 * Implementations are not required to implement inverse projections, but are
 * needed for some forms of interactivity. Also note that some inverse
 * projections are ambiguous, such as the connecting points in Dymaxian maps.
 *
 * @name pv.Geo.Projection
 * @see pv.Geo.scale
 */

/**
 * The <i>forward</i> projection.
 *
 * @function
 * @name pv.Geo.Projection.prototype.project
 * @param {pv.Geo.LatLng} latlng the latitude and longitude to project.
 * @returns {pv.Vector} the xy-coordinates of the given point.
 */

/**
 * The <i>inverse</i> projection; optional.
 *
 * @function
 * @name pv.Geo.Projection.prototype.invert
 * @param {pv.Vector} xy the x- and y-coordinates to invert.
 * @returns {pv.Geo.LatLng} the latitude and longitude of the given point.
 */
/**
 * The built-in projections.
 *
 * @see pv.Geo.Projection
 * @namespace
 */
pv.Geo.projections = {

  /** @see http://en.wikipedia.org/wiki/Mercator_projection */
  mercator: {
    project: function(latlng) {
      return {
          x: latlng.lng / 180,
          y: latlng.lat > 85 ? 1 : latlng.lat < -85 ? -1
              : Math.log(Math.tan(Math.PI / 4
              + pv.radians(latlng.lat) / 2)) / Math.PI
        };
    },
    invert: function(xy) {
      return {
          lng: xy.x * 180,
          lat: pv.degrees(2 * Math.atan(Math.exp(xy.y * Math.PI)) - Math.PI / 2)
        };
    }
  },

  /** @see http://en.wikipedia.org/wiki/Gall-Peters_projection */
  "gall-peters": {
    project: function(latlng) {
      return {
          x: latlng.lng / 180,
          y: Math.sin(pv.radians(latlng.lat))
        };
    },
    invert: function(xy) {
      return {
          lng: xy.x * 180,
          lat: pv.degrees(Math.asin(xy.y))
        };
    }
  },

  /** @see http://en.wikipedia.org/wiki/Sinusoidal_projection */
  sinusoidal: {
    project: function(latlng) {
      return {
          x: pv.radians(latlng.lng) * Math.cos(pv.radians(latlng.lat)) / Math.PI,
          y: latlng.lat / 90
        };
    },
    invert: function(xy) {
      return {
          lng: pv.degrees((xy.x * Math.PI) / Math.cos(xy.y * Math.PI / 2)),
          lat: xy.y * 90
        };
    }
  },

  /** @see http://en.wikipedia.org/wiki/Aitoff_projection */
  aitoff: {
    project: function(latlng) {
      var l = pv.radians(latlng.lng),
          f = pv.radians(latlng.lat),
          a = Math.acos(Math.cos(f) * Math.cos(l / 2));
      return {
          x: 2 * (a ? (Math.cos(f) * Math.sin(l / 2) * a / Math.sin(a)) : 0) / Math.PI,
          y: 2 * (a ? (Math.sin(f) * a / Math.sin(a)) : 0) / Math.PI
        };
    },
    invert: function(xy) {
      var x = xy.x * Math.PI / 2,
          y = xy.y * Math.PI / 2;
      return {
          lng: pv.degrees(x / Math.cos(y)),
          lat: pv.degrees(y)
        };
    }
  },

  /** @see http://en.wikipedia.org/wiki/Hammer_projection */
  hammer: {
    project: function(latlng) {
      var l = pv.radians(latlng.lng),
          f = pv.radians(latlng.lat),
          c = Math.sqrt(1 + Math.cos(f) * Math.cos(l / 2));
      return {
          x: 2 * Math.SQRT2 * Math.cos(f) * Math.sin(l / 2) / c / 3,
          y: Math.SQRT2 * Math.sin(f) / c / 1.5
        };
    },
    invert: function(xy) {
      var x = xy.x * 3,
          y = xy.y * 1.5,
          z = Math.sqrt(1 - x * x / 16 - y * y / 4);
      return {
          lng: pv.degrees(2 * Math.atan2(z * x, 2 * (2 * z * z - 1))),
          lat: pv.degrees(Math.asin(z * y))
        };
    }
  },

  /** The identity or "none" projection. */
  identity: {
    project: function(latlng) {
      return {
          x: latlng.lng / 180,
          y: latlng.lat / 90
        };
    },
    invert: function(xy) {
      return {
          lng: xy.x * 180,
          lat: xy.y * 90
        };
    }
  }
};
/**
 * Returns a geographic scale. The arguments to this constructor are optional,
 * and equivalent to calling {@link #projection}.
 *
 * @class Represents a geographic scale; a mapping between latitude-longitude
 * coordinates and screen pixel coordinates. By default, the domain is inferred
 * from the geographic coordinates, so that the domain fills the output range.
 *
 * <p>Note that geographic scales are two-dimensional transformations, rather
 * than the one-dimensional bidrectional mapping typical of other scales.
 * Rather than mapping (for example) between a numeric domain and a numeric
 * range, geographic scales map between two coordinate objects: {@link
 * pv.Geo.LatLng} and {@link pv.Vector}.
 *
 * @param {pv.Geo.Projection} [p] optional projection.
 * @see pv.Geo.scale#ticks
 */
pv.Geo.scale = function(p) {
  var rmin = {x: 0, y: 0}, // default range minimum
      rmax = {x: 1, y: 1}, // default range maximum
      d = [], // default domain
      j = pv.Geo.projections.identity, // domain <-> normalized range
      x = pv.Scale.linear(-1, 1).range(0, 1), // normalized <-> range
      y = pv.Scale.linear(-1, 1).range(1, 0), // normalized <-> range
      c = {lng: 0, lat: 0}, // Center Point
      lastLatLng, // cached latlng
      lastPoint; // cached point

  /** @private */
  function scale(latlng) {
    if (!lastLatLng
        || (latlng.lng != lastLatLng.lng)
        || (latlng.lat != lastLatLng.lat)) {
      lastLatLng = latlng;
      var p = project(latlng);
      lastPoint = {x: x(p.x), y: y(p.y)};
    }
    return lastPoint;
  }

  /** @private */
  function project(latlng) {
    var offset = {lng: latlng.lng - c.lng, lat: latlng.lat};
    return j.project(offset);
  }

  /** @private */
  function invert(xy) {
    var latlng = j.invert(xy);
    latlng.lng += c.lng;
    return latlng;
  }

  /** Returns the projected x-coordinate. */
  scale.x = function(latlng) {
    return scale(latlng).x;
  };

  /** Returns the projected y-coordinate. */
  scale.y = function(latlng) {
    return scale(latlng).y;
  };

  /**
   * Abstract; this is a local namespace on a given geographic scale.
   *
   * @namespace Tick functions for geographic scales. Because geographic scales
   * represent two-dimensional transformations (as opposed to one-dimensional
   * transformations typical of other scales), the tick values are similarly
   * represented as two-dimensional coordinates in the input domain, i.e.,
   * {@link pv.Geo.LatLng} objects.
   *
   * <p>Also, note that non-rectilinear projections, such as sinsuoidal and
   * aitoff, may not produce straight lines for constant longitude or constant
   * latitude. Therefore the returned array of ticks is a two-dimensional array,
   * sampling various latitudes as constant longitude, and vice versa.
   *
   * <p>The tick lines can therefore be approximated as polylines, either with
   * "linear" or "cardinal" interpolation. This is not as accurate as drawing
   * the true curve through the projection space, but is usually sufficient.
   *
   * @name pv.Geo.scale.prototype.ticks
   * @see pv.Geo.scale
   * @see pv.Geo.LatLng
   * @see pv.Line#interpolate
   */
  scale.ticks = {

    /**
     * Returns longitude ticks.
     *
     * @function
     * @param {number} [m] the desired number of ticks.
     * @returns {array} a nested array of <tt>pv.Geo.LatLng</tt> ticks.
     * @name pv.Geo.scale.prototype.ticks.prototype.lng
     */
    lng: function(m) {
      var lat, lng;
      if (d.length > 1) {
        var s = pv.Scale.linear();
        if (m == undefined) m = 10;
        lat = s.domain(d, function(d) { return d.lat; }).ticks(m);
        lng = s.domain(d, function(d) { return d.lng; }).ticks(m);
      } else {
        lat = pv.range(-80, 81, 10);
        lng = pv.range(-180, 181, 10);
      }
      return lng.map(function(lng) {
        return lat.map(function(lat) {
          return {lat: lat, lng: lng};
        });
      });
    },

    /**
     * Returns latitude ticks.
     *
     * @function
     * @param {number} [m] the desired number of ticks.
     * @returns {array} a nested array of <tt>pv.Geo.LatLng</tt> ticks.
     * @name pv.Geo.scale.prototype.ticks.prototype.lat
     */
    lat: function(m) {
      return pv.transpose(scale.ticks.lng(m));
    }
  };

  /**
   * Inverts the specified value in the output range, returning the
   * corresponding value in the input domain. This is frequently used to convert
   * the mouse location (see {@link pv.Mark#mouse}) to a value in the input
   * domain. Inversion is only supported for numeric ranges, and not colors.
   *
   * <p>Note that this method does not do any rounding or bounds checking. If
   * the input domain is discrete (e.g., an array index), the returned value
   * should be rounded. If the specified <tt>y</tt> value is outside the range,
   * the returned value may be equivalently outside the input domain.
   *
   * @function
   * @name pv.Geo.scale.prototype.invert
   * @param {number} y a value in the output range (a pixel location).
   * @returns {number} a value in the input domain.
   */
  scale.invert = function(p) {
    return invert({x: x.invert(p.x), y: y.invert(p.y)});
  };

  /**
   * Sets or gets the input domain. Note that unlike quantitative scales, the
   * domain cannot be reduced to a simple rectangle (i.e., minimum and maximum
   * values for latitude and longitude). Instead, the domain values must be
   * projected to normalized space, effectively finding the domain in normalized
   * space rather than in terms of latitude and longitude. Thus, changing the
   * projection requires recomputing the normalized domain.
   *
   * <p>This method can be invoked several ways:
   *
   * <p>1. <tt>domain(values...)</tt>
   *
   * <p>Specifying the domain as a series of {@link pv.Geo.LatLng}s is the most
   * explicit and recommended approach. However, if the domain values are
   * derived from data, you may find the second method more appropriate.
   *
   * <p>2. <tt>domain(array, f)</tt>
   *
   * <p>Rather than enumerating the domain explicitly, you can specify a single
   * argument of an array. In addition, you can specify an optional accessor
   * function to extract the domain values (as {@link pv.Geo.LatLng}s) from the
   * array. If the specified array has fewer than two elements, this scale will
   * default to the full normalized domain.
   *
   * <p>2. <tt>domain()</tt>
   *
   * <p>Invoking the <tt>domain</tt> method with no arguments returns the
   * current domain as an array.
   *
   * @function
   * @name pv.Geo.scale.prototype.domain
   * @param {...} domain... domain values.
   * @returns {pv.Geo.scale} <tt>this</tt>, or the current domain.
   */
  scale.domain = function(array, f) {
    if (arguments.length) {
      d = (array instanceof Array)
          ? ((arguments.length > 1) ? pv.map(array, f) : array)
          : Array.prototype.slice.call(arguments);
      if (d.length > 1) {
        var lngs = d.map(function(c) { return c.lng; });
        var lats = d.map(function(c) { return c.lat; });
        c = {
          lng: (pv.max(lngs) + pv.min(lngs)) / 2,
          lat: (pv.max(lats) + pv.min(lats)) / 2
        };
        var n = d.map(project); // normalized domain
        x.domain(n, function(p) { return p.x; });
        y.domain(n, function(p) { return p.y; });
      } else {
        c = {lng: 0, lat: 0};
        x.domain(-1, 1);
        y.domain(-1, 1);
      }
      lastLatLng = null; // invalidate the cache
      return this;
    }
    return d;
  };

  /**
   * Sets or gets the output range. This method can be invoked several ways:
   *
   * <p>1. <tt>range(min, max)</tt>
   *
   * <p>If two objects are specified, the arguments should be {@link pv.Vector}s
   * which specify the minimum and maximum values of the x- and y-coordinates
   * explicitly.
   *
   * <p>2. <tt>range(width, height)</tt>
   *
   * <p>If two numbers are specified, the arguments specify the maximum values
   * of the x- and y-coordinates explicitly; the minimum values are implicitly
   * zero.
   *
   * <p>3. <tt>range()</tt>
   *
   * <p>Invoking the <tt>range</tt> method with no arguments returns the current
   * range as an array of two {@link pv.Vector}s: the minimum (top-left) and
   * maximum (bottom-right) values.
   *
   * @function
   * @name pv.Geo.scale.prototype.range
   * @param {...} range... range values.
   * @returns {pv.Geo.scale} <tt>this</tt>, or the current range.
   */
  scale.range = function(min, max) {
    if (arguments.length) {
      if (typeof min == "object") {
        rmin = {x: Number(min.x), y: Number(min.y)};
        rmax = {x: Number(max.x), y: Number(max.y)};
      } else {
        rmin = {x: 0, y: 0};
        rmax = {x: Number(min), y: Number(max)};
      }
      x.range(rmin.x, rmax.x);
      y.range(rmax.y, rmin.y); // XXX flipped?
      lastLatLng = null; // invalidate the cache
      return this;
    }
    return [rmin, rmax];
  };

  /**
   * Sets or gets the projection. This method can be invoked several ways:
   *
   * <p>1. <tt>projection(string)</tt>
   *
   * <p>Specifying a string sets the projection to the given named projection in
   * {@link pv.Geo.projections}. If no such projection is found, the identity
   * projection is used.
   *
   * <p>2. <tt>projection(object)</tt>
   *
   * <p>Specifying an object sets the projection to the given custom projection,
   * which must implement the <i>forward</i> and <i>inverse</i> methods per the
   * {@link pv.Geo.Projection} interface.
   *
   * <p>3. <tt>projection()</tt>
   *
   * <p>Invoking the <tt>projection</tt> method with no arguments returns the
   * current object that defined the projection.
   *
   * @function
   * @name pv.Scale.geo.prototype.projection
   * @param {...} range... range values.
   * @returns {pv.Scale.geo} <tt>this</tt>, or the current range.
   */
  scale.projection = function(p) {
    if (arguments.length) {
      j = typeof p == "string"
          ? pv.Geo.projections[p] || pv.Geo.projections.identity
          : p;
      return this.domain(d); // recompute normalized domain
    }
    return p;
  };

  /**
   * Returns a view of this scale by the specified accessor function <tt>f</tt>.
   * Given a scale <tt>g</tt>, <tt>g.by(function(d) d.foo)</tt> is equivalent to
   * <tt>function(d) g(d.foo)</tt>. This method should be used judiciously; it
   * is typically more clear to invoke the scale directly, passing in the value
   * to be scaled.
   *
   * @function
   * @name pv.Geo.scale.prototype.by
   * @param {function} f an accessor function.
   * @returns {pv.Geo.scale} a view of this scale by the specified accessor
   * function.
   */
  scale.by = function(f) {
    function by() { return scale(f.apply(this, arguments)); }
    for (var method in scale) by[method] = scale[method];
    return by;
  };

  if (arguments.length) scale.projection(p);
  return scale;
};
