cytoscape-spread/cytoscape-spread.js

The Spread physics simulation layout for Cytoscape.js

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/* 0 */
/***/ (function(module, exports, __webpack_require__) {

var Thread = __webpack_require__(3).Thread;

var Voronoi = __webpack_require__(2);

var defaults = {
  animate: true, // Whether to show the layout as it's running
  ready: undefined, // Callback on layoutready
  stop: undefined, // Callback on layoutstop
  fit: true, // Reset viewport to fit default simulationBounds
  minDist: 20, // Minimum distance between nodes
  padding: 20, // Padding
  expandingFactor: -1.0, // If the network does not satisfy the minDist
  // criterium then it expands the network of this amount
  // If it is set to -1.0 the amount of expansion is automatically
  // calculated based on the minDist, the aspect ratio and the
  // number of nodes
  prelayout: { name: 'cose' }, // Layout options for the first phase
  maxExpandIterations: 4, // Maximum number of expanding iterations
  boundingBox: undefined, // Constrain layout bounds; { x1, y1, x2, y2 } or { x1, y1, w, h }
  randomize: false // Uses random initial node positions on true
};

function SpreadLayout( options ) {
  var opts = this.options = {};
  for( var i in defaults ){ opts[i] = defaults[i]; }
  for( var i in options ){ opts[i] = options[i]; }
}

SpreadLayout.prototype.run = function() {

  var layout = this;
  var options = this.options;
  var cy = options.cy;

  var bb = options.boundingBox || { x1: 0, y1: 0, w: cy.width(), h: cy.height() };
  if( bb.x2 === undefined ){ bb.x2 = bb.x1 + bb.w; }
  if( bb.w === undefined ){ bb.w = bb.x2 - bb.x1; }
  if( bb.y2 === undefined ){ bb.y2 = bb.y1 + bb.h; }
  if( bb.h === undefined ){ bb.h = bb.y2 - bb.y1; }

  var nodes = cy.nodes();
  var edges = cy.edges();
  var cWidth = cy.width();
  var cHeight = cy.height();
  var simulationBounds = bb;
  var padding = options.padding;
  var simBBFactor = Math.max( 1, Math.log(nodes.length) * 0.8 );

  if( nodes.length < 100 ){
    simBBFactor /= 2;
  }

  layout.trigger( {
    type: 'layoutstart',
    layout: layout
  } );

  var simBB = {
    x1: 0,
    y1: 0,
    x2: cWidth * simBBFactor,
    y2: cHeight * simBBFactor
  };

  if( simulationBounds ) {
    simBB.x1 = simulationBounds.x1;
    simBB.y1 = simulationBounds.y1;
    simBB.x2 = simulationBounds.x2;
    simBB.y2 = simulationBounds.y2;
  }

  simBB.x1 += padding;
  simBB.y1 += padding;
  simBB.x2 -= padding;
  simBB.y2 -= padding;

  var width = simBB.x2 - simBB.x1;
  var height = simBB.y2 - simBB.y1;

  // Get start time
  var startTime = Date.now();

  // layout doesn't work with just 1 node
  if( nodes.size() <= 1 ) {
    nodes.positions( {
      x: Math.round( ( simBB.x1 + simBB.x2 ) / 2 ),
      y: Math.round( ( simBB.y1 + simBB.y2 ) / 2 )
    } );

    if( options.fit ) {
      cy.fit( options.padding );
    }

    // Get end time
    var endTime = Date.now();
    console.info( "Layout on " + nodes.size() + " nodes took " + ( endTime - startTime ) + " ms" );

    layout.one( "layoutready", options.ready );
    layout.trigger( "layoutready" );

    layout.one( "layoutstop", options.stop );
    layout.trigger( "layoutstop" );

    return;
  }

  // First I need to create the data structure to pass to the worker
  var pData = {
    'width': width,
    'height': height,
    'minDist': options.minDist,
    'expFact': options.expandingFactor,
    'expIt': 0,
    'maxExpIt': options.maxExpandIterations,
    'vertices': [],
    'edges': [],
    'startTime': startTime
  };

  for(var i = nodes.length - 1; i >= 0 ; i--) {
    var nodeId = nodes[i].id();
    var pos = nodes[i].position();

    if( options.randomize ){
      pos = {
        x: Math.round( simBB.x1 + (simBB.x2 - simBB.x1) * Math.random() ),
        y: Math.round( simBB.y1 + (simBB.y2 - simBB.y1) * Math.random() )
      };
    }

    pData[ 'vertices' ].push( {
      id: nodeId,
      x: pos.x,
      y: pos.y
    } );
  };

  for(var i = edges.length - 1; i >= 0; i--) {
    var srcNodeId = edges[i].source().id();
    var tgtNodeId = edges[i].target().id();
    pData[ 'edges' ].push( {
      src: srcNodeId,
      tgt: tgtNodeId
    } );
  };

  //Decleration
  var t1 = layout.thread;

  // reuse old thread if possible
  if( !t1 || t1.stopped() ){
    t1 = layout.thread = Thread();

    // And to add the required scripts
    t1.require( Voronoi, 'Voronoi' );
  }

  function setPositions( pData ){ //console.log('set posns')
    // First we retrieve the important data
    // var expandIteration = pData[ 'expIt' ];
    var dataVertices = pData[ 'vertices' ];
    var vertices = [];
    for( var i = 0; i < dataVertices.length; ++i ) {
      var dv = dataVertices[ i ];
      vertices[ dv.id ] = {
        x: dv.x,
        y: dv.y
      };
    }
    /*
     * FINALLY:
     *
     * We position the nodes based on the calculation
     */
    nodes.positions(
      function( node, i ) {
        // Perform 2.x and 1.x backwards compatibility check
        if( typeof node === "number" ){
          node = i;
        }
        var id = node.id()
        var vertex = vertices[ id ];

        return {
          x: Math.round( simBB.x1 + vertex.x ),
          y: Math.round( simBB.y1 + vertex.y )
        };
      } );

    if( options.fit ) {
      cy.fit( options.padding );
    }
  }

  var didLayoutReady = false;
  t1.on('message', function(e){
    var pData = e.message; //console.log('message', e)

    if( !options.animate ){
      return;
    }

    setPositions( pData );

    if( !didLayoutReady ){
      layout.trigger( "layoutready" );

      didLayoutReady = true;
    }
  });

  layout.one( "layoutready", options.ready );

  if( options.prelayout ){
    var prelayout = cy.makeLayout( options.prelayout );
    var promise = prelayout.promiseOn('layoutstop');

    promise.then( runVoronoi );

    prelayout.run();
  } else {
    runVoronoi();
  }

  function runVoronoi(){
    t1.pass( pData ).run( function( pData ) {

      function cellCentroid( cell ) {
        var hes = cell.halfedges;
        var area = 0,
          x = 0,
          y = 0;
        var p1, p2, f;

        for( var i = 0; i < hes.length; ++i ) {
          p1 = hes[ i ].getEndpoint();
          p2 = hes[ i ].getStartpoint();

          area += p1.x * p2.y;
          area -= p1.y * p2.x;

          f = p1.x * p2.y - p2.x * p1.y;
          x += ( p1.x + p2.x ) * f;
          y += ( p1.y + p2.y ) * f;
        }

        area /= 2;
        f = area * 6;
        return {
          x: x / f,
          y: y / f
        };
      }

      function sitesDistance( ls, rs ) {
        var dx = ls.x - rs.x;
        var dy = ls.y - rs.y;
        return Math.sqrt( dx * dx + dy * dy );
      }

      Voronoi = _ref_('Voronoi');

      // I need to retrieve the important data
      var lWidth = pData[ 'width' ];
      var lHeight = pData[ 'height' ];
      var lMinDist = pData[ 'minDist' ];
      var lExpFact = pData[ 'expFact' ];
      var lMaxExpIt = pData[ 'maxExpIt' ];

      // Prepare the data to output
      var savePositions = function(){
        pData[ 'width' ] = lWidth;
        pData[ 'height' ] = lHeight;
        pData[ 'expIt' ] = expandIteration;
        pData[ 'expFact' ] = lExpFact;

        pData[ 'vertices' ] = [];
        for( var i = 0; i < fv.length; ++i ) {
          pData[ 'vertices' ].push( {
            id: fv[ i ].label,
            x: fv[ i ].x,
            y: fv[ i ].y
          } );
        }
      };

      var messagePositions = function(){
        broadcast( pData );
      };

      var dataVertices = pData[ 'vertices' ];
      var dataEdges = pData[ 'edges' ];

      var x1 = Infinity;
      var x2 = -Infinity;
      var y1 = Infinity;
      var y2 = -Infinity;

      dataVertices.forEach(function(v){
        x1 = Math.min( v.x, x1 );
        x2 = Math.max( v.x, x2 );
        y1 = Math.min( v.y, y1 );
        y2 = Math.max( v.y, y2 );
      });

      var scale = function(x, minX, maxX, scaledMinX, scaledMaxX){
        var p = (x - minX) / (maxX - minX);

        if( isNaN(p) ){
          p = Math.random();
        }

        return scaledMinX + (scaledMaxX - scaledMinX) * p;
      };

      // NB Voronoi expects all nodes to be on { x in [0, lWidth], y in [0, lHeight] }
      var fv = dataVertices.map(function(v){
        return {
          label: v.id,
          x: scale( v.x, x1, x2, 0, lWidth ),
          y: scale( v.y, y1, y2, 0, lHeight )
        };
      });

      savePositions();
      messagePositions();

      if( lMaxExpIt <= 0 ){
        return pData;
      }

      /*
       * SECOND STEP: Tiding up of the graph.
       *
       * We use the method described by Gansner and North, based on Voronoi
       * diagrams.
       *
       * Ref: doi:10.1007/3-540-37623-2_28
       */

      // We calculate the Voronoi diagram dor the position of the nodes
      var voronoi = new Voronoi();
      var bbox = {
        xl: 0,
        xr: lWidth,
        yt: 0,
        yb: lHeight
      };
      var vSites = [];
      for( var i = 0; i < fv.length; ++i ) {
        vSites[ fv[ i ].label ] = fv[ i ];
      }

      function checkMinDist( ee ) {
        var infractions = 0;
        // Then we check if the minimum distance is satisfied
        for( var eei = 0; eei < ee.length; ++eei ) {
          var e = ee[ eei ];
          if( ( e.lSite != null ) && ( e.rSite != null ) && sitesDistance( e.lSite, e.rSite ) < lMinDist ) {
            ++infractions;
          }
        }
        return infractions;
      }

      var diagram = voronoi.compute( fv, bbox );

      // Then we reposition the nodes at the centroid of their Voronoi cells
      var cells = diagram.cells;
      for( var i = 0; i < cells.length; ++i ) {
        var cell = cells[ i ];
        var site = cell.site;
        var centroid = cellCentroid( cell );
        var currv = vSites[ site.label ];
        currv.x = centroid.x;
        currv.y = centroid.y;
      }

      if( lExpFact < 0.0 ) {
        // Calculates the expanding factor
        lExpFact = Math.max( 0.05, Math.min( 0.10, lMinDist / Math.sqrt( ( lWidth * lHeight ) / fv.length ) * 0.5 ) );
        //console.info("Expanding factor is " + (options.expandingFactor * 100.0) + "%");
      }

      var prevInfractions = checkMinDist( diagram.edges );
      //console.info("Initial infractions " + prevInfractions);

      var bStop = ( prevInfractions <= 0 ) || lMaxExpIt <= 0;

      var voronoiIteration = 0;
      var expandIteration = 0;

      // var initWidth = lWidth;

      while( !bStop ) {
        ++voronoiIteration;
        for( var it = 0; it <= 4; ++it ) {
          voronoi.recycle( diagram );
          diagram = voronoi.compute( fv, bbox );

          // Then we reposition the nodes at the centroid of their Voronoi cells
          // cells = diagram.cells;
          for( var i = 0; i < cells.length; ++i ) {
            var cell = cells[ i ];
            var site = cell.site;
            var centroid = cellCentroid( cell );
            var currv = vSites[ site.label ];
            currv.x = centroid.x;
            currv.y = centroid.y;
          }
        }

        var currInfractions = checkMinDist( diagram.edges );
        //console.info("Current infractions " + currInfractions);

        if( currInfractions <= 0 ) {
          bStop = true;
        } else {
          if( currInfractions >= prevInfractions || voronoiIteration >= 4 ) {
            if( expandIteration >= lMaxExpIt ) {
              bStop = true;
            } else {
              lWidth += lWidth * lExpFact;
              lHeight += lHeight * lExpFact;
              bbox = {
                xl: 0,
                xr: lWidth,
                yt: 0,
                yb: lHeight
              };
              ++expandIteration;
              voronoiIteration = 0;
              //console.info("Expanded to ("+width+","+height+")");
            }
          }
        }
        prevInfractions = currInfractions;

        savePositions();
        messagePositions();
      }

      savePositions();
      return pData;

    } ).then( function( pData ) {
      // var expandIteration = pData[ 'expIt' ];
      var dataVertices = pData[ 'vertices' ];

      setPositions( pData );

      // Get end time
      var startTime = pData[ 'startTime' ];
      var endTime = new Date();
      console.info( "Layout on " + dataVertices.length + " nodes took " + ( endTime - startTime ) + " ms" );

      layout.one( "layoutstop", options.stop );

      if( !options.animate ){
        layout.trigger( "layoutready" );
      }

      layout.trigger( "layoutstop" );

      t1.stop();
    } );
  }


  return this;
}; // run

SpreadLayout.prototype.stop = function(){
  if( this.thread ){
    this.thread.stop();
  }

  this.trigger('layoutstop');
};

SpreadLayout.prototype.destroy = function(){
  if( this.thread ){
    this.thread.stop();
  }
};

module.exports = SpreadLayout;


/***/ }),
/* 1 */
/***/ (function(module, exports, __webpack_require__) {

"use strict";


// registers the extension on a cytoscape lib ref
var Layout = __webpack_require__(0);

var register = function( cytoscape ){
  cytoscape('layout', 'spread', Layout);
};

if( typeof cytoscape !== 'undefined' ){ // expose to global cytoscape (i.e. window.cytoscape)
  register( cytoscape );
}

module.exports = register;


/***/ }),
/* 2 */
/***/ (function(module, exports) {

/*!
Copyright (C) 2010-2013 Raymond Hill: https://github.com/gorhill/Javascript-Voronoi
MIT License: See https://github.com/gorhill/Javascript-Voronoi/LICENSE.md
*/
/*
Author: Raymond Hill (rhill@raymondhill.net)
Contributor: Jesse Morgan (morgajel@gmail.com)
File: rhill-voronoi-core.js
Version: 0.98
Date: January 21, 2013
Description: This is my personal Javascript implementation of
Steven Fortune's algorithm to compute Voronoi diagrams.

License: See https://github.com/gorhill/Javascript-Voronoi/LICENSE.md
Credits: See https://github.com/gorhill/Javascript-Voronoi/CREDITS.md
History: See https://github.com/gorhill/Javascript-Voronoi/CHANGELOG.md

## Usage:

  var sites = [{x:300,y:300}, {x:100,y:100}, {x:200,y:500}, {x:250,y:450}, {x:600,y:150}];
  // xl, xr means x left, x right
  // yt, yb means y top, y bottom
  var bbox = {xl:0, xr:800, yt:0, yb:600};
  var voronoi = new Voronoi();
  // pass an object which exhibits xl, xr, yt, yb properties. The bounding
  // box will be used to connect unbound edges, and to close open cells
  result = voronoi.compute(sites, bbox);
  // render, further analyze, etc.

Return value:
  An object with the following properties:

  result.vertices = an array of unordered, unique Voronoi.Vertex objects making
    up the Voronoi diagram.
  result.edges = an array of unordered, unique Voronoi.Edge objects making up
    the Voronoi diagram.
  result.cells = an array of Voronoi.Cell object making up the Voronoi diagram.
    A Cell object might have an empty array of halfedges, meaning no Voronoi
    cell could be computed for a particular cell.
  result.execTime = the time it took to compute the Voronoi diagram, in
    milliseconds.

Voronoi.Vertex object:
  x: The x position of the vertex.
  y: The y position of the vertex.

Voronoi.Edge object:
  lSite: the Voronoi site object at the left of this Voronoi.Edge object.
  rSite: the Voronoi site object at the right of this Voronoi.Edge object (can
    be null).
  va: an object with an 'x' and a 'y' property defining the start point
    (relative to the Voronoi site on the left) of this Voronoi.Edge object.
  vb: an object with an 'x' and a 'y' property defining the end point
    (relative to Voronoi site on the left) of this Voronoi.Edge object.

  For edges which are used to close open cells (using the supplied bounding
  box), the rSite property will be null.

Voronoi.Cell object:
  site: the Voronoi site object associated with the Voronoi cell.
  halfedges: an array of Voronoi.Halfedge objects, ordered counterclockwise,
    defining the polygon for this Voronoi cell.

Voronoi.Halfedge object:
  site: the Voronoi site object owning this Voronoi.Halfedge object.
  edge: a reference to the unique Voronoi.Edge object underlying this
    Voronoi.Halfedge object.
  getStartpoint(): a method returning an object with an 'x' and a 'y' property
    for the start point of this halfedge. Keep in mind halfedges are always
    countercockwise.
  getEndpoint(): a method returning an object with an 'x' and a 'y' property
    for the end point of this halfedge. Keep in mind halfedges are always
    countercockwise.

TODO: Identify opportunities for performance improvement.

TODO: Let the user close the Voronoi cells, do not do it automatically. Not only let
      him close the cells, but also allow him to close more than once using a different
      bounding box for the same Voronoi diagram.
*/

/*global Math */

// ---------------------------------------------------------------------------

function Voronoi() {
    this.vertices = null;
    this.edges = null;
    this.cells = null;
    this.toRecycle = null;
    this.beachsectionJunkyard = [];
    this.circleEventJunkyard = [];
    this.vertexJunkyard = [];
    this.edgeJunkyard = [];
    this.cellJunkyard = [];
    }

// ---------------------------------------------------------------------------

Voronoi.prototype.reset = function() {
    if (!this.beachline) {
        this.beachline = new this.RBTree();
        }
    // Move leftover beachsections to the beachsection junkyard.
    if (this.beachline.root) {
        var beachsection = this.beachline.getFirst(this.beachline.root);
        while (beachsection) {
            this.beachsectionJunkyard.push(beachsection); // mark for reuse
            beachsection = beachsection.rbNext;
            }
        }
    this.beachline.root = null;
    if (!this.circleEvents) {
        this.circleEvents = new this.RBTree();
        }
    this.circleEvents.root = this.firstCircleEvent = null;
    this.vertices = [];
    this.edges = [];
    this.cells = [];
    };

Voronoi.prototype.sqrt = function(n){ return Math.sqrt(n); };
Voronoi.prototype.abs = function(n){ return Math.abs(n); };
Voronoi.prototype.ε = Voronoi.ε = 1e-9;
Voronoi.prototype.invε = Voronoi.invε = 1.0 / Voronoi.ε;
Voronoi.prototype.equalWithEpsilon = function(a,b){return this.abs(a-b)<1e-9;};
Voronoi.prototype.greaterThanWithEpsilon = function(a,b){return a-b>1e-9;};
Voronoi.prototype.greaterThanOrEqualWithEpsilon = function(a,b){return b-a<1e-9;};
Voronoi.prototype.lessThanWithEpsilon = function(a,b){return b-a>1e-9;};
Voronoi.prototype.lessThanOrEqualWithEpsilon = function(a,b){return a-b<1e-9;};

// ---------------------------------------------------------------------------
// Red-Black tree code (based on C version of "rbtree" by Franck Bui-Huu
// https://github.com/fbuihuu/libtree/blob/master/rb.c

Voronoi.prototype.RBTree = function() {
    this.root = null;
    };

Voronoi.prototype.RBTree.prototype.rbInsertSuccessor = function(node, successor) {
    var parent;
    if (node) {
        // >>> rhill 2011-05-27: Performance: cache previous/next nodes
        successor.rbPrevious = node;
        successor.rbNext = node.rbNext;
        if (node.rbNext) {
            node.rbNext.rbPrevious = successor;
            }
        node.rbNext = successor;
        // <<<
        if (node.rbRight) {
            // in-place expansion of node.rbRight.getFirst();
            node = node.rbRight;
            while (node.rbLeft) {node = node.rbLeft;}
            node.rbLeft = successor;
            }
        else {
            node.rbRight = successor;
            }
        parent = node;
        }
    // rhill 2011-06-07: if node is null, successor must be inserted
    // to the left-most part of the tree
    else if (this.root) {
        node = this.getFirst(this.root);
        // >>> Performance: cache previous/next nodes
        successor.rbPrevious = null;
        successor.rbNext = node;
        node.rbPrevious = successor;
        // <<<
        node.rbLeft = successor;
        parent = node;
        }
    else {
        // >>> Performance: cache previous/next nodes
        successor.rbPrevious = successor.rbNext = null;
        // <<<
        this.root = successor;
        parent = null;
        }
    successor.rbLeft = successor.rbRight = null;
    successor.rbParent = parent;
    successor.rbRed = true;
    // Fixup the modified tree by recoloring nodes and performing
    // rotations (2 at most) hence the red-black tree properties are
    // preserved.
    var grandpa, uncle;
    node = successor;
    while (parent && parent.rbRed) {
        grandpa = parent.rbParent;
        if (parent === grandpa.rbLeft) {
            uncle = grandpa.rbRight;
            if (uncle && uncle.rbRed) {
                parent.rbRed = uncle.rbRed = false;
                grandpa.rbRed = true;
                node = grandpa;
                }
            else {
                if (node === parent.rbRight) {
                    this.rbRotateLeft(parent);
                    node = parent;
                    parent = node.rbParent;
                    }
                parent.rbRed = false;
                grandpa.rbRed = true;
                this.rbRotateRight(grandpa);
                }
            }
        else {
            uncle = grandpa.rbLeft;
            if (uncle && uncle.rbRed) {
                parent.rbRed = uncle.rbRed = false;
                grandpa.rbRed = true;
                node = grandpa;
                }
            else {
                if (node === parent.rbLeft) {
                    this.rbRotateRight(parent);
                    node = parent;
                    parent = node.rbParent;
                    }
                parent.rbRed = false;
                grandpa.rbRed = true;
                this.rbRotateLeft(grandpa);
                }
            }
        parent = node.rbParent;
        }
    this.root.rbRed = false;
    };

Voronoi.prototype.RBTree.prototype.rbRemoveNode = function(node) {
    // >>> rhill 2011-05-27: Performance: cache previous/next nodes
    if (node.rbNext) {
        node.rbNext.rbPrevious = node.rbPrevious;
        }
    if (node.rbPrevious) {
        node.rbPrevious.rbNext = node.rbNext;
        }
    node.rbNext = node.rbPrevious = null;
    // <<<
    var parent = node.rbParent,
        left = node.rbLeft,
        right = node.rbRight,
        next;
    if (!left) {
        next = right;
        }
    else if (!right) {
        next = left;
        }
    else {
        next = this.getFirst(right);
        }
    if (parent) {
        if (parent.rbLeft === node) {
            parent.rbLeft = next;
            }
        else {
            parent.rbRight = next;
            }
        }
    else {
        this.root = next;
        }
    // enforce red-black rules
    var isRed;
    if (left && right) {
        isRed = next.rbRed;
        next.rbRed = node.rbRed;
        next.rbLeft = left;
        left.rbParent = next;
        if (next !== right) {
            parent = next.rbParent;
            next.rbParent = node.rbParent;
            node = next.rbRight;
            parent.rbLeft = node;
            next.rbRight = right;
            right.rbParent = next;
            }
        else {
            next.rbParent = parent;
            parent = next;
            node = next.rbRight;
            }
        }
    else {
        isRed = node.rbRed;
        node = next;
        }
    // 'node' is now the sole successor's child and 'parent' its
    // new parent (since the successor can have been moved)
    if (node) {
        node.rbParent = parent;
        }
    // the 'easy' cases
    if (isRed) {return;}
    if (node && node.rbRed) {
        node.rbRed = false;
        return;
        }
    // the other cases
    var sibling;
    do {
        if (node === this.root) {
            break;
            }
        if (node === parent.rbLeft) {
            sibling = parent.rbRight;
            if (sibling.rbRed) {
                sibling.rbRed = false;
                parent.rbRed = true;
                this.rbRotateLeft(parent);
                sibling = parent.rbRight;
                }
            if ((sibling.rbLeft && sibling.rbLeft.rbRed) || (sibling.rbRight && sibling.rbRight.rbRed)) {
                if (!sibling.rbRight || !sibling.rbRight.rbRed) {
                    sibling.rbLeft.rbRed = false;
                    sibling.rbRed = true;
                    this.rbRotateRight(sibling);
                    sibling = parent.rbRight;
                    }
                sibling.rbRed = parent.rbRed;
                parent.rbRed = sibling.rbRight.rbRed = false;
                this.rbRotateLeft(parent);
                node = this.root;
                break;
                }
            }
        else {
            sibling = parent.rbLeft;
            if (sibling.rbRed) {
                sibling.rbRed = false;
                parent.rbRed = true;
                this.rbRotateRight(parent);
                sibling = parent.rbLeft;
                }
            if ((sibling.rbLeft && sibling.rbLeft.rbRed) || (sibling.rbRight && sibling.rbRight.rbRed)) {
                if (!sibling.rbLeft || !sibling.rbLeft.rbRed) {
                    sibling.rbRight.rbRed = false;
                    sibling.rbRed = true;
                    this.rbRotateLeft(sibling);
                    sibling = parent.rbLeft;
                    }
                sibling.rbRed = parent.rbRed;
                parent.rbRed = sibling.rbLeft.rbRed = false;
                this.rbRotateRight(parent);
                node = this.root;
                break;
                }
            }
        sibling.rbRed = true;
        node = parent;
        parent = parent.rbParent;
    } while (!node.rbRed);
    if (node) {node.rbRed = false;}
    };

Voronoi.prototype.RBTree.prototype.rbRotateLeft = function(node) {
    var p = node,
        q = node.rbRight, // can't be null
        parent = p.rbParent;
    if (parent) {
        if (parent.rbLeft === p) {
            parent.rbLeft = q;
            }
        else {
            parent.rbRight = q;
            }
        }
    else {
        this.root = q;
        }
    q.rbParent = parent;
    p.rbParent = q;
    p.rbRight = q.rbLeft;
    if (p.rbRight) {
        p.rbRight.rbParent = p;
        }
    q.rbLeft = p;
    };

Voronoi.prototype.RBTree.prototype.rbRotateRight = function(node) {
    var p = node,
        q = node.rbLeft, // can't be null
        parent = p.rbParent;
    if (parent) {
        if (parent.rbLeft === p) {
            parent.rbLeft = q;
            }
        else {
            parent.rbRight = q;
            }
        }
    else {
        this.root = q;
        }
    q.rbParent = parent;
    p.rbParent = q;
    p.rbLeft = q.rbRight;
    if (p.rbLeft) {
        p.rbLeft.rbParent = p;
        }
    q.rbRight = p;
    };

Voronoi.prototype.RBTree.prototype.getFirst = function(node) {
    while (node.rbLeft) {
        node = node.rbLeft;
        }
    return node;
    };

Voronoi.prototype.RBTree.prototype.getLast = function(node) {
    while (node.rbRight) {
        node = node.rbRight;
        }
    return node;
    };

// ---------------------------------------------------------------------------
// Diagram methods

Voronoi.prototype.Diagram = function(site) {
    this.site = site;
    };

// ---------------------------------------------------------------------------
// Cell methods

Voronoi.prototype.Cell = function(site) {
    this.site = site;
    this.halfedges = [];
    this.closeMe = false;
    };

Voronoi.prototype.Cell.prototype.init = function(site) {
    this.site = site;
    this.halfedges = [];
    this.closeMe = false;
    return this;
    };

Voronoi.prototype.createCell = function(site) {
    var cell = this.cellJunkyard.pop();
    if ( cell ) {
        return cell.init(site);
        }
    return new this.Cell(site);
    };

Voronoi.prototype.Cell.prototype.prepareHalfedges = function() {
    var halfedges = this.halfedges,
        iHalfedge = halfedges.length,
        edge;
    // get rid of unused halfedges
    // rhill 2011-05-27: Keep it simple, no point here in trying
    // to be fancy: dangling edges are a typically a minority.
    while (iHalfedge--) {
        edge = halfedges[iHalfedge].edge;
        if (!edge.vb || !edge.va) {
            halfedges.splice(iHalfedge,1);
            }
        }

    // rhill 2011-05-26: I tried to use a binary search at insertion
    // time to keep the array sorted on-the-fly (in Cell.addHalfedge()).
    // There was no real benefits in doing so, performance on
    // Firefox 3.6 was improved marginally, while performance on
    // Opera 11 was penalized marginally.
    halfedges.sort(function(a,b){return b.angle-a.angle;});
    return halfedges.length;
    };

// Return a list of the neighbor Ids
Voronoi.prototype.Cell.prototype.getNeighborIds = function() {
    var neighbors = [],
        iHalfedge = this.halfedges.length,
        edge;
    while (iHalfedge--){
        edge = this.halfedges[iHalfedge].edge;
        if (edge.lSite !== null && edge.lSite.voronoiId != this.site.voronoiId) {
            neighbors.push(edge.lSite.voronoiId);
            }
        else if (edge.rSite !== null && edge.rSite.voronoiId != this.site.voronoiId){
            neighbors.push(edge.rSite.voronoiId);
            }
        }
    return neighbors;
    };

// Compute bounding box
//
Voronoi.prototype.Cell.prototype.getBbox = function() {
    var halfedges = this.halfedges,
        iHalfedge = halfedges.length,
        xmin = Infinity,
        ymin = Infinity,
        xmax = -Infinity,
        ymax = -Infinity,
        v, vx, vy;
    while (iHalfedge--) {
        v = halfedges[iHalfedge].getStartpoint();
        vx = v.x;
        vy = v.y;
        if (vx < xmin) {xmin = vx;}
        if (vy < ymin) {ymin = vy;}
        if (vx > xmax) {xmax = vx;}
        if (vy > ymax) {ymax = vy;}
        // we dont need to take into account end point,
        // since each end point matches a start point
        }
    return {
        x: xmin,
        y: ymin,
        width: xmax-xmin,
        height: ymax-ymin
        };
    };

// Return whether a point is inside, on, or outside the cell:
//   -1: point is outside the perimeter of the cell
//    0: point is on the perimeter of the cell
//    1: point is inside the perimeter of the cell
//
Voronoi.prototype.Cell.prototype.pointIntersection = function(x, y) {
    // Check if point in polygon. Since all polygons of a Voronoi
    // diagram are convex, then:
    // http://paulbourke.net/geometry/polygonmesh/
    // Solution 3 (2D):
    //   "If the polygon is convex then one can consider the polygon
    //   "as a 'path' from the first vertex. A point is on the interior
    //   "of this polygons if it is always on the same side of all the
    //   "line segments making up the path. ...
    //   "(y - y0) (x1 - x0) - (x - x0) (y1 - y0)
    //   "if it is less than 0 then P is to the right of the line segment,
    //   "if greater than 0 it is to the left, if equal to 0 then it lies
    //   "on the line segment"
    var halfedges = this.halfedges,
        iHalfedge = halfedges.length,
        halfedge,
        p0, p1, r;
    while (iHalfedge--) {
        halfedge = halfedges[iHalfedge];
        p0 = halfedge.getStartpoint();
        p1 = halfedge.getEndpoint();
        r = (y-p0.y)*(p1.x-p0.x)-(x-p0.x)*(p1.y-p0.y);
        if (!r) {
            return 0;
            }
        if (r > 0) {
            return -1;
            }
        }
    return 1;
    };

// ---------------------------------------------------------------------------
// Edge methods
//

Voronoi.prototype.Vertex = function(x, y) {
    this.x = x;
    this.y = y;
    };

Voronoi.prototype.Edge = function(lSite, rSite) {
    this.lSite = lSite;
    this.rSite = rSite;
    this.va = this.vb = null;
    };

Voronoi.prototype.Halfedge = function(edge, lSite, rSite) {
    this.site = lSite;
    this.edge = edge;
    // 'angle' is a value to be used for properly sorting the
    // halfsegments counterclockwise. By convention, we will
    // use the angle of the line defined by the 'site to the left'
    // to the 'site to the right'.
    // However, border edges have no 'site to the right': thus we
    // use the angle of line perpendicular to the halfsegment (the
    // edge should have both end points defined in such case.)
    if (rSite) {
        this.angle = Math.atan2(rSite.y-lSite.y, rSite.x-lSite.x);
        }
    else {
        var va = edge.va,
            vb = edge.vb;
        // rhill 2011-05-31: used to call getStartpoint()/getEndpoint(),
        // but for performance purpose, these are expanded in place here.
        this.angle = edge.lSite === lSite ?
            Math.atan2(vb.x-va.x, va.y-vb.y) :
            Math.atan2(va.x-vb.x, vb.y-va.y);
        }
    };

Voronoi.prototype.createHalfedge = function(edge, lSite, rSite) {
    return new this.Halfedge(edge, lSite, rSite);
    };

Voronoi.prototype.Halfedge.prototype.getStartpoint = function() {
    return this.edge.lSite === this.site ? this.edge.va : this.edge.vb;
    };

Voronoi.prototype.Halfedge.prototype.getEndpoint = function() {
    return this.edge.lSite === this.site ? this.edge.vb : this.edge.va;
    };



// this create and add a vertex to the internal collection

Voronoi.prototype.createVertex = function(x, y) {
    var v = this.vertexJunkyard.pop();
    if ( !v ) {
        v = new this.Vertex(x, y);
        }
    else {
        v.x = x;
        v.y = y;
        }
    this.vertices.push(v);
    return v;
    };

// this create and add an edge to internal collection, and also create
// two halfedges which are added to each site's counterclockwise array
// of halfedges.

Voronoi.prototype.createEdge = function(lSite, rSite, va, vb) {
    var edge = this.edgeJunkyard.pop();
    if ( !edge ) {
        edge = new this.Edge(lSite, rSite);
        }
    else {
        edge.lSite = lSite;
        edge.rSite = rSite;
        edge.va = edge.vb = null;
        }

    this.edges.push(edge);
    if (va) {
        this.setEdgeStartpoint(edge, lSite, rSite, va);
        }
    if (vb) {
        this.setEdgeEndpoint(edge, lSite, rSite, vb);
        }
    this.cells[lSite.voronoiId].halfedges.push(this.createHalfedge(edge, lSite, rSite));
    this.cells[rSite.voronoiId].halfedges.push(this.createHalfedge(edge, rSite, lSite));
    return edge;
    };

Voronoi.prototype.createBorderEdge = function(lSite, va, vb) {
    var edge = this.edgeJunkyard.pop();
    if ( !edge ) {
        edge = new this.Edge(lSite, null);
        }
    else {
        edge.lSite = lSite;
        edge.rSite = null;
        }
    edge.va = va;
    edge.vb = vb;
    this.edges.push(edge);
    return edge;
    };

Voronoi.prototype.setEdgeStartpoint = function(edge, lSite, rSite, vertex) {
    if (!edge.va && !edge.vb) {
        edge.va = vertex;
        edge.lSite = lSite;
        edge.rSite = rSite;
        }
    else if (edge.lSite === rSite) {
        edge.vb = vertex;
        }
    else {
        edge.va = vertex;
        }
    };

Voronoi.prototype.setEdgeEndpoint = function(edge, lSite, rSite, vertex) {
    this.setEdgeStartpoint(edge, rSite, lSite, vertex);
    };

// ---------------------------------------------------------------------------
// Beachline methods

// rhill 2011-06-07: For some reasons, performance suffers significantly
// when instanciating a literal object instead of an empty ctor
Voronoi.prototype.Beachsection = function() {
    };

// rhill 2011-06-02: A lot of Beachsection instanciations
// occur during the computation of the Voronoi diagram,
// somewhere between the number of sites and twice the
// number of sites, while the number of Beachsections on the
// beachline at any given time is comparatively low. For this
// reason, we reuse already created Beachsections, in order
// to avoid new memory allocation. This resulted in a measurable
// performance gain.

Voronoi.prototype.createBeachsection = function(site) {
    var beachsection = this.beachsectionJunkyard.pop();
    if (!beachsection) {
        beachsection = new this.Beachsection();
        }
    beachsection.site = site;
    return beachsection;
    };

// calculate the left break point of a particular beach section,
// given a particular sweep line
Voronoi.prototype.leftBreakPoint = function(arc, directrix) {
    // http://en.wikipedia.org/wiki/Parabola
    // http://en.wikipedia.org/wiki/Quadratic_equation
    // h1 = x1,
    // k1 = (y1+directrix)/2,
    // h2 = x2,
    // k2 = (y2+directrix)/2,
    // p1 = k1-directrix,
    // a1 = 1/(4*p1),
    // b1 = -h1/(2*p1),
    // c1 = h1*h1/(4*p1)+k1,
    // p2 = k2-directrix,
    // a2 = 1/(4*p2),
    // b2 = -h2/(2*p2),
    // c2 = h2*h2/(4*p2)+k2,
    // x = (-(b2-b1) + Math.sqrt((b2-b1)*(b2-b1) - 4*(a2-a1)*(c2-c1))) / (2*(a2-a1))
    // When x1 become the x-origin:
    // h1 = 0,
    // k1 = (y1+directrix)/2,
    // h2 = x2-x1,
    // k2 = (y2+directrix)/2,
    // p1 = k1-directrix,
    // a1 = 1/(4*p1),
    // b1 = 0,
    // c1 = k1,
    // p2 = k2-directrix,
    // a2 = 1/(4*p2),
    // b2 = -h2/(2*p2),
    // c2 = h2*h2/(4*p2)+k2,
    // x = (-b2 + Math.sqrt(b2*b2 - 4*(a2-a1)*(c2-k1))) / (2*(a2-a1)) + x1

    // change code below at your own risk: care has been taken to
    // reduce errors due to computers' finite arithmetic precision.
    // Maybe can still be improved, will see if any more of this
    // kind of errors pop up again.
    var site = arc.site,
        rfocx = site.x,
        rfocy = site.y,
        pby2 = rfocy-directrix;
    // parabola in degenerate case where focus is on directrix
    if (!pby2) {
        return rfocx;
        }
    var lArc = arc.rbPrevious;
    if (!lArc) {
        return -Infinity;
        }
    site = lArc.site;
    var lfocx = site.x,
        lfocy = site.y,
        plby2 = lfocy-directrix;
    // parabola in degenerate case where focus is on directrix
    if (!plby2) {
        return lfocx;
        }
    var hl = lfocx-rfocx,
        aby2 = 1/pby2-1/plby2,
        b = hl/plby2;
    if (aby2) {
        return (-b+this.sqrt(b*b-2*aby2*(hl*hl/(-2*plby2)-lfocy+plby2/2+rfocy-pby2/2)))/aby2+rfocx;
        }
    // both parabolas have same distance to directrix, thus break point is midway
    return (rfocx+lfocx)/2;
    };

// calculate the right break point of a particular beach section,
// given a particular directrix
Voronoi.prototype.rightBreakPoint = function(arc, directrix) {
    var rArc = arc.rbNext;
    if (rArc) {
        return this.leftBreakPoint(rArc, directrix);
        }
    var site = arc.site;
    return site.y === directrix ? site.x : Infinity;
    };

Voronoi.prototype.detachBeachsection = function(beachsection) {
    this.detachCircleEvent(beachsection); // detach potentially attached circle event
    this.beachline.rbRemoveNode(beachsection); // remove from RB-tree
    this.beachsectionJunkyard.push(beachsection); // mark for reuse
    };

Voronoi.prototype.removeBeachsection = function(beachsection) {
    var circle = beachsection.circleEvent,
        x = circle.x,
        y = circle.ycenter,
        vertex = this.createVertex(x, y),
        previous = beachsection.rbPrevious,
        next = beachsection.rbNext,
        disappearingTransitions = [beachsection],
        abs_fn = Math.abs;

    // remove collapsed beachsection from beachline
    this.detachBeachsection(beachsection);

    // there could be more than one empty arc at the deletion point, this
    // happens when more than two edges are linked by the same vertex,
    // so we will collect all those edges by looking up both sides of
    // the deletion point.
    // by the way, there is *always* a predecessor/successor to any collapsed
    // beach section, it's just impossible to have a collapsing first/last
    // beach sections on the beachline, since they obviously are unconstrained
    // on their left/right side.

    // look left
    var lArc = previous;
    while (lArc.circleEvent && abs_fn(x-lArc.circleEvent.x)<1e-9 && abs_fn(y-lArc.circleEvent.ycenter)<1e-9) {
        previous = lArc.rbPrevious;
        disappearingTransitions.unshift(lArc);
        this.detachBeachsection(lArc); // mark for reuse
        lArc = previous;
        }
    // even though it is not disappearing, I will also add the beach section
    // immediately to the left of the left-most collapsed beach section, for
    // convenience, since we need to refer to it later as this beach section
    // is the 'left' site of an edge for which a start point is set.
    disappearingTransitions.unshift(lArc);
    this.detachCircleEvent(lArc);

    // look right
    var rArc = next;
    while (rArc.circleEvent && abs_fn(x-rArc.circleEvent.x)<1e-9 && abs_fn(y-rArc.circleEvent.ycenter)<1e-9) {
        next = rArc.rbNext;
        disappearingTransitions.push(rArc);
        this.detachBeachsection(rArc); // mark for reuse
        rArc = next;
        }
    // we also have to add the beach section immediately to the right of the
    // right-most collapsed beach section, since there is also a disappearing
    // transition representing an edge's start point on its left.
    disappearingTransitions.push(rArc);
    this.detachCircleEvent(rArc);

    // walk through all the disappearing transitions between beach sections and
    // set the start point of their (implied) edge.
    var nArcs = disappearingTransitions.length,
        iArc;
    for (iArc=1; iArc<nArcs; iArc++) {
        rArc = disappearingTransitions[iArc];
        lArc = disappearingTransitions[iArc-1];
        this.setEdgeStartpoint(rArc.edge, lArc.site, rArc.site, vertex);
        }

    // create a new edge as we have now a new transition between
    // two beach sections which were previously not adjacent.
    // since this edge appears as a new vertex is defined, the vertex
    // actually define an end point of the edge (relative to the site
    // on the left)
    lArc = disappearingTransitions[0];
    rArc = disappearingTransitions[nArcs-1];
    rArc.edge = this.createEdge(lArc.site, rArc.site, undefined, vertex);

    // create circle events if any for beach sections left in the beachline
    // adjacent to collapsed sections
    this.attachCircleEvent(lArc);
    this.attachCircleEvent(rArc);
    };

Voronoi.prototype.addBeachsection = function(site) {
    var x = site.x,
        directrix = site.y;

    // find the left and right beach sections which will surround the newly
    // created beach section.
    // rhill 2011-06-01: This loop is one of the most often executed,
    // hence we expand in-place the comparison-against-epsilon calls.
    var lArc, rArc,
        dxl, dxr,
        node = this.beachline.root;

    while (node) {
        dxl = this.leftBreakPoint(node,directrix)-x;
        // x lessThanWithEpsilon xl => falls somewhere before the left edge of the beachsection
        if (dxl > 1e-9) {
            // this case should never happen
            // if (!node.rbLeft) {
            //    rArc = node.rbLeft;
            //    break;
            //    }
            node = node.rbLeft;
            }
        else {
            dxr = x-this.rightBreakPoint(node,directrix);
            // x greaterThanWithEpsilon xr => falls somewhere after the right edge of the beachsection
            if (dxr > 1e-9) {
                if (!node.rbRight) {
                    lArc = node;
                    break;
                    }
                node = node.rbRight;
                }
            else {
                // x equalWithEpsilon xl => falls exactly on the left edge of the beachsection
                if (dxl > -1e-9) {
                    lArc = node.rbPrevious;
                    rArc = node;
                    }
                // x equalWithEpsilon xr => falls exactly on the right edge of the beachsection
                else if (dxr > -1e-9) {
                    lArc = node;
                    rArc = node.rbNext;
                    }
                // falls exactly somewhere in the middle of the beachsection
                else {
                    lArc = rArc = node;
                    }
                break;
                }
            }
        }
    // at this point, keep in mind that lArc and/or rArc could be
    // undefined or null.

    // create a new beach section object for the site and add it to RB-tree
    var newArc = this.createBeachsection(site);
    this.beachline.rbInsertSuccessor(lArc, newArc);

    // cases:
    //

    // [null,null]
    // least likely case: new beach section is the first beach section on the
    // beachline.
    // This case means:
    //   no new transition appears
    //   no collapsing beach section
    //   new beachsection become root of the RB-tree
    if (!lArc && !rArc) {
        return;
        }

    // [lArc,rArc] where lArc == rArc
    // most likely case: new beach section split an existing beach
    // section.
    // This case means:
    //   one new transition appears
    //   the left and right beach section might be collapsing as a result
    //   two new nodes added to the RB-tree
    if (lArc === rArc) {
        // invalidate circle event of split beach section
        this.detachCircleEvent(lArc);

        // split the beach section into two separate beach sections
        rArc = this.createBeachsection(lArc.site);
        this.beachline.rbInsertSuccessor(newArc, rArc);

        // since we have a new transition between two beach sections,
        // a new edge is born
        newArc.edge = rArc.edge = this.createEdge(lArc.site, newArc.site);

        // check whether the left and right beach sections are collapsing
        // and if so create circle events, to be notified when the point of
        // collapse is reached.
        this.attachCircleEvent(lArc);
        this.attachCircleEvent(rArc);
        return;
        }

    // [lArc,null]
    // even less likely case: new beach section is the *last* beach section
    // on the beachline -- this can happen *only* if *all* the previous beach
    // sections currently on the beachline share the same y value as
    // the new beach section.
    // This case means:
    //   one new transition appears
    //   no collapsing beach section as a result
    //   new beach section become right-most node of the RB-tree
    if (lArc && !rArc) {
        newArc.edge = this.createEdge(lArc.site,newArc.site);
        return;
        }

    // [null,rArc]
    // impossible case: because sites are strictly processed from top to bottom,
    // and left to right, which guarantees that there will always be a beach section
    // on the left -- except of course when there are no beach section at all on
    // the beach line, which case was handled above.
    // rhill 2011-06-02: No point testing in non-debug version
    //if (!lArc && rArc) {
    //    throw "Voronoi.addBeachsection(): What is this I don't even";
    //    }

    // [lArc,rArc] where lArc != rArc
    // somewhat less likely case: new beach section falls *exactly* in between two
    // existing beach sections
    // This case m