jrtechs-vis/lib/network/mixins/physics/BarnesHutMixin.js

/**
 * This function calculates the forces the nodes apply on eachother based on a gravitational model.
 * The Barnes Hut method is used to speed up this N-body simulation.
 *
 * @private
 */
exports._calculateNodeForces = function() {
  if (this.constants.physics.barnesHut.gravitationalConstant != 0) {
    var node;
    var nodes = this.calculationNodes;
    var nodeIndices = this.calculationNodeIndices;
    var nodeCount = nodeIndices.length;

    this._formBarnesHutTree(nodes,nodeIndices);

    var barnesHutTree = this.barnesHutTree;

    // place the nodes one by one recursively
    for (var i = 0; i < nodeCount; i++) {
      node = nodes[nodeIndices[i]];
      // starting with root is irrelevant, it never passes the BarnesHut condition
      this._getForceContribution(barnesHutTree.root.children.NW,node);
      this._getForceContribution(barnesHutTree.root.children.NE,node);
      this._getForceContribution(barnesHutTree.root.children.SW,node);
      this._getForceContribution(barnesHutTree.root.children.SE,node);
    }
  }
};


/**
 * This function traverses the barnesHutTree. It checks when it can approximate distant nodes with their center of mass.
 * If a region contains a single node, we check if it is not itself, then we apply the force.
 *
 * @param parentBranch
 * @param node
 * @private
 */
exports._getForceContribution = function(parentBranch,node) {
  // we get no force contribution from an empty region
  if (parentBranch.childrenCount > 0) {
    var dx,dy,distance;

    // get the distance from the center of mass to the node.
    dx = parentBranch.centerOfMass.x - node.x;
    dy = parentBranch.centerOfMass.y - node.y;
    distance = Math.sqrt(dx * dx + dy * dy);

    // BarnesHut condition
    // original condition : s/d < theta = passed  ===  d/s > 1/theta = passed
    // calcSize = 1/s --> d * 1/s > 1/theta = passed
    if (distance * parentBranch.calcSize > this.constants.physics.barnesHut.theta) {
      // duplicate code to reduce function calls to speed up program
      if (distance == 0) {
        distance = 0.1*Math.random();
        dx = distance;
      }
      var gravityForce = this.constants.physics.barnesHut.gravitationalConstant * parentBranch.mass * node.mass / (distance * distance * distance);
      var fx = dx * gravityForce;
      var fy = dy * gravityForce;
      node.fx += fx;
      node.fy += fy;
    }
    else {
      // Did not pass the condition, go into children if available
      if (parentBranch.childrenCount == 4) {
        this._getForceContribution(parentBranch.children.NW,node);
        this._getForceContribution(parentBranch.children.NE,node);
        this._getForceContribution(parentBranch.children.SW,node);
        this._getForceContribution(parentBranch.children.SE,node);
      }
      else { // parentBranch must have only one node, if it was empty we wouldnt be here
        if (parentBranch.children.data.id != node.id) { // if it is not self
          // duplicate code to reduce function calls to speed up program
          if (distance == 0) {
            distance = 0.5*Math.random();
            dx = distance;
          }
          var gravityForce = this.constants.physics.barnesHut.gravitationalConstant * parentBranch.mass * node.mass / (distance * distance * distance);
          var fx = dx * gravityForce;
          var fy = dy * gravityForce;
          node.fx += fx;
          node.fy += fy;
        }
      }
    }
  }
};

/**
 * This function constructs the barnesHut tree recursively. It creates the root, splits it and starts placing the nodes.
 *
 * @param nodes
 * @param nodeIndices
 * @private
 */
exports._formBarnesHutTree = function(nodes,nodeIndices) {
  var node;
  var nodeCount = nodeIndices.length;

  var minX = Number.MAX_VALUE,
    minY = Number.MAX_VALUE,
    maxX =-Number.MAX_VALUE,
    maxY =-Number.MAX_VALUE;

  // get the range of the nodes
  for (var i = 0; i < nodeCount; i++) {
    var x = nodes[nodeIndices[i]].x;
    var y = nodes[nodeIndices[i]].y;
    if (x < minX) { minX = x; }
    if (x > maxX) { maxX = x; }
    if (y < minY) { minY = y; }
    if (y > maxY) { maxY = y; }
  }
  // make the range a square
  var sizeDiff = Math.abs(maxX - minX) - Math.abs(maxY - minY); // difference between X and Y
  if (sizeDiff > 0) {minY -= 0.5 * sizeDiff; maxY += 0.5 * sizeDiff;} // xSize > ySize
  else              {minX += 0.5 * sizeDiff; maxX -= 0.5 * sizeDiff;} // xSize < ySize


  var minimumTreeSize = 1e-5;
  var rootSize = Math.max(minimumTreeSize,Math.abs(maxX - minX));
  var halfRootSize = 0.5 * rootSize;
  var centerX = 0.5 * (minX + maxX), centerY = 0.5 * (minY + maxY);

  // construct the barnesHutTree
  var barnesHutTree = {
    root:{
      centerOfMass: {x:0, y:0},
      mass:0,
      range: {
        minX: centerX-halfRootSize,maxX:centerX+halfRootSize,
        minY: centerY-halfRootSize,maxY:centerY+halfRootSize
      },
      size: rootSize,
      calcSize: 1 / rootSize,
      children: { data:null},
      maxWidth: 0,
      level: 0,
      childrenCount: 4
    }
  };
  this._splitBranch(barnesHutTree.root);

  // place the nodes one by one recursively
  for (i = 0; i < nodeCount; i++) {
    node = nodes[nodeIndices[i]];
    this._placeInTree(barnesHutTree.root,node);
  }

  // make global
  this.barnesHutTree = barnesHutTree
};


/**
 * this updates the mass of a branch. this is increased by adding a node.
 *
 * @param parentBranch
 * @param node
 * @private
 */
exports._updateBranchMass = function(parentBranch, node) {
  var totalMass = parentBranch.mass + node.mass;
  var totalMassInv = 1/totalMass;

  parentBranch.centerOfMass.x = parentBranch.centerOfMass.x * parentBranch.mass + node.x * node.mass;
  parentBranch.centerOfMass.x *= totalMassInv;

  parentBranch.centerOfMass.y = parentBranch.centerOfMass.y * parentBranch.mass + node.y * node.mass;
  parentBranch.centerOfMass.y *= totalMassInv;

  parentBranch.mass = totalMass;
  var biggestSize = Math.max(Math.max(node.height,node.radius),node.width);
  parentBranch.maxWidth = (parentBranch.maxWidth < biggestSize) ? biggestSize : parentBranch.maxWidth;

};


/**
 * determine in which branch the node will be placed.
 *
 * @param parentBranch
 * @param node
 * @param skipMassUpdate
 * @private
 */
exports._placeInTree = function(parentBranch,node,skipMassUpdate) {
  if (skipMassUpdate != true || skipMassUpdate === undefined) {
    // update the mass of the branch.
    this._updateBranchMass(parentBranch,node);
  }

  if (parentBranch.children.NW.range.maxX > node.x) { // in NW or SW
    if (parentBranch.children.NW.range.maxY > node.y) { // in NW
      this._placeInRegion(parentBranch,node,"NW");
    }
    else { // in SW
      this._placeInRegion(parentBranch,node,"SW");
    }
  }
  else { // in NE or SE
    if (parentBranch.children.NW.range.maxY > node.y) { // in NE
      this._placeInRegion(parentBranch,node,"NE");
    }
    else { // in SE
      this._placeInRegion(parentBranch,node,"SE");
    }
  }
};


/**
 * actually place the node in a region (or branch)
 *
 * @param parentBranch
 * @param node
 * @param region
 * @private
 */
exports._placeInRegion = function(parentBranch,node,region) {
  switch (parentBranch.children[region].childrenCount) {
    case 0: // place node here
      parentBranch.children[region].children.data = node;
      parentBranch.children[region].childrenCount = 1;
      this._updateBranchMass(parentBranch.children[region],node);
      break;
    case 1: // convert into children
      // if there are two nodes exactly overlapping (on init, on opening of cluster etc.)
      // we move one node a pixel and we do not put it in the tree.
      if (parentBranch.children[region].children.data.x == node.x &&
          parentBranch.children[region].children.data.y == node.y) {
        node.x += Math.random();
        node.y += Math.random();
      }
      else {
        this._splitBranch(parentBranch.children[region]);
        this._placeInTree(parentBranch.children[region],node);
      }
      break;
    case 4: // place in branch
      this._placeInTree(parentBranch.children[region],node);
      break;
  }
};


/**
 * this function splits a branch into 4 sub branches. If the branch contained a node, we place it in the subbranch
 * after the split is complete.
 *
 * @param parentBranch
 * @private
 */
exports._splitBranch = function(parentBranch) {
  // if the branch is shaded with a node, replace the node in the new subset.
  var containedNode = null;
  if (parentBranch.childrenCount == 1) {
    containedNode = parentBranch.children.data;
    parentBranch.mass = 0; parentBranch.centerOfMass.x = 0; parentBranch.centerOfMass.y = 0;
  }
  parentBranch.childrenCount = 4;
  parentBranch.children.data = null;
  this._insertRegion(parentBranch,"NW");
  this._insertRegion(parentBranch,"NE");
  this._insertRegion(parentBranch,"SW");
  this._insertRegion(parentBranch,"SE");

  if (containedNode != null) {
    this._placeInTree(parentBranch,containedNode);
  }
};


/**
 * This function subdivides the region into four new segments.
 * Specifically, this inserts a single new segment.
 * It fills the children section of the parentBranch
 *
 * @param parentBranch
 * @param region
 * @param parentRange
 * @private
 */
exports._insertRegion = function(parentBranch, region) {
  var minX,maxX,minY,maxY;
  var childSize = 0.5 * parentBranch.size;
  switch (region) {
    case "NW":
      minX = parentBranch.range.minX;
      maxX = parentBranch.range.minX + childSize;
      minY = parentBranch.range.minY;
      maxY = parentBranch.range.minY + childSize;
      break;
    case "NE":
      minX = parentBranch.range.minX + childSize;
      maxX = parentBranch.range.maxX;
      minY = parentBranch.range.minY;
      maxY = parentBranch.range.minY + childSize;
      break;
    case "SW":
      minX = parentBranch.range.minX;
      maxX = parentBranch.range.minX + childSize;
      minY = parentBranch.range.minY + childSize;
      maxY = parentBranch.range.maxY;
      break;
    case "SE":
      minX = parentBranch.range.minX + childSize;
      maxX = parentBranch.range.maxX;
      minY = parentBranch.range.minY + childSize;
      maxY = parentBranch.range.maxY;
      break;
  }


  parentBranch.children[region] = {
    centerOfMass:{x:0,y:0},
    mass:0,
    range:{minX:minX,maxX:maxX,minY:minY,maxY:maxY},
    size: 0.5 * parentBranch.size,
    calcSize: 2 * parentBranch.calcSize,
    children: {data:null},
    maxWidth: 0,
    level: parentBranch.level+1,
    childrenCount: 0
  };
};


/**
 * This function is for debugging purposed, it draws the tree.
 *
 * @param ctx
 * @param color
 * @private
 */
exports._drawTree = function(ctx,color) {
  if (this.barnesHutTree !== undefined) {

    ctx.lineWidth = 1;

    this._drawBranch(this.barnesHutTree.root,ctx,color);
  }
};


/**
 * This function is for debugging purposes. It draws the branches recursively.
 *
 * @param branch
 * @param ctx
 * @param color
 * @private
 */
exports._drawBranch = function(branch,ctx,color) {
  if (color === undefined) {
    color = "#FF0000";
  }

  if (branch.childrenCount == 4) {
    this._drawBranch(branch.children.NW,ctx);
    this._drawBranch(branch.children.NE,ctx);
    this._drawBranch(branch.children.SE,ctx);
    this._drawBranch(branch.children.SW,ctx);
  }
  ctx.strokeStyle = color;
  ctx.beginPath();
  ctx.moveTo(branch.range.minX,branch.range.minY);
  ctx.lineTo(branch.range.maxX,branch.range.minY);
  ctx.stroke();

  ctx.beginPath();
  ctx.moveTo(branch.range.maxX,branch.range.minY);
  ctx.lineTo(branch.range.maxX,branch.range.maxY);
  ctx.stroke();

  ctx.beginPath();
  ctx.moveTo(branch.range.maxX,branch.range.maxY);
  ctx.lineTo(branch.range.minX,branch.range.maxY);
  ctx.stroke();

  ctx.beginPath();
  ctx.moveTo(branch.range.minX,branch.range.maxY);
  ctx.lineTo(branch.range.minX,branch.range.minY);
  ctx.stroke();

  /*
   if (branch.mass > 0) {
   ctx.circle(branch.centerOfMass.x, branch.centerOfMass.y, 3*branch.mass);
   ctx.stroke();
   }
   */
};