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393 lines
12 KiB
393 lines
12 KiB
/**
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* This function calculates the forces the nodes apply on eachother based on a gravitational model.
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* The Barnes Hut method is used to speed up this N-body simulation.
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*
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* @private
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*/
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exports._calculateNodeForces = function() {
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if (this.constants.physics.barnesHut.gravitationalConstant != 0) {
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var node;
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var nodes = this.calculationNodes;
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var nodeIndices = this.calculationNodeIndices;
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var nodeCount = nodeIndices.length;
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this._formBarnesHutTree(nodes,nodeIndices);
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var barnesHutTree = this.barnesHutTree;
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// place the nodes one by one recursively
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for (var i = 0; i < nodeCount; i++) {
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node = nodes[nodeIndices[i]];
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// starting with root is irrelevant, it never passes the BarnesHut condition
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this._getForceContribution(barnesHutTree.root.children.NW,node);
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this._getForceContribution(barnesHutTree.root.children.NE,node);
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this._getForceContribution(barnesHutTree.root.children.SW,node);
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this._getForceContribution(barnesHutTree.root.children.SE,node);
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}
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}
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};
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/**
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* This function traverses the barnesHutTree. It checks when it can approximate distant nodes with their center of mass.
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* If a region contains a single node, we check if it is not itself, then we apply the force.
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*
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* @param parentBranch
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* @param node
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* @private
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*/
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exports._getForceContribution = function(parentBranch,node) {
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// we get no force contribution from an empty region
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if (parentBranch.childrenCount > 0) {
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var dx,dy,distance;
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// get the distance from the center of mass to the node.
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dx = parentBranch.centerOfMass.x - node.x;
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dy = parentBranch.centerOfMass.y - node.y;
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distance = Math.sqrt(dx * dx + dy * dy);
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// BarnesHut condition
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// original condition : s/d < theta = passed === d/s > 1/theta = passed
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// calcSize = 1/s --> d * 1/s > 1/theta = passed
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if (distance * parentBranch.calcSize > this.constants.physics.barnesHut.theta) {
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// duplicate code to reduce function calls to speed up program
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if (distance == 0) {
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distance = 0.1*Math.random();
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dx = distance;
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}
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var gravityForce = this.constants.physics.barnesHut.gravitationalConstant * parentBranch.mass * node.mass / (distance * distance * distance);
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var fx = dx * gravityForce;
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var fy = dy * gravityForce;
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node.fx += fx;
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node.fy += fy;
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}
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else {
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// Did not pass the condition, go into children if available
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if (parentBranch.childrenCount == 4) {
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this._getForceContribution(parentBranch.children.NW,node);
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this._getForceContribution(parentBranch.children.NE,node);
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this._getForceContribution(parentBranch.children.SW,node);
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this._getForceContribution(parentBranch.children.SE,node);
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}
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else { // parentBranch must have only one node, if it was empty we wouldnt be here
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if (parentBranch.children.data.id != node.id) { // if it is not self
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// duplicate code to reduce function calls to speed up program
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if (distance == 0) {
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distance = 0.5*Math.random();
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dx = distance;
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}
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var gravityForce = this.constants.physics.barnesHut.gravitationalConstant * parentBranch.mass * node.mass / (distance * distance * distance);
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var fx = dx * gravityForce;
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var fy = dy * gravityForce;
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node.fx += fx;
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node.fy += fy;
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}
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}
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}
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}
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};
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/**
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* This function constructs the barnesHut tree recursively. It creates the root, splits it and starts placing the nodes.
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*
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* @param nodes
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* @param nodeIndices
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* @private
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*/
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exports._formBarnesHutTree = function(nodes,nodeIndices) {
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var node;
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var nodeCount = nodeIndices.length;
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var minX = Number.MAX_VALUE,
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minY = Number.MAX_VALUE,
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maxX =-Number.MAX_VALUE,
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maxY =-Number.MAX_VALUE;
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// get the range of the nodes
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for (var i = 0; i < nodeCount; i++) {
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var x = nodes[nodeIndices[i]].x;
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var y = nodes[nodeIndices[i]].y;
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if (x < minX) { minX = x; }
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if (x > maxX) { maxX = x; }
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if (y < minY) { minY = y; }
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if (y > maxY) { maxY = y; }
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}
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// make the range a square
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var sizeDiff = Math.abs(maxX - minX) - Math.abs(maxY - minY); // difference between X and Y
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if (sizeDiff > 0) {minY -= 0.5 * sizeDiff; maxY += 0.5 * sizeDiff;} // xSize > ySize
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else {minX += 0.5 * sizeDiff; maxX -= 0.5 * sizeDiff;} // xSize < ySize
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var minimumTreeSize = 1e-5;
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var rootSize = Math.max(minimumTreeSize,Math.abs(maxX - minX));
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var halfRootSize = 0.5 * rootSize;
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var centerX = 0.5 * (minX + maxX), centerY = 0.5 * (minY + maxY);
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// construct the barnesHutTree
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var barnesHutTree = {
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root:{
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centerOfMass: {x:0, y:0},
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mass:0,
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range: {
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minX: centerX-halfRootSize,maxX:centerX+halfRootSize,
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minY: centerY-halfRootSize,maxY:centerY+halfRootSize
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},
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size: rootSize,
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calcSize: 1 / rootSize,
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children: { data:null},
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maxWidth: 0,
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level: 0,
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childrenCount: 4
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}
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};
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this._splitBranch(barnesHutTree.root);
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// place the nodes one by one recursively
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for (i = 0; i < nodeCount; i++) {
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node = nodes[nodeIndices[i]];
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this._placeInTree(barnesHutTree.root,node);
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}
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// make global
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this.barnesHutTree = barnesHutTree
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};
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/**
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* this updates the mass of a branch. this is increased by adding a node.
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*
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* @param parentBranch
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* @param node
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* @private
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*/
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exports._updateBranchMass = function(parentBranch, node) {
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var totalMass = parentBranch.mass + node.mass;
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var totalMassInv = 1/totalMass;
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parentBranch.centerOfMass.x = parentBranch.centerOfMass.x * parentBranch.mass + node.x * node.mass;
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parentBranch.centerOfMass.x *= totalMassInv;
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parentBranch.centerOfMass.y = parentBranch.centerOfMass.y * parentBranch.mass + node.y * node.mass;
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parentBranch.centerOfMass.y *= totalMassInv;
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parentBranch.mass = totalMass;
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var biggestSize = Math.max(Math.max(node.height,node.radius),node.width);
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parentBranch.maxWidth = (parentBranch.maxWidth < biggestSize) ? biggestSize : parentBranch.maxWidth;
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};
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/**
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* determine in which branch the node will be placed.
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*
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* @param parentBranch
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* @param node
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* @param skipMassUpdate
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* @private
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*/
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exports._placeInTree = function(parentBranch,node,skipMassUpdate) {
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if (skipMassUpdate != true || skipMassUpdate === undefined) {
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// update the mass of the branch.
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this._updateBranchMass(parentBranch,node);
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}
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if (parentBranch.children.NW.range.maxX > node.x) { // in NW or SW
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if (parentBranch.children.NW.range.maxY > node.y) { // in NW
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this._placeInRegion(parentBranch,node,"NW");
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}
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else { // in SW
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this._placeInRegion(parentBranch,node,"SW");
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}
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}
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else { // in NE or SE
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if (parentBranch.children.NW.range.maxY > node.y) { // in NE
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this._placeInRegion(parentBranch,node,"NE");
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}
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else { // in SE
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this._placeInRegion(parentBranch,node,"SE");
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}
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}
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};
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/**
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* actually place the node in a region (or branch)
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*
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* @param parentBranch
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* @param node
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* @param region
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* @private
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*/
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exports._placeInRegion = function(parentBranch,node,region) {
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switch (parentBranch.children[region].childrenCount) {
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case 0: // place node here
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parentBranch.children[region].children.data = node;
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parentBranch.children[region].childrenCount = 1;
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this._updateBranchMass(parentBranch.children[region],node);
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break;
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case 1: // convert into children
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// if there are two nodes exactly overlapping (on init, on opening of cluster etc.)
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// we move one node a pixel and we do not put it in the tree.
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if (parentBranch.children[region].children.data.x == node.x &&
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parentBranch.children[region].children.data.y == node.y) {
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node.x += Math.random();
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node.y += Math.random();
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}
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else {
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this._splitBranch(parentBranch.children[region]);
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this._placeInTree(parentBranch.children[region],node);
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}
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break;
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case 4: // place in branch
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this._placeInTree(parentBranch.children[region],node);
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break;
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}
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};
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/**
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* this function splits a branch into 4 sub branches. If the branch contained a node, we place it in the subbranch
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* after the split is complete.
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*
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* @param parentBranch
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* @private
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*/
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exports._splitBranch = function(parentBranch) {
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// if the branch is shaded with a node, replace the node in the new subset.
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var containedNode = null;
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if (parentBranch.childrenCount == 1) {
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containedNode = parentBranch.children.data;
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parentBranch.mass = 0; parentBranch.centerOfMass.x = 0; parentBranch.centerOfMass.y = 0;
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}
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parentBranch.childrenCount = 4;
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parentBranch.children.data = null;
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this._insertRegion(parentBranch,"NW");
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this._insertRegion(parentBranch,"NE");
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this._insertRegion(parentBranch,"SW");
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this._insertRegion(parentBranch,"SE");
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if (containedNode != null) {
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this._placeInTree(parentBranch,containedNode);
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}
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};
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/**
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* This function subdivides the region into four new segments.
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* Specifically, this inserts a single new segment.
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* It fills the children section of the parentBranch
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*
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* @param parentBranch
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* @param region
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* @param parentRange
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* @private
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*/
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exports._insertRegion = function(parentBranch, region) {
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var minX,maxX,minY,maxY;
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var childSize = 0.5 * parentBranch.size;
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switch (region) {
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case "NW":
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minX = parentBranch.range.minX;
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maxX = parentBranch.range.minX + childSize;
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minY = parentBranch.range.minY;
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maxY = parentBranch.range.minY + childSize;
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break;
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case "NE":
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minX = parentBranch.range.minX + childSize;
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maxX = parentBranch.range.maxX;
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minY = parentBranch.range.minY;
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maxY = parentBranch.range.minY + childSize;
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break;
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case "SW":
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minX = parentBranch.range.minX;
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maxX = parentBranch.range.minX + childSize;
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minY = parentBranch.range.minY + childSize;
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maxY = parentBranch.range.maxY;
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break;
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case "SE":
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minX = parentBranch.range.minX + childSize;
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maxX = parentBranch.range.maxX;
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minY = parentBranch.range.minY + childSize;
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maxY = parentBranch.range.maxY;
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break;
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}
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parentBranch.children[region] = {
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centerOfMass:{x:0,y:0},
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mass:0,
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range:{minX:minX,maxX:maxX,minY:minY,maxY:maxY},
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size: 0.5 * parentBranch.size,
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calcSize: 2 * parentBranch.calcSize,
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children: {data:null},
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maxWidth: 0,
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level: parentBranch.level+1,
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childrenCount: 0
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};
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};
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/**
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* This function is for debugging purposed, it draws the tree.
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*
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* @param ctx
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* @param color
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* @private
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*/
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exports._drawTree = function(ctx,color) {
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if (this.barnesHutTree !== undefined) {
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ctx.lineWidth = 1;
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this._drawBranch(this.barnesHutTree.root,ctx,color);
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}
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};
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/**
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* This function is for debugging purposes. It draws the branches recursively.
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*
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* @param branch
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* @param ctx
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* @param color
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* @private
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*/
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exports._drawBranch = function(branch,ctx,color) {
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if (color === undefined) {
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color = "#FF0000";
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}
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if (branch.childrenCount == 4) {
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this._drawBranch(branch.children.NW,ctx);
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this._drawBranch(branch.children.NE,ctx);
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this._drawBranch(branch.children.SE,ctx);
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this._drawBranch(branch.children.SW,ctx);
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}
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ctx.strokeStyle = color;
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ctx.beginPath();
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ctx.moveTo(branch.range.minX,branch.range.minY);
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ctx.lineTo(branch.range.maxX,branch.range.minY);
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(branch.range.maxX,branch.range.minY);
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ctx.lineTo(branch.range.maxX,branch.range.maxY);
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(branch.range.maxX,branch.range.maxY);
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ctx.lineTo(branch.range.minX,branch.range.maxY);
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ctx.stroke();
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ctx.beginPath();
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ctx.moveTo(branch.range.minX,branch.range.maxY);
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ctx.lineTo(branch.range.minX,branch.range.minY);
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ctx.stroke();
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/*
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if (branch.mass > 0) {
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ctx.circle(branch.centerOfMass.x, branch.centerOfMass.y, 3*branch.mass);
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ctx.stroke();
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}
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*/
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};
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