vis.js is a dynamic, browser-based visualization library
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/**
* 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();
}
*/
};