const createPatternBuilder = require('./createPatternBuilder'); const getVariableName = require('./getVariableName'); module.exports = generateQuadTreeFunction; module.exports.generateQuadTreeFunctionBody = generateQuadTreeFunctionBody; // These exports are for InlineTransform tool. // InlineTransform: getInsertStackCode module.exports.getInsertStackCode = getInsertStackCode; // InlineTransform: getQuadNodeCode module.exports.getQuadNodeCode = getQuadNodeCode; // InlineTransform: isSamePosition module.exports.isSamePosition = isSamePosition; // InlineTransform: getChildBodyCode module.exports.getChildBodyCode = getChildBodyCode; // InlineTransform: setChildBodyCode module.exports.setChildBodyCode = setChildBodyCode; function generateQuadTreeFunction(dimension) { let code = generateQuadTreeFunctionBody(dimension); return (new Function(code))(); } function generateQuadTreeFunctionBody(dimension) { let pattern = createPatternBuilder(dimension); let quadCount = Math.pow(2, dimension); let code = ` ${getInsertStackCode()} ${getQuadNodeCode(dimension)} ${isSamePosition(dimension)} ${getChildBodyCode(dimension)} ${setChildBodyCode(dimension)} function createQuadTree(options, random) { options = options || {}; options.gravity = typeof options.gravity === 'number' ? options.gravity : -1; options.theta = typeof options.theta === 'number' ? options.theta : 0.8; var gravity = options.gravity; var updateQueue = []; var insertStack = new InsertStack(); var theta = options.theta; var nodesCache = []; var currentInCache = 0; var root = newNode(); return { insertBodies: insertBodies, /** * Gets root node if it is present */ getRoot: function() { return root; }, updateBodyForce: update, options: function(newOptions) { if (newOptions) { if (typeof newOptions.gravity === 'number') { gravity = newOptions.gravity; } if (typeof newOptions.theta === 'number') { theta = newOptions.theta; } return this; } return { gravity: gravity, theta: theta }; } }; function newNode() { // To avoid pressure on GC we reuse nodes. var node = nodesCache[currentInCache]; if (node) { ${assignQuads(' node.')} node.body = null; node.mass = ${pattern('node.mass_{var} = ', {join: ''})}0; ${pattern('node.min_{var} = node.max_{var} = ', {join: ''})}0; } else { node = new QuadNode(); nodesCache[currentInCache] = node; } ++currentInCache; return node; } function update(sourceBody) { var queue = updateQueue; var v; ${pattern('var d{var};', {indent: 4})} var r; ${pattern('var f{var} = 0;', {indent: 4})} var queueLength = 1; var shiftIdx = 0; var pushIdx = 1; queue[0] = root; while (queueLength) { var node = queue[shiftIdx]; var body = node.body; queueLength -= 1; shiftIdx += 1; var differentBody = (body !== sourceBody); if (body && differentBody) { // If the current node is a leaf node (and it is not source body), // calculate the force exerted by the current node on body, and add this // amount to body's net force. ${pattern('d{var} = body.pos.{var} - sourceBody.pos.{var};', {indent: 8})} r = Math.sqrt(${pattern('d{var} * d{var}', {join: ' + '})}); if (r === 0) { // Poor man's protection against zero distance. ${pattern('d{var} = (random.nextDouble() - 0.5) / 50;', {indent: 10})} r = Math.sqrt(${pattern('d{var} * d{var}', {join: ' + '})}); } // This is standard gravitation force calculation but we divide // by r^3 to save two operations when normalizing force vector. v = gravity * body.mass * sourceBody.mass / (r * r * r); ${pattern('f{var} += v * d{var};', {indent: 8})} } else if (differentBody) { // Otherwise, calculate the ratio s / r, where s is the width of the region // represented by the internal node, and r is the distance between the body // and the node's center-of-mass ${pattern('d{var} = node.mass_{var} / node.mass - sourceBody.pos.{var};', {indent: 8})} r = Math.sqrt(${pattern('d{var} * d{var}', {join: ' + '})}); if (r === 0) { // Sorry about code duplication. I don't want to create many functions // right away. Just want to see performance first. ${pattern('d{var} = (random.nextDouble() - 0.5) / 50;', {indent: 10})} r = Math.sqrt(${pattern('d{var} * d{var}', {join: ' + '})}); } // If s / r < θ, treat this internal node as a single body, and calculate the // force it exerts on sourceBody, and add this amount to sourceBody's net force. if ((node.max_${getVariableName(0)} - node.min_${getVariableName(0)}) / r < theta) { // in the if statement above we consider node's width only // because the region was made into square during tree creation. // Thus there is no difference between using width or height. v = gravity * node.mass * sourceBody.mass / (r * r * r); ${pattern('f{var} += v * d{var};', {indent: 10})} } else { // Otherwise, run the procedure recursively on each of the current node's children. // I intentionally unfolded this loop, to save several CPU cycles. ${runRecursiveOnChildren()} } } } ${pattern('sourceBody.force.{var} += f{var};', {indent: 4})} } function insertBodies(bodies) { ${pattern('var {var}min = Number.MAX_VALUE;', {indent: 4})} ${pattern('var {var}max = Number.MIN_VALUE;', {indent: 4})} var i = bodies.length; // To reduce quad tree depth we are looking for exact bounding box of all particles. while (i--) { var pos = bodies[i].pos; ${pattern('if (pos.{var} < {var}min) {var}min = pos.{var};', {indent: 6})} ${pattern('if (pos.{var} > {var}max) {var}max = pos.{var};', {indent: 6})} } // Makes the bounds square. var maxSideLength = -Infinity; ${pattern('if ({var}max - {var}min > maxSideLength) maxSideLength = {var}max - {var}min ;', {indent: 4})} currentInCache = 0; root = newNode(); ${pattern('root.min_{var} = {var}min;', {indent: 4})} ${pattern('root.max_{var} = {var}min + maxSideLength;', {indent: 4})} i = bodies.length - 1; if (i >= 0) { root.body = bodies[i]; } while (i--) { insert(bodies[i], root); } } function insert(newBody) { insertStack.reset(); insertStack.push(root, newBody); while (!insertStack.isEmpty()) { var stackItem = insertStack.pop(); var node = stackItem.node; var body = stackItem.body; if (!node.body) { // This is internal node. Update the total mass of the node and center-of-mass. ${pattern('var {var} = body.pos.{var};', {indent: 8})} node.mass += body.mass; ${pattern('node.mass_{var} += body.mass * {var};', {indent: 8})} // Recursively insert the body in the appropriate quadrant. // But first find the appropriate quadrant. var quadIdx = 0; // Assume we are in the 0's quad. ${pattern('var min_{var} = node.min_{var};', {indent: 8})} ${pattern('var max_{var} = (min_{var} + node.max_{var}) / 2;', {indent: 8})} ${assignInsertionQuadIndex(8)} var child = getChild(node, quadIdx); if (!child) { // The node is internal but this quadrant is not taken. Add // subnode to it. child = newNode(); ${pattern('child.min_{var} = min_{var};', {indent: 10})} ${pattern('child.max_{var} = max_{var};', {indent: 10})} child.body = body; setChild(node, quadIdx, child); } else { // continue searching in this quadrant. insertStack.push(child, body); } } else { // We are trying to add to the leaf node. // We have to convert current leaf into internal node // and continue adding two nodes. var oldBody = node.body; node.body = null; // internal nodes do not cary bodies if (isSamePosition(oldBody.pos, body.pos)) { // Prevent infinite subdivision by bumping one node // anywhere in this quadrant var retriesCount = 3; do { var offset = random.nextDouble(); ${pattern('var d{var} = (node.max_{var} - node.min_{var}) * offset;', {indent: 12})} ${pattern('oldBody.pos.{var} = node.min_{var} + d{var};', {indent: 12})} retriesCount -= 1; // Make sure we don't bump it out of the box. If we do, next iteration should fix it } while (retriesCount > 0 && isSamePosition(oldBody.pos, body.pos)); if (retriesCount === 0 && isSamePosition(oldBody.pos, body.pos)) { // This is very bad, we ran out of precision. // if we do not return from the method we'll get into // infinite loop here. So we sacrifice correctness of layout, and keep the app running // Next layout iteration should get larger bounding box in the first step and fix this return; } } // Next iteration should subdivide node further. insertStack.push(node, oldBody); insertStack.push(node, body); } } } } return createQuadTree; `; return code; function assignInsertionQuadIndex(indentCount) { let insertionCode = []; let indent = Array(indentCount + 1).join(' '); for (let i = 0; i < dimension; ++i) { insertionCode.push(indent + `if (${getVariableName(i)} > max_${getVariableName(i)}) {`); insertionCode.push(indent + ` quadIdx = quadIdx + ${Math.pow(2, i)};`); insertionCode.push(indent + ` min_${getVariableName(i)} = max_${getVariableName(i)};`); insertionCode.push(indent + ` max_${getVariableName(i)} = node.max_${getVariableName(i)};`); insertionCode.push(indent + `}`); } return insertionCode.join('\n'); // if (x > max_x) { // somewhere in the eastern part. // quadIdx = quadIdx + 1; // left = right; // right = node.right; // } } function runRecursiveOnChildren() { let indent = Array(11).join(' '); let recursiveCode = []; for (let i = 0; i < quadCount; ++i) { recursiveCode.push(indent + `if (node.quad${i}) {`); recursiveCode.push(indent + ` queue[pushIdx] = node.quad${i};`); recursiveCode.push(indent + ` queueLength += 1;`); recursiveCode.push(indent + ` pushIdx += 1;`); recursiveCode.push(indent + `}`); } return recursiveCode.join('\n'); // if (node.quad0) { // queue[pushIdx] = node.quad0; // queueLength += 1; // pushIdx += 1; // } } function assignQuads(indent) { // this.quad0 = null; // this.quad1 = null; // this.quad2 = null; // this.quad3 = null; let quads = []; for (let i = 0; i < quadCount; ++i) { quads.push(`${indent}quad${i} = null;`); } return quads.join('\n'); } } function isSamePosition(dimension) { let pattern = createPatternBuilder(dimension); return ` function isSamePosition(point1, point2) { ${pattern('var d{var} = Math.abs(point1.{var} - point2.{var});', {indent: 2})} return ${pattern('d{var} < 1e-8', {join: ' && '})}; } `; } function setChildBodyCode(dimension) { var quadCount = Math.pow(2, dimension); return ` function setChild(node, idx, child) { ${setChildBody()} }`; function setChildBody() { let childBody = []; for (let i = 0; i < quadCount; ++i) { let prefix = (i === 0) ? ' ' : ' else '; childBody.push(`${prefix}if (idx === ${i}) node.quad${i} = child;`); } return childBody.join('\n'); // if (idx === 0) node.quad0 = child; // else if (idx === 1) node.quad1 = child; // else if (idx === 2) node.quad2 = child; // else if (idx === 3) node.quad3 = child; } } function getChildBodyCode(dimension) { return `function getChild(node, idx) { ${getChildBody()} return null; }`; function getChildBody() { let childBody = []; let quadCount = Math.pow(2, dimension); for (let i = 0; i < quadCount; ++i) { childBody.push(` if (idx === ${i}) return node.quad${i};`); } return childBody.join('\n'); // if (idx === 0) return node.quad0; // if (idx === 1) return node.quad1; // if (idx === 2) return node.quad2; // if (idx === 3) return node.quad3; } } function getQuadNodeCode(dimension) { let pattern = createPatternBuilder(dimension); let quadCount = Math.pow(2, dimension); var quadNodeCode = ` function QuadNode() { // body stored inside this node. In quad tree only leaf nodes (by construction) // contain bodies: this.body = null; // Child nodes are stored in quads. Each quad is presented by number: // 0 | 1 // ----- // 2 | 3 ${assignQuads(' this.')} // Total mass of current node this.mass = 0; // Center of mass coordinates ${pattern('this.mass_{var} = 0;', {indent: 2})} // bounding box coordinates ${pattern('this.min_{var} = 0;', {indent: 2})} ${pattern('this.max_{var} = 0;', {indent: 2})} } `; return quadNodeCode; function assignQuads(indent) { // this.quad0 = null; // this.quad1 = null; // this.quad2 = null; // this.quad3 = null; let quads = []; for (let i = 0; i < quadCount; ++i) { quads.push(`${indent}quad${i} = null;`); } return quads.join('\n'); } } function getInsertStackCode() { return ` /** * Our implementation of QuadTree is non-recursive to avoid GC hit * This data structure represent stack of elements * which we are trying to insert into quad tree. */ function InsertStack () { this.stack = []; this.popIdx = 0; } InsertStack.prototype = { isEmpty: function() { return this.popIdx === 0; }, push: function (node, body) { var item = this.stack[this.popIdx]; if (!item) { // we are trying to avoid memory pressure: create new element // only when absolutely necessary this.stack[this.popIdx] = new InsertStackElement(node, body); } else { item.node = node; item.body = body; } ++this.popIdx; }, pop: function () { if (this.popIdx > 0) { return this.stack[--this.popIdx]; } }, reset: function () { this.popIdx = 0; } }; function InsertStackElement(node, body) { this.node = node; // QuadTree node this.body = body; // physical body which needs to be inserted to node } `; }