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158 lines
4.7 KiB
158 lines
4.7 KiB
/**
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* Created by Alex on 8/7/2015.
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*/
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import FloydWarshall from "./FloydWarshall.js"
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class KamadaKawai {
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constructor(body, edgeLength, edgeStrength) {
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this.body = body;
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this.springLength = edgeLength;
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this.springConstant = edgeStrength;
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this.distanceSolver = new FloydWarshall();
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}
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setOptions(options) {
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if (options) {
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if (options.springLength) {
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this.springLength = options.springLength;
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}
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if (options.springConstant) {
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this.springConstant = options.springConstant;
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}
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}
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}
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solve(nodesArray, edgesArray) {
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console.time("FLOYD - getDistances");
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let D_matrix = this.distanceSolver.getDistances(this.body, nodesArray, edgesArray); // distance matrix
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console.timeEnd("FLOYD - getDistances");
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// get the L Matrix
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this._createL_matrix(D_matrix);
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// get the K Matrix
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this._createK_matrix(D_matrix);
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console.time("positioning")
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let threshold = 0.01;
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let counter = 0;
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let maxIterations = Math.min(10*this.body.nodeIndices.length);;
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let maxEnergy = 1e9; // just to pass the first check.
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let highE_nodeId = 0, dE_dx = 0, dE_dy = 0;
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while (maxEnergy > threshold && counter < maxIterations) {
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counter += 1;
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[highE_nodeId, maxEnergy, dE_dx, dE_dy] = this._getHighestEnergyNode();
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this._moveNode(highE_nodeId, dE_dx, dE_dy);
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}
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console.timeEnd("positioning")
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}
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_getHighestEnergyNode() {
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let nodesArray = this.body.nodeIndices;
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let maxEnergy = 0;
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let maxEnergyNode = nodesArray[0];
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let energies = {dE_dx: 0, dE_dy: 0};
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for (let nodeIdx = 0; nodeIdx < nodesArray.length; nodeIdx++) {
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let m = nodesArray[nodeIdx];
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let [delta_m,dE_dx,dE_dy] = this._getEnergy(m);
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if (maxEnergy < delta_m) {
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maxEnergy = delta_m;
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maxEnergyNode = m;
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energies.dE_dx = dE_dx;
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energies.dE_dy = dE_dy;
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}
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}
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return [maxEnergyNode, maxEnergy, energies.dE_dx, energies.dE_dy];
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}
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_getEnergy(m) {
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let nodesArray = this.body.nodeIndices;
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let nodes = this.body.nodes;
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let x_m = nodes[m].x;
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let y_m = nodes[m].y;
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let dE_dx = 0;
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let dE_dy = 0;
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for (let iIdx = 0; iIdx < nodesArray.length; iIdx++) {
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let i = nodesArray[iIdx];
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if (i !== m) {
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let x_i = nodes[i].x;
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let y_i = nodes[i].y;
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let denominator = 1.0 / Math.sqrt(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2));
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dE_dx += this.K_matrix[m][i] * ((x_m - x_i) - this.L_matrix[m][i] * (x_m - x_i) * denominator);
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dE_dy += this.K_matrix[m][i] * ((y_m - y_i) - this.L_matrix[m][i] * (y_m - y_i) * denominator);
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}
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}
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let delta_m = Math.sqrt(Math.pow(dE_dx, 2) + Math.pow(dE_dy, 2));
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return [delta_m, dE_dx, dE_dy];
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}
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_moveNode(m, dE_dx, dE_dy) {
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let nodesArray = this.body.nodeIndices;
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let nodes = this.body.nodes;
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let d2E_dx2 = 0;
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let d2E_dxdy = 0;
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let d2E_dy2 = 0;
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let x_m = nodes[m].x;
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let y_m = nodes[m].y;
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for (let iIdx = 0; iIdx < nodesArray.length; iIdx++) {
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let i = nodesArray[iIdx];
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if (i !== m) {
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let x_i = nodes[i].x;
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let y_i = nodes[i].y;
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let denominator = 1.0 / Math.pow(Math.pow(x_m - x_i, 2) + Math.pow(y_m - y_i, 2), 1.5);
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d2E_dx2 += this.K_matrix[m][i] * (1 - this.L_matrix[m][i] * Math.pow(y_m - y_i, 2) * denominator);
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d2E_dxdy += this.K_matrix[m][i] * (this.L_matrix[m][i] * (x_m - x_i) * (y_m - y_i) * denominator);
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d2E_dy2 += this.K_matrix[m][i] * (1 - this.L_matrix[m][i] * Math.pow(x_m - x_i, 2) * denominator);
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}
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}
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// make the variable names easier to make the solving of the linear system easier to read
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let A = d2E_dx2, B = d2E_dxdy, C = dE_dx, D = d2E_dy2, E = dE_dy;
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// solve the linear system for dx and dy
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let dy = (C / A + E / B) / (B / A - D / B);
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let dx = -(B * dy + C) / A;
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// move the node
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nodes[m].x += dx;
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nodes[m].y += dy;
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}
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_createL_matrix(D_matrix) {
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let nodesArray = this.body.nodeIndices;
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let edgeLength = this.springLength;
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this.L_matrix = [];
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for (let i = 0; i < nodesArray.length; i++) {
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this.L_matrix[nodesArray[i]] = {};
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for (let j = 0; j < nodesArray.length; j++) {
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this.L_matrix[nodesArray[i]][nodesArray[j]] = edgeLength * D_matrix[nodesArray[i]][nodesArray[j]];
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}
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}
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}
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_createK_matrix(D_matrix) {
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let nodesArray = this.body.nodeIndices;
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let edgeStrength = this.springConstant;
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this.K_matrix = [];
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for (let i = 0; i < nodesArray.length; i++) {
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this.K_matrix[nodesArray[i]] = {};
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for (let j = 0; j < nodesArray.length; j++) {
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this.K_matrix[nodesArray[i]][nodesArray[j]] = edgeStrength * Math.pow(D_matrix[nodesArray[i]][nodesArray[j]], -2);
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}
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}
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}
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}
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export default KamadaKawai;
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