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Created May 16, 2019 04:53
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Test of WaveEquation Neumann
Raw
index.html
<div id="canvas-frame"></div>
Raw
script.js
// forked from Rihei Endo's "WaveEquation Neumann" http://www.natural-science.or.jp/WebGL/WaveEquation_Neumann.html
var DOT_SIZE = 8;
var X_START_POS = 4;
var Y_START_POS = 4;
var Z_START_POS = 0;
// ‥‥‥‥‥‥‥‥‥‥‥‥‥□□□
// ‥‥‥‥‥‥〓〓〓〓〓‥‥□□□
// ‥‥‥‥‥〓〓〓〓〓〓〓〓〓□□
// ‥‥‥‥‥■■■□□■□‥■■■
// ‥‥‥‥■□■□□□■□□■■■
// ‥‥‥‥■□■■□□□■□□□■
// ‥‥‥‥■■□□□□■■■■■‥
// ‥‥‥‥‥‥□□□□□□□■‥‥
// ‥‥■■■■■〓■■■〓■‥‥‥
// ‥■■■■■■■〓■■■〓‥‥■
// □□■■■■■■〓〓〓〓〓‥‥■
// □□□‥〓〓■〓〓□〓〓□〓■■
// ‥□‥■〓〓〓〓〓〓〓〓〓〓■■
// ‥‥■■■〓〓〓〓〓〓〓〓〓■■
// ‥■■■〓〓〓〓〓〓〓‥‥‥‥‥
// ‥■‥‥〓〓〓〓‥‥‥‥‥‥‥‥
var dataSet = [
"BK","BK","BK","BK","BK","BK","BK","BK","BK","BK","BK","BK","BK","BG","BG","BG",
"BK","BK","BK","BK","BK","BK","RD","RD","RD","RD","RD","BK","BK","BG","BG","BG",
"BK","BK","BK","BK","BK","RD","RD","RD","RD","RD","RD","RD","RD","RD","BG","BG",
"BK","BK","BK","BK","BK","BR","BR","BR","BG","BG","BR","BG","BK","RD","RD","RD",
"BK","BK","BK","BK","BR","BG","BR","BG","BG","BG","BR","BG","BG","RD","RD","RD",
"BK","BK","BK","BK","BR","BG","BR","BR","BG","BG","BG","BR","BG","BG","BG","RD",
"BK","BK","BK","BK","BR","BR","BG","BG","BG","BG","BR","BR","BR","BR","RD","BK",
"BK","BK","BK","BK","BK","BK","BG","BG","BG","BG","BG","BG","BG","RD","BK","BK",
"BK","BK","RD","RD","RD","RD","RD","BL","RD","RD","RD","BL","RD","BK","BK","BK",
"BK","RD","RD","RD","RD","RD","RD","RD","BL","RD","RD","RD","BL","BK","BK","BR",
"BG","BG","RD","RD","RD","RD","RD","RD","BL","BL","BL","BL","BL","BK","BK","BR",
"BG","BG","BG","BK","BL","BL","RD","BL","BL","YL","BL","BL","YL","BL","BR","BR",
"BK","BG","BK","BR","BL","BL","BL","BL","BL","BL","BL","BL","BL","BL","BR","BR",
"BK","BK","BR","BR","BR","BL","BL","BL","BL","BL","BL","BL","BL","BL","BR","BR",
"BK","BR","BR","BR","BL","BL","BL","BL","BL","BL","BL","BK","BK","BK","BK","BK",
"BK","BR","BK","BK","BL","BL","BL","BL","BK","BK","BK","BK","BK","BK","BK","BK"
];
function getRgbColor(colorType)
{
var colorHash = {
"BK":"#000000", // black
"WH":"#FFFFFF", // white
"BG":"#FFCCCC", // beige
"BR":"#800000", // brown
"RD":"#FF0000", // red
"YL":"#FFFF00", // yellow
"GN":"#00FF00", // green
"WT":"#00FFFF", // water
"BL":"#0000FF", // blue
"PR":"#800080" // purple
};
return colorHash[colorType];
}
var N = 24;
var l = 5.0;
var dt = 0.1;
var dd = 1.0;
var v = 4;
var BC = "Dirichlet";
var peakPosition = {
x: 0,
y: 0,
z: 75,
sigma2: 50
};
var peakPosition_bound = {
x_min: -50,
x_max: 50,
y_min: -50,
y_max: 50,
z_min: -50,
z_max: 100,
sigma2_min: 10,
sigma2_max: 100
};
var restartFlag = false;
var stopFlag = false;
var Tn = 3;
var f = new Array(Tn);
function initialCondition(parameter) {
var x0 = parameter.x;
var y0 = parameter.y;
var z0 = parameter.z;
var sigma2 = parameter.sigma2;
for (var t = 0; t < Tn; t++) {
f[t] = new Array(N);
for (i = 0; i <= N; i++) {
f[t][i] = new Array(N);
for (j = 0; j <= N; j++) {
var x = (-N / 2 + i) * l;
var y = (-N / 2 + j) * l;
var z = z0 * Math.exp(-(Math.pow(x - x0, 2) + Math.pow(y - y0, 2)) / (2 * sigma2));
f[0][i][j] = z;
}
}
}
for (var i = 1; i <= N - 1; i++) {
for (var j = 1; j <= N - 1; j++) {
f[1][i][j] = f[0][i][j] + v * v / 2.0 * dt * dt / (dd * dd) * (f[0][i + 1][j] + f[0][i - 1][j] + f[0][i][j + 1] + f[0][i][j - 1] - 4.0 * f[0][i][j]);
}
}
if (BC == "Dirichlet") {
for (var i = 0; i <= N; i++) {
f[1][i][0] = f[1][i][N] = f[1][0][i] = f[1][N][i] = 0.0;
}
} else if (BC == "Neumann") {
for (var i = 1; i <= N - 1; i++) {
f[1][i][0] = f[1][i][1];
f[1][i][N] = f[1][i][N - 1];
f[1][0][i] = f[1][1][i];
f[1][N][i] = f[1][N - 1][i];
}
f[1][0][0] = (f[1][0][1] + f[1][1][0]) / 2;
f[1][0][N] = (f[1][0][N - 1] + f[1][1][N]) / 2;
f[1][N][0] = (f[1][N - 1][0] + f[1][N][1]) / 2;
f[1][N][N] = (f[1][N - 1][N] + f[1][N][N - 1]) / 2;
}
}
window.addEventListener("load", function() {
initialCondition(peakPosition);
threeStart();
});
function threeStart() {
initThree();
initCamera();
initLight();
initObject();
loop();
}
var renderer,
scene,
canvasFrame;
function initThree() {
canvasFrame = document.getElementById('canvas-frame');
renderer = new THREE.WebGLRenderer({
antialias: true
});
if (!renderer) alert('Failed to initialize Three.js');
renderer.setSize(canvasFrame.clientWidth, canvasFrame.clientHeight);
canvasFrame.appendChild(renderer.domElement);
renderer.setClearColor(0x000000, 1.0);
scene = new THREE.Scene();
}
var camera;
var theta = 0;
function initCamera() {
camera = new THREE.PerspectiveCamera(45, canvasFrame.clientWidth / canvasFrame.clientHeight, 1, 10000);
camera.position.set(160, 0, 100);
camera.up.set(0, 0, 1);
camera.lookAt({
x: 0,
y: 0,
z: 0
});
}
var directionalLight,
ambientLight;
function initLight() {
directionalLight = new THREE.DirectionalLight(0xDDDDDD, 1.0, 0);
directionalLight.position.set(30, 30, 100);
ambientLight = new THREE.AmbientLight(0x222222);
scene.add(ambientLight);
scene.add(directionalLight);
}
var axis,
lattice,
cubes = [];
function initObject() {
initialCondition(peakPosition);
var geometry = new THREE.Geometry();
var colors = [];
for (i = 0; i <= N; i++) {
for (j = 0; j <= N; j++) {
var x = (-N / 2 + i) * l;
var y = (-N / 2 + j) * l;
var z = f[0][i][j];
geometry.vertices.push(new THREE.Vector3(x, y, z));
var ii = i - X_START_POS;
var jj = j - Y_START_POS;
var color = new THREE.Color();
if ((ii >= 0 && ii < 16) && (jj >= 0 && jj < 16)) {
var pos = jj * 16 + (15 - ii);
if (dataSet[pos] != "BK") {
color.setStyle(getRgbColor(dataSet[pos]));
}
}
colors.push(color);
}
}
geometry.colors = colors;
geometry.computeFaceNormals();
geometry.computeVertexNormals();
// ball.png
var dataUrl = 'data:image/png; charset=utf-8;base64,' +
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var sprite = THREE.ImageUtils.loadTexture(dataUrl);
var material = new THREE.PointCloudMaterial({
map: sprite,
size: DOT_SIZE * 2.0,
transparent: true,
opacity: 0.7,
vertexColors: true
});
//立方体オブジェクトの生成
lattice = new THREE.PointCloud(geometry, material);
}
var step = 0;
function loop() {
camera.lookAt(scene.position);
camera.position.x = 200 * Math.sin(theta * Math.PI / 180);
camera.position.y = 100;
camera.position.z = 200 * Math.cos(theta * Math.PI / 180);
theta += 0.5;
var time = step * dt;
if (stopFlag == false) {
step++;
time = step * dt;
for (var i = 1; i <= N - 1; i++) {
for (var j = 1; j <= N - 1; j++) {
f[2][i][j] = 2.0 * f[1][i][j] - f[0][i][j] + v * v * dt * dt / (dd * dd) * (f[1][i + 1][j] + f[1][i - 1][j] + f[1][i][j + 1] + f[1][i][j - 1] - 4.0 * f[1][i][j]);
}
}
if (BC == "Dirichlet") {
for (var i = 0; i <= N; i++) {
f[2][i][0] = f[2][i][N] = f[2][0][i] = f[2][N][i] = 0.0;
}
} else if (BC == "Neumann") {
for (var i = 1; i <= N - 1; i++) {
f[2][i][0] = f[2][i][1];
f[2][i][N] = f[2][i][N - 1];
f[2][0][i] = f[2][1][i];
f[2][N][i] = f[2][N - 1][i];
}
f[2][0][0] = (f[2][0][1] + f[2][1][0]) / 2;
f[2][0][N] = (f[2][0][N - 1] + f[2][1][N]) / 2;
f[2][N][0] = (f[2][N - 1][0] + f[2][N][1]) / 2;
f[2][N][N] = (f[2][N - 1][N] + f[2][N][N - 1]) / 2;
}
for (var i = 0; i <= N; i++) {
for (var j = 0; j <= N; j++) {
f[0][i][j] = f[1][i][j];
f[1][i][j] = f[2][i][j];
}
}
}
var a = 0;
for (i = 0; i <= N; i++) {
for (j = 0; j <= N; j++) {
var x = (-N / 2 + i) * l;
var y = (-N / 2 + j) * l;
var z = f[1][i][j];
lattice.geometry.vertices[a].z = z;
a++;
}
}
lattice.geometry.normalsNeedUpdate = true;
lattice.geometry.verticesNeedUpdate = true;
lattice.geometry.computeFaceNormals();
lattice.geometry.computeVertexNormals();
scene.add(lattice);
renderer.clear();
renderer.render(scene, camera);
scene.remove(lattice);
requestAnimationFrame(loop);
}
Raw
scripts
<script src="https://threejs.org/build/three.min.js"></script>
Raw
style.css
* {
margin: 0;
padding: 0;
border: 0;
overflow: hidden;
}
body
{
background-color:#000000;
}
div#canvas-frame
{
margin:0px auto;
width:465px;
height:465px;
}
Raw
test-of-waveequation-neumann.markdown
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