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654 lines
14 KiB
654 lines
14 KiB
3 years ago
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<!DOCTYPE html>
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<html lang="en">
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<head>
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<title>three.js webgl - multiple elements with text</title>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
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<link type="text/css" rel="stylesheet" href="main.css">
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<style>
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* {
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box-sizing: border-box;
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-moz-box-sizing: border-box;
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}
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body {
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background-color: #fff;
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color: #444;
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margin: auto;
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padding: .5in;
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max-width: 7in;
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text-align: justify;
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}
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a {
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color: #08f;
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}
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#info {
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left: 0px;
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}
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.view {
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width: 5in;
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height: 5in;
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margin: auto;
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}
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#c {
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position: fixed;
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left: 0px; top: 0px;
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width: 100%;
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height: 100%;
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background-color: #fff;
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z-index: -1;
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}
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.math {
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text-align: center;
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}
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.math-frac {
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display: inline-block;
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vertical-align: middle;
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}
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.math-num {
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display: block;
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}
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.math-denom {
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display: block;
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border-top: 1px solid;
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}
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.math-sqrt {
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display: inline-block;
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transform: scale(1, 1.3);
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}
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.math-sqrt-stem {
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display: inline-block;
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border-top: 1px solid;
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margin-top: 5px;
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}
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</style>
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</head>
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<body>
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<canvas id="c"></canvas>
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<div id="info"><a href="https://threejs.org" target="_blank" rel="noopener">three.js</a> - multiple elements with text - webgl</div>
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<!-- Import maps polyfill -->
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<!-- Remove this when import maps will be widely supported -->
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<script async src="https://unpkg.com/es-module-shims@1.3.6/dist/es-module-shims.js"></script>
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<script type="importmap">
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{
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"imports": {
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"three": "../build/three.module.js",
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"three/addons/": "./jsm/"
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}
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}
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</script>
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<script type="module">
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import * as THREE from 'three';
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import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
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const scenes = [];
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const clock = new THREE.Clock();
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let views, t, canvas, renderer;
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window.onload = init;
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function init() {
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const balls = 20;
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const size = .25;
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const colors = [
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'rgb(0,127,255)', 'rgb(255,0,0)', 'rgb(0,255,0)', 'rgb(0,255,255)',
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'rgb(255,0,255)', 'rgb(255,0,127)', 'rgb(255,255,0)', 'rgb(0,255,127)'
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];
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canvas = document.getElementById( 'c' );
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renderer = new THREE.WebGLRenderer( { canvas: canvas, antialias: true } );
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renderer.setPixelRatio( window.devicePixelRatio );
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views = document.querySelectorAll( '.view' );
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for ( let n = 0; n < views.length; n ++ ) {
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const scene = new THREE.Scene();
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scene.background = new THREE.Color( 0xffffff );
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const geometry0 = new THREE.BufferGeometry();
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const geometry1 = new THREE.BufferGeometry();
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const vertices = [];
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if ( views[ n ].lattice ) {
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const range = balls / 2;
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for ( let i = - range; i <= range; i ++ ) {
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for ( let j = - range; j <= range; j ++ ) {
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for ( let k = - range; k <= range; k ++ ) {
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vertices.push( i, j, k );
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}
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}
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}
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} else {
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for ( let m = 0; m < Math.pow( balls, 3 ); m ++ ) {
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const i = balls * Math.random() - balls / 2;
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const j = balls * Math.random() - balls / 2;
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const k = balls * Math.random() - balls / 2;
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vertices.push( i, j, k );
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}
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}
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geometry0.setAttribute( 'position', new THREE.Float32BufferAttribute( vertices, 3 ) );
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geometry1.setAttribute( 'position', new THREE.Float32BufferAttribute( vertices.slice(), 3 ) );
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const index = Math.floor( colors.length * Math.random() );
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const canvas2 = document.createElement( 'canvas' );
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canvas2.width = 128;
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canvas2.height = 128;
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const context = canvas2.getContext( '2d' );
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context.arc( 64, 64, 64, 0, 2 * Math.PI );
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context.fillStyle = colors[ index ];
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context.fill();
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const texture = new THREE.CanvasTexture( canvas2 );
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const material = new THREE.PointsMaterial( { size: size, map: texture, transparent: true, alphaTest: 0.1 } );
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scene.add( new THREE.Points( geometry0, material ) );
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scene.userData.view = views[ n ];
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scene.userData.geometry1 = geometry1;
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const camera = new THREE.PerspectiveCamera( 75, 1, 0.1, 100 );
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camera.position.set( 0, 0, 1.2 * balls );
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scene.userData.camera = camera;
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const controls = new OrbitControls( camera, views[ n ] );
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scene.userData.controls = controls;
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scenes.push( scene );
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}
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t = 0;
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animate();
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}
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function updateSize() {
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const width = canvas.clientWidth;
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const height = canvas.clientHeight;
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if ( canvas.width !== width || canvas.height != height ) {
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renderer.setSize( width, height, false );
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}
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}
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function animate() {
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render();
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requestAnimationFrame( animate );
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}
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function render() {
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updateSize();
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renderer.setClearColor( 0xffffff );
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renderer.setScissorTest( false );
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renderer.clear();
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renderer.setClearColor( 0x000000 );
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renderer.setScissorTest( true );
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scenes.forEach( function ( scene ) {
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const rect = scene.userData.view.getBoundingClientRect();
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// check if it's offscreen. If so skip it
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if ( rect.bottom < 0 || rect.top > renderer.domElement.clientHeight ||
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rect.right < 0 || rect.left > renderer.domElement.clientWidth ) {
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return; // it's off screen
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}
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// set the viewport
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const width = rect.right - rect.left;
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const height = rect.bottom - rect.top;
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const left = rect.left;
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const bottom = renderer.domElement.clientHeight - rect.bottom;
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renderer.setViewport( left, bottom, width, height );
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renderer.setScissor( left, bottom, width, height );
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renderer.render( scene, scene.userData.camera );
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const points = scene.children[ 0 ];
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const position = points.geometry.attributes.position;
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const point = new THREE.Vector3();
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const offset = new THREE.Vector3();
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for ( let i = 0; i < position.count; i ++ ) {
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point.fromBufferAttribute( scene.userData.geometry1.attributes.position, i );
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scene.userData.view.displacement( point.x, point.y, point.z, t / 5, offset );
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position.setXYZ( i, point.x + offset.x, point.y + offset.y, point.z + offset.z );
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}
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position.needsUpdate = true;
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} );
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t += clock.getDelta() * 60;
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}
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</script>
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<p>Sound waves whose geometry is determined by a single dimension, plane waves, obey the wave equation</p>
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<!-- css math formatting inspired by http://mathquill.com/mathquill/mathquill.css -->
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<div class="math">
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<span class="math-frac">
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<span class="math-num">
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∂<sup>2</sup><i>u</i>
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</span>
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<span class="math-denom">
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∂<i>r</i><sup>2</sup>
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</span>
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</span>
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−
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<span class="math-frac">
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<span class="math-num">
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1<sup></sup> <!-- sup for vertical alignment -->
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</span>
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<span class="math-denom">
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<i>c</i><sup>2</sup>
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</span>
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</span>
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<span class="math-frac">
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<span class="math-num">
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∂<sup>2</sup><i>u</i>
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</span>
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<span class="math-denom">
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∂<i>t</i><sup>2</sup>
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</span>
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</span>
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= 0
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</div>
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<p>where <i>c</i> designates the speed of sound in the medium. The monochromatic solution for plane waves will be taken to be</p>
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<div class="math">
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<i>u</i>(<i>r</i>,<i>t</i>) = sin(<i>k</i><i>r</i> ± ω<i>t</i>)
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</div>
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<p>where ω is the frequency and <i>k</i>=ω/<i>c</i> is the wave number. The sign chosen in the argument determines the direction of movement of the waves.</p>
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<p>Here is a plane wave moving on a three-dimensional lattice of atoms:</p>
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<div class="view">
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<script>
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/* eslint-disable prefer-const*/
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let parent = document.scripts[ document.scripts.length - 1 ].parentNode;
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parent.displacement = function ( x, y, z, t, target ) {
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return target.set( Math.sin( x - t ), 0, 0 );
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};
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parent.lattice = true;
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</script>
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</div>
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<p>Here is a plane wave moving through a three-dimensional random distribution of molecules:</p>
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<div class="view">
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<script>
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parent = document.scripts[ document.scripts.length - 1 ].parentNode;
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parent.displacement = function ( x, y, z, t, target ) {
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return target.set( Math.sin( x - t ), 0, 0 );
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};
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parent.lattice = false;
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</script>
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</div>
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<p>Sound waves whose geometry is determined by two dimensions, cylindrical waves, obey the wave equation</p>
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<div class="math">
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<span class="math-frac">
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<span class="math-num">
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∂<sup>2</sup><i>u</i>
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</span>
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<span class="math-denom">
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∂<i>r</i><sup>2</sup>
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</span>
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</span>
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+
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<span class="math-frac">
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<span class="math-num">
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1
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</span>
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<span class="math-denom">
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<i>r</i>
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</span>
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</span>
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<span class="math-frac">
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<span class="math-num">
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∂<i>u</i>
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</span>
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<span class="math-denom">
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∂<i>r</i>
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</span>
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</span>
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−
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<span class="math-frac">
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<span class="math-num">
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1<sup></sup> <!-- sup for vertical alignment -->
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</span>
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<span class="math-denom">
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<i>c</i><sup>2</sup>
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</span>
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</span>
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<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
∂<sup>2</sup><i>u</i>
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
∂<i>t</i><sup>2</sup>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
= 0
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>The monochromatic solution for cylindrical sound waves will be taken to be</p>
|
||
|
|
|
||
|
|
<div class="math">
|
||
|
|
|
||
|
|
<i>u</i>(<i>r</i>,<i>t</i>) =
|
||
|
|
|
||
|
|
<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
sin(<i>k</i><i>r</i> ± ω<i>t</i>)
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
<span class="math-sqrt">√</span><span class="math-sqrt-stem"><i>r</i></span>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>Here is a cylindrical wave moving on a three-dimensional lattice of atoms:</p>
|
||
|
|
|
||
|
|
<div class="view">
|
||
|
|
|
||
|
|
<script>
|
||
|
|
|
||
|
|
parent = document.scripts[ document.scripts.length - 1 ].parentNode;
|
||
|
|
|
||
|
|
parent.displacement = function ( x, y, z, t, target ) {
|
||
|
|
|
||
|
|
if ( x * x + y * y < 0.01 ) {
|
||
|
|
|
||
|
|
return target.set( 0, 0, 0 );
|
||
|
|
|
||
|
|
} else {
|
||
|
|
|
||
|
|
const rho = Math.sqrt( x * x + y * y );
|
||
|
|
const phi = Math.atan2( y, x );
|
||
|
|
|
||
|
|
return target.set( 1.5 * Math.cos( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 1.5 * Math.sin( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 0 );
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
parent.lattice = true;
|
||
|
|
|
||
|
|
</script>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>Here is a cylindrical wave moving through a three-dimensional random distribution of molecules:</p>
|
||
|
|
|
||
|
|
<div class="view">
|
||
|
|
|
||
|
|
<script>
|
||
|
|
|
||
|
|
parent = document.scripts[ document.scripts.length - 1 ].parentNode;
|
||
|
|
|
||
|
|
parent.displacement = function ( x, y, z, t, target ) {
|
||
|
|
|
||
|
|
if ( x * x + y * y < 0.01 ) {
|
||
|
|
|
||
|
|
return target.set( 0, 0, 0 );
|
||
|
|
|
||
|
|
} else {
|
||
|
|
|
||
|
|
const rho = Math.sqrt( x * x + y * y );
|
||
|
|
const phi = Math.atan2( y, x );
|
||
|
|
|
||
|
|
return target.set( 1.5 * Math.cos( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 1.5 * Math.sin( phi ) * Math.sin( rho - t ) / Math.sqrt( rho ), 0 );
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
parent.lattice = false;
|
||
|
|
|
||
|
|
</script>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>Sound waves whose geometry is determined by three dimensions, spherical waves, obey the wave equation</p>
|
||
|
|
|
||
|
|
<div class="math">
|
||
|
|
|
||
|
|
<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
∂<sup>2</sup><i>u</i>
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
∂<i>r</i><sup>2</sup>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
+
|
||
|
|
|
||
|
|
<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
2
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
<i>r</i>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
∂<i>u</i>
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
∂<i>r</i>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
−
|
||
|
|
|
||
|
|
<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
1<sup></sup> <!-- sup for vertical alignment -->
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
<i>c</i><sup>2</sup>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
∂<sup>2</sup><i>u</i>
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
∂<i>t</i><sup>2</sup>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
= 0
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>The monochromatic solution for spherical sound waves will be taken to be</p>
|
||
|
|
|
||
|
|
<div class="math">
|
||
|
|
|
||
|
|
<i>u</i>(<i>r</i>,<i>t</i>) =
|
||
|
|
|
||
|
|
<span class="math-frac">
|
||
|
|
<span class="math-num">
|
||
|
|
sin(<i>k</i><i>r</i> ± ω<i>t</i>)
|
||
|
|
</span>
|
||
|
|
<span class="math-denom">
|
||
|
|
<i>r</i>
|
||
|
|
</span>
|
||
|
|
</span>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>Here is a spherical wave moving on a three-dimensional lattice of atoms:</p>
|
||
|
|
|
||
|
|
<div class="view">
|
||
|
|
|
||
|
|
<script>
|
||
|
|
|
||
|
|
parent = document.scripts[ document.scripts.length - 1 ].parentNode;
|
||
|
|
|
||
|
|
parent.displacement = function ( x, y, z, t, target ) {
|
||
|
|
|
||
|
|
if ( x * x + y * y + z * z < 0.01 ) {
|
||
|
|
|
||
|
|
return target.set( 0, 0, 0 );
|
||
|
|
|
||
|
|
} else {
|
||
|
|
|
||
|
|
const r = Math.sqrt( x * x + y * y + z * z );
|
||
|
|
const theta = Math.acos( z / r );
|
||
|
|
const phi = Math.atan2( y, x );
|
||
|
|
|
||
|
|
return target.set( 3 * Math.cos( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.sin( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.cos( theta ) * Math.sin( r - t ) / r );
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
parent.lattice = true;
|
||
|
|
|
||
|
|
</script>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>Here is a spherical wave moving through a three-dimensional random distribution of molecules:</p>
|
||
|
|
|
||
|
|
<div class="view">
|
||
|
|
|
||
|
|
<script>
|
||
|
|
|
||
|
|
parent = document.scripts[ document.scripts.length - 1 ].parentNode;
|
||
|
|
|
||
|
|
parent.displacement = function ( x, y, z, t, target ) {
|
||
|
|
|
||
|
|
if ( x * x + y * y + z * z < 0.01 ) {
|
||
|
|
|
||
|
|
return target.set( 0, 0, 0 );
|
||
|
|
|
||
|
|
} else {
|
||
|
|
|
||
|
|
const r = Math.sqrt( x * x + y * y + z * z );
|
||
|
|
const theta = Math.acos( z / r );
|
||
|
|
const phi = Math.atan2( y, x );
|
||
|
|
|
||
|
|
return target.set( 3 * Math.cos( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.sin( phi ) * Math.sin( theta ) * Math.sin( r - t ) / r, 3 * Math.cos( theta ) * Math.sin( r - t ) / r );
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
parent.lattice = false;
|
||
|
|
|
||
|
|
</script>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<p>The mathematical description of sound waves can be carried to higher dimensions, but one needs to wait for Four.js and its higher-dimensional successors to attempt visualizations.</p>
|
||
|
|
|
||
|
|
</body>
|
||
|
|
</html>
|