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<!DOCTYPE html>
<html lang="en">
<head>
<title>Verge3D webgl - multiple elements with text</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
<link type="text/css" rel="stylesheet" href="main.css">
<style>
* {
box-sizing: border-box;
-moz-box-sizing: border-box;
}
body {
background-color: #fff;
color: #444;
margin: auto;
padding: .5in;
max-width: 7in;
text-align: justify;
}
a {
color: #08f;
}
#info {
left: 0px;
}
.view {
width: 5in;
height: 5in;
margin: auto;
}
#c {
position: fixed;
left: 0px; top: 0px;
width: 100%;
height: 100%;
background-color: #fff;
z-index: -1;
}
.math {
text-align: center;
}
.math-frac {
display: inline-block;
vertical-align: middle;
}
.math-num {
display: block;
}
.math-denom {
display: block;
border-top: 1px solid;
}
.math-sqrt {
display: inline-block;
transform: scale(1, 1.3);
}
.math-sqrt-stem {
display: inline-block;
border-top: 1px solid;
margin-top: 5px;
}
</style>
</head>
<body>
<canvas id="c"></canvas>
<div id="info"><a href="https://www.soft8soft.com/verge3d" target="_blank" rel="noopener">Verge3D</a> - multiple elements with text - webgl</div>
<!-- Import maps polyfill -->
<!-- Remove this when import maps will be widely supported -->
<script async src="https://unpkg.com/es-module-shims@1.3.6/dist/es-module-shims.js"></script>
<script type="importmap">
{
"imports": {
"v3d": "../build/v3d.module.js",
"v3d/addons/": "./jsm/"
}
}
</script>
<script type="module">
import * as v3d from 'v3d';
import { OrbitControls } from 'v3d/addons/controls/OrbitControls.js';
const scenes = [];
const clock = new v3d.Clock();
let views, t, canvas, renderer;
window.onload = init;
function init() {
const balls = 20;
const size = .25;
const colors = [
'rgb(0,127,255)', 'rgb(255,0,0)', 'rgb(0,255,0)', 'rgb(0,255,255)',
'rgb(255,0,255)', 'rgb(255,0,127)', 'rgb(255,255,0)', 'rgb(0,255,127)'
];
canvas = document.getElementById('c');
renderer = new v3d.WebGLRenderer({ canvas: canvas, antialias: true });
renderer.setPixelRatio(window.devicePixelRatio);
views = document.querySelectorAll('.view');
for (let n = 0; n < views.length; n ++) {
const scene = new v3d.Scene();
scene.background = new v3d.Color(0xffffff);
const geometry0 = new v3d.BufferGeometry();
const geometry1 = new v3d.BufferGeometry();
const vertices = [];
if (views[n].lattice) {
const range = balls / 2;
for (let i = -range; i <= range; i++) {
for (let j = -range; j <= range; j ++) {
for (let k = -range; k <= range; k ++) {
vertices.push(i, j, k);
}
}
}
} else {
for (let m = 0; m < Math.pow(balls, 3); m ++) {
const i = balls * Math.random() - balls / 2;
const j = balls * Math.random() - balls / 2;
const k = balls * Math.random() - balls / 2;
vertices.push(i, j, k);
}
}
geometry0.setAttribute('position', new v3d.Float32BufferAttribute(vertices, 3));
geometry1.setAttribute('position', new v3d.Float32BufferAttribute(vertices.slice(), 3));
const index = Math.floor(colors.length * Math.random());
const canvas2 = document.createElement('canvas');
canvas2.width = 128;
canvas2.height = 128;
const context = canvas2.getContext('2d');
context.arc(64, 64, 64, 0, 2 * Math.PI);
context.fillStyle = colors[index];
context.fill();
const texture = new v3d.CanvasTexture(canvas2);
const material = new v3d.PointsMaterial({ size: size, map: texture, transparent: true, alphaTest: 0.1 });
scene.add(new v3d.Points(geometry0, material));
scene.userData.view = views[n];
scene.userData.geometry1 = geometry1;
const camera = new v3d.PerspectiveCamera(75, 1, 0.1, 100);
camera.position.set(0, 0, 1.2 * balls);
scene.userData.camera = camera;
const controls = new OrbitControls(camera, views[n]);
scene.userData.controls = controls;
scenes.push(scene);
}
t = 0;
animate();
}
function updateSize() {
const width = canvas.clientWidth;
const height = canvas.clientHeight;
if (canvas.width !== width || canvas.height != height) {
renderer.setSize(width, height, false);
}
}
function animate() {
render();
requestAnimationFrame(animate);
}
function render() {
updateSize();
renderer.setClearColor(0xffffff);
renderer.setScissorTest(false);
renderer.clear();
renderer.setClearColor(0x000000);
renderer.setScissorTest(true);
scenes.forEach(function(scene) {
const rect = scene.userData.view.getBoundingClientRect();
// check if it's offscreen. If so skip it
if (rect.bottom < 0 || rect.top > renderer.domElement.clientHeight ||
rect.right < 0 || rect.left > renderer.domElement.clientWidth) {
return; // it's off screen
}
// set the viewport
const width = rect.right - rect.left;
const height = rect.bottom - rect.top;
const left = rect.left;
const bottom = renderer.domElement.clientHeight - rect.bottom;
renderer.setViewport(left, bottom, width, height);
renderer.setScissor(left, bottom, width, height);
renderer.render(scene, scene.userData.camera);
const points = scene.children[0];
const position = points.geometry.attributes.position;
const point = new v3d.Vector3();
const offset = new v3d.Vector3();
for (let i = 0; i < position.count; i++) {
point.fromBufferAttribute(scene.userData.geometry1.attributes.position, i);
scene.userData.view.displacement(point.x, point.y, point.z, t / 5, offset);
position.setXYZ(i, point.x + offset.x, point.y + offset.y, point.z + offset.z);
}
position.needsUpdate = true;
});
t += clock.getDelta() * 60;
}
</script>
<p>Sound waves whose geometry is determined by a single dimension, plane waves, obey the wave equation</p>
<!-- css math formatting inspired by http://mathquill.com/mathquill/mathquill.css -->
<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">
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>where <i>c</i> designates the speed of sound in the medium. The monochromatic solution for plane waves will be taken to be</p>
<div class="math">
<i>u</i>(<i>r</i>,<i>t</i>) = sin(<i>k</i><i>r</i> ± ω<i>t</i>)
</div>
<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>
<p>Here is a plane wave moving on a three-dimensional lattice of atoms:</p>
<div class="view">
<script>
/* eslint-disable prefer-const*/
let parent = document.scripts[document.scripts.length - 1].parentNode;
parent.displacement = function(x, y, z, t, target) {
return target.set(Math.sin(x - t), 0, 0);
};
parent.lattice = true;
</script>
</div>
<p>Here is a plane 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) {
return target.set(Math.sin(x - t), 0, 0);
};
parent.lattice = false;
</script>
</div>
<p>Sound waves whose geometry is determined by two dimensions, cylindrical 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">
1
</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 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>