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unwrap_torus.html
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<!DOCTYPE html>
<html lang="en">
<head>
<title>Torus folding</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
<style>
body {
font-family: Monospace;
background-color: #ffffff;
margin: 0px;
overflow: hidden;
}
#info {
position: absolute;
top: 0px;
width: 100%;
padding: 5px;
text-align:center;
}
</style>
</head>
<body>
<canvas id="debug" style="position:absolute; left:100px"></canvas>
<script src="js/three.js"></script>
<script src="js/OrbitControls.js"></script>
<script>
// Initialize global user-set variables
var unwrapDeltaT = 3;
// Initialize global variables
var container;
var camera, scene, renderer;
var clock = new THREE.Clock();
var windowHalfX = window.innerWidth / 2;
var material, geometry, object;
// Torus variables
var animationSteps = 400;
var rows = 20;
var cols = 40;
var planeWidth = 700;
var planeHeight = 200;
var torusa = planeHeight/(2*Math.PI);
var torusR = planeWidth/(2*Math.PI)-torusa;
var thetaTarget = (rows-2)*Math.PI/rows;
var phiTarget = (cols-2)*Math.PI/cols;
var deltaTheta = (Math.PI-thetaTarget)/animationSteps;
var deltaPhi = -(Math.PI-phiTarget)/animationSteps;
var widthSteps = Array(rows+1);
for (var r = 0; r <= rows; r++) {
var ringRadiusTarget = torusR-torusa*Math.cos(-r*(Math.PI-thetaTarget));
var ringCircumferenceTarget = 2*Math.PI*ringRadiusTarget;
widthSteps[r] = -(ringCircumferenceTarget-planeWidth)/animationSteps/cols;
}
var directions = Array((rows+1)*(cols+1));
var speeds = Array((rows+1)*(cols+1));
var torusVertices = Array((rows+1)*(cols+1));
var firstRun = true;
var light;
init();
animate();
function init() {
container = document.createElement( 'div' );
document.body.appendChild( container );
var clock = new THREE.Clock();
camera = new THREE.PerspectiveCamera( 50, window.innerWidth / window.innerHeight, 0.1, 1000000 );
camera.up = new THREE.Vector3(0, 0, 1);
camera.position.set(400,0,400);
scene = new THREE.Scene();
scene.background = new THREE.Color( 0xffffff );
// Lights
// scene.add( new THREE.AmbientLight( 0xffffff, 0.3 ) );
var pointLight = new THREE.PointLight( 0xffffff, 2 );
pointLight.position.set(200,0,200);
scene.add(pointLight);
var pointLight2 = new THREE.PointLight( 0xffffff, 2 );
pointLight2.position.set(-200,0,200);
scene.add(pointLight);
// var geom = new THREE.PlaneGeometry( 1000, 1000, 32 );
// var mat = new THREE.MeshPhongMaterial( {color: 0x000000, side: THREE.DoubleSide, shininess: 0} );
// var plane = new THREE.Mesh( geom, mat );
// scene.add( plane );
// Surface
var map = new THREE.TextureLoader().load( 'assets/textures/texture.png' );
map.wrapS = map.wrapT = THREE.ClampToEdgeWrapping; // was RepeatWrapping
map.anisotropy = 16;
function getSurfacePoint(u, v, vector) {
vector.y = (u-0.5)*planeWidth;
vector.z = (v-0.5)*planeHeight;
}
geometry = new THREE.ParametricGeometry( getSurfacePoint, cols, rows );
material = new THREE.MeshLambertMaterial( { map: map, side: THREE.DoubleSide, transparent: false, depthWrite: true} );
// Show a particular vertex by changing its z position
// var ind = 20*(cols+1)+0;
// geometry.vertices[ind]=new THREE.Vector3(geometry.vertices[ind].x, geometry.vertices[ind].y, 200)
object = new THREE.Mesh( geometry, material );
object.scale.multiplyScalar( 1 );
scene.add( object );
var axesHelper = new THREE.AxesHelper( 50 );
scene.add( axesHelper );
renderer = new THREE.WebGLRenderer( { antialias: true } );
renderer.setPixelRatio( window.devicePixelRatio );
renderer.setSize( window.innerWidth, window.innerHeight );
container.appendChild( renderer.domElement );
// Browser camera controls
controls = new THREE.OrbitControls(camera, renderer.domElement);
controls.enableDamping = true;
controls.dampingFactor = 1;
controls.enableZoom = true;
controls.maxDistance = 150000;
controls.minDistance = 10;
window.addEventListener( 'resize', onWindowResize, false );
for (var r = 0; r <= rows; r++)
{
for (var c = 0; c <= cols; c++)
{
var i = r*(cols+1)+c;
var theta = r/rows*2*Math.PI;
var phi = c/cols*2*Math.PI;
var target = new THREE.Vector3((torusR+torusa*Math.cos(theta+Math.PI))*Math.cos(phi+Math.PI)-(torusa+torusR),
(torusR+torusa*Math.cos(theta+Math.PI))*Math.sin(phi+Math.PI),
torusa*Math.sin(theta+Math.PI));
torusVertices[i] = target.clone();
directions[i] = target.sub(geometry.vertices[i]);
speeds[i] = 1/animationSteps*directions[i].length();
directions[i].normalize();
}
}
geometry.verticesNeedUpdate = true;
geometry.elementsNeedUpdate = true;
geometry.morphTargetsNeedUpdate = true;
geometry.uvsNeedUpdate = true;
geometry.normalsNeedUpdate = true;
geometry.colorsNeedUpdate = true;
geometry.tangentsNeedUpdate = true;
geometry.vertices = torusVertices;
unwrapAnimation();
}
function changeTexture(name) {
object.material.map = THREE.ImageUtils.loadTexture(name);
object.material.needsUpdate = true;
}
function unwrapAnimation() {
for (var i = 0; i < animationSteps; i++) {
setTimeout(unwrapTheta, unwrapDeltaT*i);
}
setTimeout(unwrapPhiAnimation, unwrapDeltaT*animationSteps);
}
function unwrapPhiAnimation() {
for (var i = 0; i < animationSteps; i++)
setTimeout(unwrapPhi, unwrapDeltaT*i);
}
function onWindowResize() {
windowHalfX = window.innerWidth / 2;
camera.aspect = window.innerWidth / window.innerHeight;
camera.updateProjectionMatrix();
renderer.setSize( window.innerWidth, window.innerHeight );
}
function animate() {
var et = clock.getElapsedTime();
requestAnimationFrame( animate );
render();
}
function rotationAxis(axisPoint, point1, point2) {
var axis = axisPoint.clone().negate();
var vec1 = point1.clone().add(axis);
var vec2 = point2.clone().add(axis);
return vec1.cross(vec2);
}
function rotateAboutAxis(point, axisPoint, axisDirection, angle) {
// Source: https://sites.google.com/site/glennmurray/Home/rotation-matrices-and-formulas/rotation-about-an-arbitrary-axis-in-3-dimensions
axisDirection.normalize();
var a = axisPoint.x;
var b = axisPoint.y;
var c = axisPoint.z;
var x = point.x;
var y = point.y;
var z = point.z;
var u = axisDirection.x;
var v = axisDirection.y;
var w = axisDirection.z;
point.x = (a*(v**2+w**2)-u*(b*v+c*w-u*x-v*y-w*z))*(1-Math.cos(angle))+x*Math.cos(angle)+(-c*v+b*w-w*y+v*z)*Math.sin(angle);
point.y = (b*(u**2+w**2)-v*(a*u+c*w-u*x-v*y-w*z))*(1-Math.cos(angle))+y*Math.cos(angle)+(c*u-a*w+w*x-u*z)*Math.sin(angle);
point.z = (c*(u**2+v**2)-w*(a*u+b*v-u*x-v*y-w*z))*(1-Math.cos(angle))+z*Math.cos(angle)+(-b*u+a*v-v*x+u*y)*Math.sin(angle);
}
function render() {
renderer.render( scene, camera );
}
function wrap() {
var vs = geometry.vertices;
for (var r = 0; r <= rows; r++)
{
for (var c = 0; c <= cols; c++)
{
var hingeIndex = r*(cols+1)+c;
var axisPoint = vs[hingeIndex];
var step = widthSteps[r];
var targetIndex = hingeIndex;
if (c === cols/2)
step = 0;
else if (c === cols/2 + 1)
{
step = widthSteps[r]/2;
targetIndex = r*(cols+1)+c-1;
}
else if (c === cols/2 - 1)
{
step = widthSteps[r]/2;
targetIndex = r*(cols+1)+c+1;
}
else if (c > cols/2 + 1)
targetIndex = r*(cols+1)+c-1;
else if (c < cols/2 - 1)
targetIndex = r*(cols+1)+c+1;
var displacement = geometry.vertices[targetIndex].clone().addScaledVector(axisPoint, -1).normalize();
axisPoint.addScaledVector(displacement, step);
// ROTATE PHI
// Axis about which to rotate points on all other columns
var cAxis = new THREE.Vector3(0, 1, 0);
// Rotate
if (c === cols/2)
{
for (var ci = c+1; ci <= cols; ci++)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, deltaPhi/2);
}
for (var ci = c-1; ci >= 0; ci--)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, -deltaPhi/2);
}
}
else if (c > cols/2)
{
for (var ci = c+1; ci <= cols; ci++)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, deltaPhi);
}
}
else if (c < cols/2)
{
for (var ci = c-1; ci >= 0; ci--)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, -deltaPhi);
}
}
// ROTATE THETA
// Axis about which to rotate points on all other rows
if (firstRun)
var rAxis = new THREE.Vector3(1, 0, 0);
else
{
if (r <= rows - 2)
{
var sign = 1;
var [point1, point2] = [vs[(r+1)*(cols+1)+c], vs[(r+2)*(cols+1)+c]];
}
else
{
var sign = 1;
var [point1, point2] = [vs[(r-1)*(cols+1)+c], vs[(r-2)*(cols+1)+c]];
}
var rAxis = rotationAxis(vs[hingeIndex], point1, point2).multiplyScalar(sign);
}
// Rotate
if (r === rows/2)
{
for (var ri = rows/2+1; ri <= rows+1; ri++)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, deltaTheta/2);
}
for (var ri = rows/2-1; ri >= 0; ri--)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, -deltaTheta/2);
}
}
else if (r > rows/2)
{
for (var ri = r+1; ri <= rows+1; ri++)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, deltaTheta);
}
}
else if (r < rows/2)
{
for (var ri = r-1; ri >= 0; ri--)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, -deltaTheta);
}
}
}
}
geometry.verticesNeedUpdate = true;
geometry.elementsNeedUpdate = true;
geometry.morphTargetsNeedUpdate = true;
geometry.uvsNeedUpdate = true;
geometry.normalsNeedUpdate = true;
geometry.colorsNeedUpdate = true;
geometry.tangentsNeedUpdate = true;
}
function unwrapTheta() {
//camera.lookAt( new THREE.Vector3(0, 0, -torusR) );
var vs = geometry.vertices;
// ROTATE THETA
for (var r = 0; r <= rows; r++)
{
for (var c = 0; c <= cols; c++)
{
var hingeIndex = r*(cols+1)+c;
var axisPoint = vs[hingeIndex];
// var step = widthSteps[r];
// var targetIndex = hingeIndex;
// if (c === cols/2)
// step = 0;
// else if (c === cols/2 + 1)
// {
// step = widthSteps[r]/2;
// targetIndex = r*(cols+1)+c-1;
// }
// else if (c === cols/2 - 1)
// {
// step = widthSteps[r]/2;
// targetIndex = r*(cols+1)+c+1;
// }
// else if (c > cols/2 + 1)
// targetIndex = r*(cols+1)+c-1;
// else if (c < cols/2 - 1)
// targetIndex = r*(cols+1)+c+1;
// var displacement = geometry.vertices[targetIndex].clone().addScaledVector(axisPoint, -1).normalize();
// axisPoint.addScaledVector(displacement, step);
// Axis about which to rotate points on all other rows
if (r <= rows - 2)
{
var sign = -1;
var [point1, point2] = [vs[(r+1)*(cols+1)+c], vs[(r+2)*(cols+1)+c]];
}
else
{
var sign = 1;
var [point1, point2] = [vs[(r-1)*(cols+1)+c], vs[(r-2)*(cols+1)+c]];
}
var rAxis = rotationAxis(vs[hingeIndex], point1, point2).multiplyScalar(sign);
// Rotate
if (r === rows/2)
{
for (var ri = rows/2+1; ri <= rows+1; ri++)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, deltaTheta/2);
}
for (var ri = rows/2-1; ri >= 0; ri--)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, -deltaTheta/2);
}
}
else if (r > rows/2)
{
for (var ri = r+1; ri <= rows+1; ri++)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, deltaTheta);
}
}
else if (r < rows/2)
{
for (var ri = r-1; ri >= 0; ri--)
{
var ind = ri*(cols+1)+c;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, rAxis, -deltaTheta);
}
}
}
}
geometry.verticesNeedUpdate = true;
geometry.elementsNeedUpdate = true;
geometry.morphTargetsNeedUpdate = true;
geometry.uvsNeedUpdate = true;
geometry.normalsNeedUpdate = true;
geometry.colorsNeedUpdate = true;
geometry.tangentsNeedUpdate = true;
}
function unwrapPhi() {
//camera.lookAt( new THREE.Vector3(0, 0, -torusR) );
var vs = geometry.vertices;
// ROTATE PHI
for (var r = 0; r <= rows; r++)
{
for (var c = 0; c <= cols; c++)
{
var hingeIndex = r*(cols+1)+c;
var axisPoint = vs[hingeIndex];
// var step = widthSteps[r];
// var targetIndex = hingeIndex;
// if (c === cols/2)
// step = 0;
// else if (c === cols/2 + 1)
// {
// step = widthSteps[r]/2;
// targetIndex = r*(cols+1)+c-1;
// }
// else if (c === cols/2 - 1)
// {
// step = widthSteps[r]/2;
// targetIndex = r*(cols+1)+c+1;
// }
// else if (c > cols/2 + 1)
// targetIndex = r*(cols+1)+c-1;
// else if (c < cols/2 - 1)
// targetIndex = r*(cols+1)+c+1;
// var displacement = geometry.vertices[targetIndex].clone().addScaledVector(axisPoint, -1).normalize();
// axisPoint.addScaledVector(displacement, step);
// Axis about which to rotate points on all other columns
if (c <= cols - 2)
{
var sign = 1;
var [point1, point2] = [vs[r*(cols+1)+c+1], vs[r*(cols+1)+c+2]];
}
else
{
var sign = -1;
var [point1, point2] = [vs[r*(cols+1)+c-1], vs[r*(cols+1)+c-2]];
}
var cAxis = rotationAxis(vs[hingeIndex], point1, point2).multiplyScalar(sign);
// Rotate
if (c === cols/2)
{
for (var ci = c+1; ci <= cols; ci++)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, deltaPhi/2);
}
for (var ci = c-1; ci >= 0; ci--)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, -deltaPhi/2);
}
}
else if (c > cols/2)
{
for (var ci = c+1; ci <= cols; ci++)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, deltaPhi);
}
}
else if (c < cols/2)
{
for (var ci = c-1; ci >= 0; ci--)
{
var ind = r*(cols+1)+ci;
if (ind < vs.length && ind >= 0)
rotateAboutAxis(vs[ind], axisPoint, cAxis, -deltaPhi);
}
}
}
}
geometry.verticesNeedUpdate = true;
geometry.elementsNeedUpdate = true;
geometry.morphTargetsNeedUpdate = true;
geometry.uvsNeedUpdate = true;
geometry.normalsNeedUpdate = true;
geometry.colorsNeedUpdate = true;
geometry.tangentsNeedUpdate = true;
}
function beeline() {
for (var r = 0; r <= rows; r++)
{
for (var c = 0; c <= cols; c++)
{
var i = r*(cols+1)+c;
geometry.vertices[i].addScaledVector(directions[i], speeds[i]);
}
}
geometry.verticesNeedUpdate = true;
geometry.elementsNeedUpdate = true;
geometry.morphTargetsNeedUpdate = true;
geometry.uvsNeedUpdate = true;
geometry.normalsNeedUpdate = true;
geometry.colorsNeedUpdate = true;
geometry.tangentsNeedUpdate = true;
}
</script>
</body>
</html>