tenMinutePhysics/15-selfCollision.html

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<!DOCTYPE html>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<html lang="en">
	<head>
		<title>Cloth Self Collision Handling</title>
		<style>
			body {
				font-family: verdana; 
				font-size: 15px;
			}			
			.button {
			background-color: #606060;
			border: none;
			color: white;
			padding: 15px 32px;
			font-size: 16px;
			margin: 4px 2px;
			cursor: pointer;
		}
		</style>	
	</head>
	
	<body>

        <h1>Cloth Self Collision Handling</h1> 
		<button id = "buttonRun" onclick="run()" class="button">Run</button>
		<button onclick="restart()" class="button">Restart</button>
		<input type = "checkbox" onclick = "onShowEdges()"> Show edges</p>
		<input type = "checkbox" onclick = "onCollision()" checked> Handle collisions</p>
	
		<span id = "numTris">0</span> tris&nbsp;&nbsp;
		<span id = "numVerts">0</span> verts&nbsp;&nbsp;
		<span id = "ms">0.000</span> ms per frame
		<br>
		Bending compliance:
		<input type = "range" min = "0" max = "10" value = "1" id = "bendingComplianceSlider" class = "slider"> 


		<br><br>		
        <div id="container"></div>
        
        <script src="https://unpkg.com/three@0.139.2/build/three.min.js"></script>
        <script src="https://unpkg.com/three@0.139.2/examples/js/controls/OrbitControls.js"></script>
		<script>

			// ----- math on vector arrays -------------------------------------------------------------

			function vecSetZero(a,anr) {
				anr *= 3;
				a[anr++] = 0.0;
				a[anr++] = 0.0;
				a[anr]   = 0.0;
			}

			function vecScale(a,anr, scale) {
				anr *= 3;
				a[anr++] *= scale;
				a[anr++] *= scale;
				a[anr]   *= scale;
			}

			function vecCopy(a,anr, b,bnr) {
				anr *= 3; bnr *= 3;
				a[anr++] = b[bnr++]; 
				a[anr++] = b[bnr++]; 
				a[anr]   = b[bnr];
			}
			
			function vecAdd(a,anr, b,bnr, scale = 1.0) {
				anr *= 3; bnr *= 3;
				a[anr++] += b[bnr++] * scale; 
				a[anr++] += b[bnr++] * scale; 
				a[anr]   += b[bnr] * scale;
			}

			function vecSetDiff(dst,dnr, a,anr, b,bnr, scale = 1.0) {
				dnr *= 3; anr *= 3; bnr *= 3;
				dst[dnr++] = (a[anr++] - b[bnr++]) * scale;
				dst[dnr++] = (a[anr++] - b[bnr++]) * scale;
				dst[dnr]   = (a[anr] - b[bnr]) * scale;
			}

			function vecSetSum(dst,dnr, a,anr, b,bnr, scale = 1.0) {
				dnr *= 3; anr *= 3; bnr *= 3;
				dst[dnr++] = (a[anr++] + b[bnr++]) * scale;
				dst[dnr++] = (a[anr++] + b[bnr++]) * scale;
				dst[dnr]   = (a[anr] + b[bnr]) * scale;
			}

			function vecLengthSquared(a,anr) {
				anr *= 3;
				let a0 = a[anr], a1 = a[anr + 1], a2 = a[anr + 2];
				return a0 * a0 + a1 * a1 + a2 * a2;
			}

			function vecDistSquared(a,anr, b,bnr) {
				anr *= 3; bnr *= 3;
				let a0 = a[anr] - b[bnr], a1 = a[anr + 1] - b[bnr + 1], a2 = a[anr + 2] - b[bnr + 2];
				return a0 * a0 + a1 * a1 + a2 * a2;
			}	

			function vecDot(a,anr, b,bnr) {
				anr *= 3; bnr *= 3;
				return a[anr] * b[bnr] + a[anr + 1] * b[bnr + 1] + a[anr + 2] * b[bnr + 2];
			}	

			function vecSetCross(a,anr, b,bnr, c,cnr) {
				anr *= 3; bnr *= 3; cnr *= 3;
				a[anr++] = b[bnr + 1] * c[cnr + 2] - b[bnr + 2] * c[cnr + 1];
				a[anr++] = b[bnr + 2] * c[cnr + 0] - b[bnr + 0] * c[cnr + 2];
				a[anr]   = b[bnr + 0] * c[cnr + 1] - b[bnr + 1] * c[cnr + 0];
			}			
			
			var gThreeScene;
			var gRenderer;
			var gCamera;
			var gCameraControl;
			var gGrabber;
			var gMouseDown = false;

			// ------------------------------------------------------------------

			var gPhysicsScene = 
			{
				gravity : [0.0, -10.0, 0.0],
				dt : 1.0 / 60.0,
				numSubsteps : 10,
				paused: true,
				showEdges: false,
				cloth: null,				
			};

			// ------------------------------------------------------------------
			function onShowEdges() 
			{
				gPhysicsScene.showEdges = !gPhysicsScene.showEdges;
				for (var i = 0; i < gPhysicsScene.objects.length; i++) {
					gPhysicsScene.objects[i].edgeMesh.visible = gPhysicsScene.showEdges;
					gPhysicsScene.objects[i].triMesh.visible = !gPhysicsScene.showEdges;
				}
			}			

			// ------------------------------------------------------------------
			function onCollision() 
			{
				if (gPhysicsScene.cloth)
					gPhysicsScene.cloth.handleCollisions = !gPhysicsScene.cloth.handleCollisions;
			}			

			// ------------------------------------------------------------------
			class Hash {
				constructor(spacing, maxNumObjects) 
				{
					this.spacing = spacing;
					this.tableSize = 5 * maxNumObjects;
					this.cellStart = new Int32Array(this.tableSize + 1);
					this.cellEntries = new Int32Array(maxNumObjects);
					this.queryIds = new Int32Array(maxNumObjects);
					this.querySize = 0;

					this.maxNumObjects = maxNumObjects;
					this.firstAdjId = new Int32Array(maxNumObjects + 1);
					this.adjIds = new Int32Array(10 * maxNumObjects);
				}

				hashCoords(xi, yi, zi) {
					var h = (xi * 92837111) ^ (yi * 689287499) ^ (zi * 283923481);	// fantasy function
					return Math.abs(h) % this.tableSize; 
				}

				intCoord(coord) {
					return Math.floor(coord / this.spacing);
				}

				hashPos(pos, nr) {
					return this.hashCoords(
						this.intCoord(pos[3 * nr]), 
						this.intCoord(pos[3 * nr + 1]),
						this.intCoord(pos[3 * nr + 2]));
				}

				create(pos) {
					var numObjects = Math.min(pos.length / 3, this.cellEntries.length);

					// determine cell sizes

					this.cellStart.fill(0);
					this.cellEntries.fill(0);

					for (var i = 0; i < numObjects; i++) {
						var h = this.hashPos(pos, i);
						this.cellStart[h]++;
					}

					// determine cells starts

					var start = 0;
					for (var i = 0; i < this.tableSize; i++) {
						start += this.cellStart[i];
						this.cellStart[i] = start;
					}
					this.cellStart[this.tableSize] = start;	// guard

					// fill in objects ids

					for (var i = 0; i < numObjects; i++) {
						var h = this.hashPos(pos, i);
						this.cellStart[h]--;
						this.cellEntries[this.cellStart[h]] = i;
					}
				}

				query(pos, nr, maxDist) {
					var x0 = this.intCoord(pos[3 * nr] - maxDist);
					var y0 = this.intCoord(pos[3 * nr + 1] - maxDist);
					var z0 = this.intCoord(pos[3 * nr + 2] - maxDist);

					var x1 = this.intCoord(pos[3 * nr] + maxDist);
					var y1 = this.intCoord(pos[3 * nr + 1] + maxDist);
					var z1 = this.intCoord(pos[3 * nr + 2] + maxDist);

					this.querySize = 0;

					for (var xi = x0; xi <= x1; xi++) {
						for (var yi = y0; yi <= y1; yi++) {
							for (var zi = z0; zi <= z1; zi++) {
								var h = this.hashCoords(xi, yi, zi);
								var start = this.cellStart[h];
								var end = this.cellStart[h + 1];

								for (var i = start; i < end; i++) {
									this.queryIds[this.querySize] = this.cellEntries[i];
									this.querySize++;
								}
							}
						}
					}
				}

				queryAll(pos, maxDist) {

					var num = 0;
					var maxDist2 = maxDist * maxDist;

					for (var i = 0; i < this.maxNumObjects; i++) {
						var id0 = i;
						this.firstAdjId[id0] = num;
						this.query(pos, id0, maxDist);

						for (var j = 0; j < this.querySize; j++) {
							var id1 = this.queryIds[j];
							if (id1 >= id0)
								continue;
							var dist2 = vecDistSquared(pos, id0, pos, id1);
							if (dist2 > maxDist2)
								continue;
							
							if (num >= this.adjIds.length) {
								var newIds = new Int32Array(2 * num);  // dynamic array
								newIds.set(this.adjIds);
								this.adjIds = newIds;
							}
							this.adjIds[num++] = id1;
						}
					}

					this.firstAdjId[this.maxNumObjects] = num;
				}
			};

			// ------------------------------------------------------------------
			class Cloth {
				constructor(scene, numX, numY, spacing, thickness, bendingCompliance = 1.0)
				{
					// particles

					var jitter = 0.001 * spacing;

					this.numParticles = numX * numY;
					this.pos = new Float32Array(3 * this.numParticles);
					this.prevPos = new Float32Array(3 * this.numParticles);
					this.restPos = new Float32Array(3 * this.numParticles);
					this.vel = new Float32Array(3 * this.numParticles);
					this.invMass = new Float32Array(this.numParticles);
					this.thickness = thickness;
					this.handleCollisions = true;
					this.vecs = new Float32Array(4 * 3);

						// particles

					var attach = false;

					for (var i = 0; i < numX; i++) {
						for (var j = 0; j < numY; j++) {
							var id = i * numY + j;
							this.pos[3 * id] = - numX * spacing * 0.5 + i * spacing;
							this.pos[3 * id + 1] = 0.2 + j * spacing;
							this.pos[3 * id + 2] = 0.0;
							this.invMass[id] = 1.0;
							if (attach && j == numY - 1 && (i == 0 || i == numX - 1))
								this.invMass[id] = 0.0;
						}
					}

					for (var i = 0; i < this.pos.length; i++) 
						this.pos[i] += -jitter * 2.0 * jitter * Math.random()

					this.hash = new Hash(spacing, this.numParticles);

					this.restPos.set(this.pos);
					this.vel.fill(0.0);

					// constraints

					var numConstraintTypes = 6;

					this.ids = new Int32Array(this.numParticles * numConstraintTypes * 2);
					this.compliances = new Float32Array(this.numParticles * numConstraintTypes);
					var offsets = [0,0, 0,1,  0,0, 1,0,  0,0, 1,1,  0,1, 1,0,  0,0, 0,2,  0,0, 2,0];
					var num = 0;

					var stretchCompliance = 0.0;
					var shearCompliance = 0.0001;

					var compliances = [stretchCompliance, stretchCompliance, shearCompliance, shearCompliance, bendingCompliance, bendingCompliance];

					for (var constType = 0; constType < numConstraintTypes; constType++) {
						for (var i = 0; i < numX; i++) {
							for (var j = 0; j < numY; j++) {
								var p = 4 * constType;

								var i0 = i + offsets[p];
								var j0 = j + offsets[p + 1];
								var i1 = i + offsets[p + 2];
								var j1 = j + offsets[p + 3];
								if (i0 < numX && j0 < numY && i1 < numX && j1 < numY) {
									this.ids[num++] = i0 * numY + j0;
									this.ids[num++] = i1 * numY + j1;
									this.compliances[Math.floor(num / 2)] = compliances[constType];
								}
							}
						}
					}

					// randomize

					this.numConstraints = Math.floor(num / 2);

					// for (var i = 0; i < this.numConstraints; i++) {
					// 	var j = i + Math.floor(Math.random() * (this.numConstraints - i));
					// 	var c = this.compliances[i]; this.compliances[i] = this.compliances[j]; this.compliances[j] = c;
					// 	var id = this.ids[2 * i]; this.ids[2 * i] = this.ids[2 * j]; this.ids[2 * j] = id;
					// 	id = this.ids[2 * i + 1]; this.ids[2 * i + 1] = this.ids[2 * j + 1]; this.ids[2 * j + 1] = id;
					// }

					// pre-compute rest lengths

					this.restLens = new Float32Array(this.numConstraints);
					for (var i = 0; i < this.numConstraints; i++) {
						var id0 = this.ids[2 * i];
						var id1 = this.ids[2 * i + 1];
						this.restLens[i] = Math.sqrt(vecDistSquared(this.pos,id0, this.pos,id1));
					}

					// visual meshes

					var triIds = [];
					var edgeIds = [];

					for (var i = 0; i < numX; i++) {
						for (var j = 0; j < numY; j++) {
							var id = i * numY + j;
							if (i < numX - 1 && j < numY - 1) {
								triIds.push(id + 1); triIds.push(id); triIds.push(id + 1 + numY);
								triIds.push(id + 1 + numY); triIds.push(id); triIds.push(id + numY);
							}
							if (i < numX - 1) {
								edgeIds.push(id);
								edgeIds.push(id + numY);
							}
							if (j < numY - 1) {
								edgeIds.push(id);
								edgeIds.push(id + 1);
							}
						}
					}					

					geometry = new THREE.BufferGeometry();
					geometry.setAttribute('position', new THREE.BufferAttribute(this.pos, 3));
					geometry.setIndex(triIds);
					var visMaterial = new THREE.MeshPhongMaterial({color: 0xff0000, side: THREE.FrontSide});
					this.triMesh = new THREE.Mesh(geometry, visMaterial);
					this.triMesh.castShadow = true;
					this.triMesh.userData = this;	// for raycasting
					this.triMesh.layers.enable(1);
					scene.add(this.triMesh);

					var backMaterial = new THREE.MeshPhongMaterial({color: 0xff8000, side: THREE.BackSide});
					this.backMesh = new THREE.Mesh(geometry, backMaterial);
					this.backMesh.userData = this;	// for raycasting
					this.backMesh.layers.enable(1);
					
					scene.add(this.backMesh);
					geometry.computeVertexNormals();

					// visual edge mesh

					var geometry = new THREE.BufferGeometry();
					geometry.setAttribute('position', new THREE.BufferAttribute(this.pos, 3));
					geometry.setIndex(edgeIds);
					var lineMaterial = new THREE.LineBasicMaterial({color: 0xff0000, linewidth: 2});
					this.edgeMesh = new THREE.LineSegments(geometry, lineMaterial);
					this.edgeMesh.visible = false;
					scene.add(this.edgeMesh);

					this.updateVisMeshes();
				}

				simulate(frameDt, numSubSteps, gravity)
				{
					var dt = frameDt / numSubSteps;
					var maxVelocity = 0.2 * this.thickness / dt;

					if (this.handleCollisions) {
						this.hash.create(this.pos);
						var maxTravelDist = maxVelocity * frameDt;
						this.hash.queryAll(this.pos, maxTravelDist);
					}
					
					for (var step = 0; step < numSubSteps; step++)  {

						// integrate 

						for (var i = 0; i < this.numParticles; i++) {
							if (this.invMass[i] > 0.0) {
								vecAdd(this.vel,i, gravity,0, dt);
								var v = Math.sqrt(vecLengthSquared(this.vel,i));
								var maxV = 0.2 * this.thickness / dt;
								if (v > maxV) {
									vecScale(this.vel,i, maxV / v);
								}
								vecCopy(this.prevPos,i, this.pos,i);
								vecAdd(this.pos,i, this.vel,i, dt);
							}
						}

						// solve

						this.solveGroundCollisions();

						this.solveConstraints(dt);
						if (this.handleCollisions)
						 	this.solveCollisions(dt);

						// update velocities

						for (var i = 0; i < this.numParticles; i++) {
							if (this.invMass[i] > 0.0)
								vecSetDiff(this.vel,i, this.pos,i, this.prevPos,i, 1.0 / dt);
						}
					}

					this.updateVisMeshes();
				}
				
				solveConstraints(dt) {
					for (var i = 0; i < this.numConstraints; i++) {
						var id0 = this.ids[2 * i];
						var id1 = this.ids[2 * i + 1];
						var w0 = this.invMass[id0];
						var w1 = this.invMass[id1];
						var w = w0 + w1;
						if (w == 0.0)
							continue;

						vecSetDiff(this.vecs,0, this.pos,id0, this.pos,id1);
						var len = Math.sqrt(vecLengthSquared(this.vecs,0));
						if (len == 0.0)
							continue;
						vecScale(this.vecs,0, 1.0 / len);
						var restLen = this.restLens[i];
						var C = len - restLen;
						var alpha = this.compliances[i] / dt /dt;
						var s = -C / (w + alpha);
						vecAdd(this.pos,id0, this.vecs,0, s * w0);
						vecAdd(this.pos,id1, this.vecs,0, -s * w1);
					}
					var done = 0;
				}

				solveGroundCollisions() {
					for (var i = 0; i < this.numParticles; i++) {
						if (this.invMass[i] == 0.0)
							continue;
						var y = this.pos[3 * i + 1];
						if (y < 0.5 * this.thickness) {
							var damping = 1.0
							vecSetDiff(this.vecs,0, this.pos,i, this.prevPos,i);
							vecAdd(this.pos,i, this.vecs,0, -damping);
							this.pos[3 * i + 1] = 0.5 * this.thickness;
						}
					}
				}

				solveCollisions(dt) { 

					var thickness2 = this.thickness * this.thickness;

					for (var i = 0; i < this.numParticles; i++) {
						if (this.invMass[i] == 0.0)
							continue;
						var id0 = i;
						var first = this.hash.firstAdjId[i];
						var last = this.hash.firstAdjId[i + 1];

						for (var j = first; j < last; j++) {

							var id1 = this.hash.adjIds[j];
							if (this.invMass[id1] == 0.0)
								continue;

							vecSetDiff(this.vecs,0, this.pos,id1, this.pos,id0);

							var dist2 = vecLengthSquared(this.vecs,0);
							if (dist2 > thickness2 || dist2 == 0.0)
								continue;
							var restDist2 = vecDistSquared(this.restPos,id0, this.restPos,id1);

							var minDist = this.thickness;
							if (dist2 > restDist2)
								continue;
							if (restDist2 < thickness2)
								minDist = Math.sqrt(restDist2);

							// position correction
							var dist = Math.sqrt(dist2);
							vecScale(this.vecs,0, (minDist - dist) / dist);
							vecAdd(this.pos,id0, this.vecs,0, -0.5);
							vecAdd(this.pos,id1, this.vecs,0,  0.5);

							// velocities
							vecSetDiff(this.vecs,0, this.pos,id0, this.prevPos, id0);
							vecSetDiff(this.vecs,1, this.pos,id1, this.prevPos, id1);

							// average velocity
							vecSetSum(this.vecs,2, this.vecs,0, this.vecs,1, 0.5);

							// velocity corrections
							vecSetDiff(this.vecs,0, this.vecs,2, this.vecs,0);
							vecSetDiff(this.vecs,1, this.vecs,2, this.vecs,1);
							
							// add corrections
							var friction = 0.0;
							vecAdd(this.pos,id0, this.vecs,0, friction);
							vecAdd(this.pos,id1, this.vecs,1, friction);
						}
					}
				}
				
				updateVisMeshes() {
					this.triMesh.geometry.computeVertexNormals();
					this.triMesh.geometry.attributes.position.needsUpdate = true;
					this.triMesh.geometry.computeBoundingSphere();

					this.edgeMesh.geometry.attributes.position.needsUpdate = true;
				}

				startGrab(pos) 
				{
					var p = [pos.x, pos.y, pos.z];
					var minD2 = Number.MAX_VALUE;
					this.grabId = -1;
					for (let i = 0; i < this.numParticles; i++) {
						var d2 = vecDistSquared(p,0, this.pos,i);
						if (d2 < minD2) {
							minD2 = d2;
							this.grabId = i;
						}
					}

					if (this.grabId >= 0) {
						this.grabInvMass = this.invMass[this.grabId];
						this.invMass[this.grabId] = 0.0;
						vecCopy(this.pos,this.grabId, p,0);	
					}
				}

				moveGrabbed(pos, vel) 
				{
					if (this.grabId >= 0) {
						var p = [pos.x, pos.y, pos.z];
						vecCopy(this.pos,this.grabId, p,0);
					}
				}

				endGrab(pos, vel) 
				{
					if (this.grabId >= 0) {
						this.invMass[this.grabId] = this.grabInvMass;
						var v = [vel.x, vel.y, vel.z];
						vecCopy(this.vel,this.grabId, v,0);
					}
					this.grabId = -1;
				}								
			}

			var timeFrames = 0;
			var timeSum = 0;	

			// ------------------------------------------------------------------
			function simulate() 
			{
				if (gPhysicsScene.paused)
					return;

				var startTime = performance.now();

				gPhysicsScene.cloth.simulate(gPhysicsScene.dt, gPhysicsScene.numSubsteps, gPhysicsScene.gravity);

				gGrabber.increaseTime(gPhysicsScene.dt);

				var endTime = performance.now();
				timeSum += endTime - startTime; 
				timeFrames++;

				if (timeFrames > 10) {
					timeSum /= timeFrames;
					document.getElementById("ms").innerHTML = timeSum.toFixed(3);		
					timeFrames = 0;
					timeSum = 0;
				}					
			}

			// ------------------------------------------
					
			function initThreeScene() 
			{
				gThreeScene = new THREE.Scene();
				
				// Lights
				
				gThreeScene.add( new THREE.AmbientLight( 0x505050 ) );	
				gThreeScene.fog = new THREE.Fog( 0x000000, 0, 15 );				

				var spotLight = new THREE.SpotLight( 0xffffff );
				spotLight.angle = Math.PI / 5;
				spotLight.penumbra = 0.2;
				spotLight.position.set( 2, 3, 3 );
				spotLight.castShadow = true;
				spotLight.shadow.camera.near = 3;
				spotLight.shadow.camera.far = 10;
				spotLight.shadow.mapSize.width = 1024;
				spotLight.shadow.mapSize.height = 1024;
				gThreeScene.add( spotLight );

				var dirLight = new THREE.DirectionalLight( 0x55505a, 1 );
				dirLight.position.set( 0, 3, 0 );
				dirLight.castShadow = true;
				dirLight.shadow.camera.near = 1;
				dirLight.shadow.camera.far = 10;

				dirLight.shadow.camera.right = 1;
				dirLight.shadow.camera.left = - 1;
				dirLight.shadow.camera.top	= 1;
				dirLight.shadow.camera.bottom = - 1;

				dirLight.shadow.mapSize.width = 1024;
				dirLight.shadow.mapSize.height = 1024;
				gThreeScene.add( dirLight );
				
				// Geometry

				var ground = new THREE.Mesh(
					new THREE.PlaneBufferGeometry( 20, 20, 1, 1 ),
					new THREE.MeshPhongMaterial( { color: 0xa0adaf, shininess: 150 } )
				);				

				ground.rotation.x = - Math.PI / 2; // rotates X/Y to X/Z
				ground.receiveShadow = true;
				gThreeScene.add( ground );
				
				var helper = new THREE.GridHelper( 20, 20 );
				helper.material.opacity = 1.0;
				helper.material.transparent = true;
				helper.position.set(0, 0.002, 0);
				gThreeScene.add( helper );				
				
				// Renderer

				gRenderer = new THREE.WebGLRenderer();
				gRenderer.shadowMap.enabled = true;
				gRenderer.setPixelRatio( window.devicePixelRatio );
				gRenderer.setSize( 0.8 * window.innerWidth, 0.8 * window.innerHeight );
				window.addEventListener( 'resize', onWindowResize, false );
				container.appendChild( gRenderer.domElement );
				
				// Camera
						
				gCamera = new THREE.PerspectiveCamera( 70, window.innerWidth / window.innerHeight, 0.01, 100);
			    gCamera.position.set(0, 0.3, 0.5);
				gCamera.updateMatrixWorld();	

				gThreeScene.add(gCamera);

				gCameraControl = new THREE.OrbitControls(gCamera, gRenderer.domElement);
				gCameraControl.zoomSpeed = 0.8;
    			gCameraControl.panSpeed = 0.4;
				gCameraControl
				gCameraControl.target = new THREE.Vector3(0.0, 0.1, 0.0);
				gCameraControl.update();

				// grabber

				gGrabber = new Grabber();
				container.addEventListener( 'pointerdown', onPointer, false );
				container.addEventListener( 'pointermove', onPointer, false );
				container.addEventListener( 'pointerup', onPointer, false );
			}

			function initPhysics(triIds) 
			{
				var spacing = 0.01;
				var thickness = 0.01;
				var numX = 30;
				var numY = 200;

				gPhysicsScene.cloth = new Cloth(gThreeScene, numX, numY, spacing, thickness);
				document.getElementById("numTris").innerHTML = numX * numY * 2;
				document.getElementById("numVerts").innerHTML = numX * numY;
			}

			// ------- grabber -----------------------------------------------------------

			class Grabber {
				constructor() {
					this.raycaster = new THREE.Raycaster();
					this.raycaster.layers.set(1);
					this.raycaster.params.Line.threshold = 0.1;
					this.physicsObject = null;
					this.distance = 0.0;
					this.prevPos = new THREE.Vector3();
					this.vel = new THREE.Vector3();
					this.time = 0.0;
				}
				increaseTime(dt) {
					this.time += dt;
				}
				updateRaycaster(x, y) {
					var rect = gRenderer.domElement.getBoundingClientRect();
					this.mousePos = new THREE.Vector2();
					this.mousePos.x = ((x - rect.left) / rect.width ) * 2 - 1;
					this.mousePos.y = -((y - rect.top) / rect.height ) * 2 + 1;
					this.raycaster.setFromCamera( this.mousePos, gCamera );
				}
				start(x, y) {
					this.physicsObject = null;
					this.updateRaycaster(x, y);
					var intersects = this.raycaster.intersectObjects( gThreeScene.children );
					if (intersects.length > 0) {
						var obj = intersects[0].object.userData;
						if (obj) {
							this.physicsObject = obj;
							this.distance = intersects[0].distance;
							var pos = this.raycaster.ray.origin.clone();
							pos.addScaledVector(this.raycaster.ray.direction, this.distance);
							this.physicsObject.startGrab(pos);
							this.prevPos.copy(pos);
							this.vel.set(0.0, 0.0, 0.0);
							this.time = 0.0;
							if (gPhysicsScene.paused)
								run();
						}
					}
				}
				move(x, y) {
					if (this.physicsObject) {
						this.updateRaycaster(x, y);
						var pos = this.raycaster.ray.origin.clone();
						pos.addScaledVector(this.raycaster.ray.direction, this.distance);

						this.vel.copy(pos);
						this.vel.sub(this.prevPos);
						if (this.time > 0.0)
							this.vel.divideScalar(this.time);
						else
							this.vel.set(0.0, 0.0, 0.0);
						this.prevPos.copy(pos);
						this.time = 0.0;

						this.physicsObject.moveGrabbed(pos, this.vel);
					}
				}
				end(x, y) {
					if (this.physicsObject) { 
						this.physicsObject.endGrab(this.prevPos, this.vel);
						this.physicsObject = null;
					}
				}
			}			

			function onPointer( evt ) 
			{
				event.preventDefault();
				if (evt.type == "pointerdown") {
					gGrabber.start(evt.clientX, evt.clientY);
					gMouseDown = true;
					if (gGrabber.physicsObject) {
						gCameraControl.saveState();
						gCameraControl.enabled = false;
					}
				}
				else if (evt.type == "pointermove" && gMouseDown) {
					gGrabber.move(evt.clientX, evt.clientY);
				}
				else if (evt.type == "pointerup") {
					if (gGrabber.physicsObject) {
						gGrabber.end();
						gCameraControl.reset();
					}
					gMouseDown = false;
					gCameraControl.enabled = true;
				}
			}	

			document.getElementById("bendingComplianceSlider").oninput = function() {
				for (var i = 0; i < gPhysicsScene.objects.length; i++) 
					gPhysicsScene.objects[i].bendingCompliance = this.value;
			}
			
			// ------------------------------------------------------

			function onWindowResize() {

				gCamera.aspect = window.innerWidth / window.innerHeight;
				gCamera.updateProjectionMatrix();
				gRenderer.setSize( window.innerWidth, window.innerHeight );
			}

			function run() {
				var button = document.getElementById('buttonRun');
				if (gPhysicsScene.paused)
					button.innerHTML = "Stop";
				else
					button.innerHTML = "Run";
				gPhysicsScene.paused = !gPhysicsScene.paused;
			}

			function restart() {
				location.reload();
			}
			
			// make browser to call us repeatedly -----------------------------------

			function update() {
				simulate();
				gRenderer.render(gThreeScene, gCamera);
				requestAnimationFrame(update);
			}
					
			initThreeScene();
			onWindowResize();
			initPhysics();
			update();
			
		</script>
	</body>
</html>