examples/webgl_animation_cloth.html

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		<title>three.js webgl - cloth simulation</title>
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		<div id="info">Simple Cloth Simulation<br/>
			Verlet integration with relaxed constraints<br/>
		</div>

		<script type="module">

			import * as THREE from '../build/three.module.js';

			import Stats from './jsm/libs/stats.module.js';
			import { GUI } from './jsm/libs/dat.gui.module.js';

			import { OrbitControls } from './jsm/controls/OrbitControls.js';

			/*
			 * Cloth Simulation using a relaxed constraints solver
			 */

			// Suggested Readings

			// Advanced Character Physics by Thomas Jakobsen Character
			// http://freespace.virgin.net/hugo.elias/models/m_cloth.htm
			// http://en.wikipedia.org/wiki/Cloth_modeling
			// http://cg.alexandra.dk/tag/spring-mass-system/
			// Real-time Cloth Animation http://www.darwin3d.com/gamedev/articles/col0599.pdf

			var params = {
				enableWind: true,
				showBall: false,
				tooglePins: togglePins
			};

			var DAMPING = 0.03;
			var DRAG = 1 - DAMPING;
			var MASS = 0.1;
			var restDistance = 25;

			var xSegs = 10;
			var ySegs = 10;

			var clothFunction = plane( restDistance * xSegs, restDistance * ySegs );

			var cloth = new Cloth( xSegs, ySegs );

			var GRAVITY = 981 * 1.4;
			var gravity = new THREE.Vector3( 0, - GRAVITY, 0 ).multiplyScalar( MASS );


			var TIMESTEP = 18 / 1000;
			var TIMESTEP_SQ = TIMESTEP * TIMESTEP;

			var pins = [];

			var windForce = new THREE.Vector3( 0, 0, 0 );

			var ballPosition = new THREE.Vector3( 0, - 45, 0 );
			var ballSize = 60; //40

			var tmpForce = new THREE.Vector3();

			var lastTime;


			function plane( width, height ) {

				return function ( u, v, target ) {

					var x = ( u - 0.5 ) * width;
					var y = ( v + 0.5 ) * height;
					var z = 0;

					target.set( x, y, z );

				};

			}

			function Particle( x, y, z, mass ) {

				this.position = new THREE.Vector3();
				this.previous = new THREE.Vector3();
				this.original = new THREE.Vector3();
				this.a = new THREE.Vector3( 0, 0, 0 ); // acceleration
				this.mass = mass;
				this.invMass = 1 / mass;
				this.tmp = new THREE.Vector3();
				this.tmp2 = new THREE.Vector3();

				// init

				clothFunction( x, y, this.position ); // position
				clothFunction( x, y, this.previous ); // previous
				clothFunction( x, y, this.original );

			}

			// Force -> Acceleration

			Particle.prototype.addForce = function ( force ) {

				this.a.add(
					this.tmp2.copy( force ).multiplyScalar( this.invMass )
				);

			};


			// Performs Verlet integration

			Particle.prototype.integrate = function ( timesq ) {

				var newPos = this.tmp.subVectors( this.position, this.previous );
				newPos.multiplyScalar( DRAG ).add( this.position );
				newPos.add( this.a.multiplyScalar( timesq ) );

				this.tmp = this.previous;
				this.previous = this.position;
				this.position = newPos;

				this.a.set( 0, 0, 0 );

			};


			var diff = new THREE.Vector3();

			function satisfyConstraints( p1, p2, distance ) {

				diff.subVectors( p2.position, p1.position );
				var currentDist = diff.length();
				if ( currentDist === 0 ) return; // prevents division by 0
				var correction = diff.multiplyScalar( 1 - distance / currentDist );
				var correctionHalf = correction.multiplyScalar( 0.5 );
				p1.position.add( correctionHalf );
				p2.position.sub( correctionHalf );

			}


			function Cloth( w, h ) {

				w = w || 10;
				h = h || 10;
				this.w = w;
				this.h = h;

				var particles = [];
				var constraints = [];

				var u, v;

				// Create particles
				for ( v = 0; v <= h; v ++ ) {

					for ( u = 0; u <= w; u ++ ) {

						particles.push(
							new Particle( u / w, v / h, 0, MASS )
						);

					}

				}

				// Structural

				for ( v = 0; v < h; v ++ ) {

					for ( u = 0; u < w; u ++ ) {

						constraints.push( [
							particles[ index( u, v ) ],
							particles[ index( u, v + 1 ) ],
							restDistance
						] );

						constraints.push( [
							particles[ index( u, v ) ],
							particles[ index( u + 1, v ) ],
							restDistance
						] );

					}

				}

				for ( u = w, v = 0; v < h; v ++ ) {

					constraints.push( [
						particles[ index( u, v ) ],
						particles[ index( u, v + 1 ) ],
						restDistance

					] );

				}

				for ( v = h, u = 0; u < w; u ++ ) {

					constraints.push( [
						particles[ index( u, v ) ],
						particles[ index( u + 1, v ) ],
						restDistance
					] );

				}


				// While many systems use shear and bend springs,
				// the relaxed constraints model seems to be just fine
				// using structural springs.
				// Shear
				// var diagonalDist = Math.sqrt(restDistance * restDistance * 2);


				// for (v=0;v<h;v++) {
				// 	for (u=0;u<w;u++) {

				// 		constraints.push([
				// 			particles[index(u, v)],
				// 			particles[index(u+1, v+1)],
				// 			diagonalDist
				// 		]);

				// 		constraints.push([
				// 			particles[index(u+1, v)],
				// 			particles[index(u, v+1)],
				// 			diagonalDist
				// 		]);

				// 	}
				// }


				this.particles = particles;
				this.constraints = constraints;

				function index( u, v ) {

					return u + v * ( w + 1 );

				}

				this.index = index;

			}

			function simulate( time ) {

				if ( ! lastTime ) {

					lastTime = time;
					return;

				}

				var i, j, il, particles, particle, constraints, constraint;

				// Aerodynamics forces

				if ( params.enableWind ) {

					var indx;
					var normal = new THREE.Vector3();
					var indices = clothGeometry.index;
					var normals = clothGeometry.attributes.normal;

					particles = cloth.particles;

					for ( i = 0, il = indices.count; i < il; i += 3 ) {

						for ( j = 0; j < 3; j ++ ) {

							indx = indices.getX( i + j );
							normal.fromBufferAttribute( normals, indx );
							tmpForce.copy( normal ).normalize().multiplyScalar( normal.dot( windForce ) );
							particles[ indx ].addForce( tmpForce );

						}

					}

				}

				for ( particles = cloth.particles, i = 0, il = particles.length; i < il; i ++ ) {

					particle = particles[ i ];
					particle.addForce( gravity );

					particle.integrate( TIMESTEP_SQ );

				}

				// Start Constraints

				constraints = cloth.constraints;
				il = constraints.length;

				for ( i = 0; i < il; i ++ ) {

					constraint = constraints[ i ];
					satisfyConstraints( constraint[ 0 ], constraint[ 1 ], constraint[ 2 ] );

				}

				// Ball Constraints

				ballPosition.z = - Math.sin( Date.now() / 600 ) * 90; //+ 40;
				ballPosition.x = Math.cos( Date.now() / 400 ) * 70;

				if ( params.showBall ) {

					sphere.visible = true;

					for ( particles = cloth.particles, i = 0, il = particles.length; i < il; i ++ ) {

						particle = particles[ i ];
						var pos = particle.position;
						diff.subVectors( pos, ballPosition );
						if ( diff.length() < ballSize ) {

							// collided
							diff.normalize().multiplyScalar( ballSize );
							pos.copy( ballPosition ).add( diff );

						}

					}

				} else {

					sphere.visible = false;

				}


				// Floor Constraints

				for ( particles = cloth.particles, i = 0, il = particles.length; i < il; i ++ ) {

					particle = particles[ i ];
					pos = particle.position;
					if ( pos.y < - 250 ) {

						pos.y = - 250;

					}

				}

				// Pin Constraints

				for ( i = 0, il = pins.length; i < il; i ++ ) {

					var xy = pins[ i ];
					var p = particles[ xy ];
					p.position.copy( p.original );
					p.previous.copy( p.original );

				}


			}

			/* testing cloth simulation */

			var pinsFormation = [];
			var pins = [ 6 ];

			pinsFormation.push( pins );

			pins = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
			pinsFormation.push( pins );

			pins = [ 0 ];
			pinsFormation.push( pins );

			pins = []; // cut the rope ;)
			pinsFormation.push( pins );

			pins = [ 0, cloth.w ]; // classic 2 pins
			pinsFormation.push( pins );

			pins = pinsFormation[ 1 ];

			function togglePins() {

				pins = pinsFormation[ ~ ~ ( Math.random() * pinsFormation.length ) ];

			}

			var container, stats;
			var camera, scene, renderer;

			var clothGeometry;
			var sphere;
			var object;

			init();
			animate();

			function init() {

				container = document.createElement( 'div' );
				document.body.appendChild( container );

				// scene

				scene = new THREE.Scene();
				scene.background = new THREE.Color( 0xcce0ff );
				scene.fog = new THREE.Fog( 0xcce0ff, 500, 10000 );

				// camera

				camera = new THREE.PerspectiveCamera( 30, window.innerWidth / window.innerHeight, 1, 10000 );
				camera.position.set( 1000, 50, 1500 );

				// lights

				scene.add( new THREE.AmbientLight( 0x666666 ) );

				var light = new THREE.DirectionalLight( 0xdfebff, 1 );
				light.position.set( 50, 200, 100 );
				light.position.multiplyScalar( 1.3 );

				light.castShadow = true;

				light.shadow.mapSize.width = 1024;
				light.shadow.mapSize.height = 1024;

				var d = 300;

				light.shadow.camera.left = - d;
				light.shadow.camera.right = d;
				light.shadow.camera.top = d;
				light.shadow.camera.bottom = - d;

				light.shadow.camera.far = 1000;

				scene.add( light );

				// cloth material

				var loader = new THREE.TextureLoader();
				var clothTexture = loader.load( 'textures/patterns/circuit_pattern.png' );
				clothTexture.anisotropy = 16;

				var clothMaterial = new THREE.MeshLambertMaterial( {
					map: clothTexture,
					side: THREE.DoubleSide,
					alphaTest: 0.5
				} );

				// cloth geometry

				clothGeometry = new THREE.ParametricBufferGeometry( clothFunction, cloth.w, cloth.h );

				// cloth mesh

				object = new THREE.Mesh( clothGeometry, clothMaterial );
				object.position.set( 0, 0, 0 );
				object.castShadow = true;
				scene.add( object );

				object.customDepthMaterial = new THREE.MeshDepthMaterial( {
					depthPacking: THREE.RGBADepthPacking,
					map: clothTexture,
					alphaTest: 0.5
				} );

				// sphere

				var ballGeo = new THREE.SphereBufferGeometry( ballSize, 32, 16 );
				var ballMaterial = new THREE.MeshLambertMaterial();

				sphere = new THREE.Mesh( ballGeo, ballMaterial );
				sphere.castShadow = true;
				sphere.receiveShadow = true;
				sphere.visible = false;
				scene.add( sphere );

				// ground

				var groundTexture = loader.load( 'textures/terrain/grasslight-big.jpg' );
				groundTexture.wrapS = groundTexture.wrapT = THREE.RepeatWrapping;
				groundTexture.repeat.set( 25, 25 );
				groundTexture.anisotropy = 16;
				groundTexture.encoding = THREE.sRGBEncoding;

				var groundMaterial = new THREE.MeshLambertMaterial( { map: groundTexture } );

				var mesh = new THREE.Mesh( new THREE.PlaneBufferGeometry( 20000, 20000 ), groundMaterial );
				mesh.position.y = - 250;
				mesh.rotation.x = - Math.PI / 2;
				mesh.receiveShadow = true;
				scene.add( mesh );

				// poles

				var poleGeo = new THREE.BoxBufferGeometry( 5, 375, 5 );
				var poleMat = new THREE.MeshLambertMaterial();

				var mesh = new THREE.Mesh( poleGeo, poleMat );
				mesh.position.x = - 125;
				mesh.position.y = - 62;
				mesh.receiveShadow = true;
				mesh.castShadow = true;
				scene.add( mesh );

				var mesh = new THREE.Mesh( poleGeo, poleMat );
				mesh.position.x = 125;
				mesh.position.y = - 62;
				mesh.receiveShadow = true;
				mesh.castShadow = true;
				scene.add( mesh );

				var mesh = new THREE.Mesh( new THREE.BoxBufferGeometry( 255, 5, 5 ), poleMat );
				mesh.position.y = - 250 + ( 750 / 2 );
				mesh.position.x = 0;
				mesh.receiveShadow = true;
				mesh.castShadow = true;
				scene.add( mesh );

				var gg = new THREE.BoxBufferGeometry( 10, 10, 10 );
				var mesh = new THREE.Mesh( gg, poleMat );
				mesh.position.y = - 250;
				mesh.position.x = 125;
				mesh.receiveShadow = true;
				mesh.castShadow = true;
				scene.add( mesh );

				var mesh = new THREE.Mesh( gg, poleMat );
				mesh.position.y = - 250;
				mesh.position.x = - 125;
				mesh.receiveShadow = true;
				mesh.castShadow = true;
				scene.add( mesh );

				// renderer

				renderer = new THREE.WebGLRenderer( { antialias: true } );
				renderer.setPixelRatio( window.devicePixelRatio );
				renderer.setSize( window.innerWidth, window.innerHeight );

				container.appendChild( renderer.domElement );

				renderer.outputEncoding = THREE.sRGBEncoding;

				renderer.shadowMap.enabled = true;

				// controls
				var controls = new OrbitControls( camera, renderer.domElement );
				controls.maxPolarAngle = Math.PI * 0.5;
				controls.minDistance = 1000;
				controls.maxDistance = 5000;

				// performance monitor

				stats = new Stats();
				container.appendChild( stats.dom );

				//

				window.addEventListener( 'resize', onWindowResize, false );

				//

				var gui = new GUI();
				gui.add( params, 'enableWind' );
				gui.add( params, 'showBall' );
				gui.add( params, 'tooglePins' );

			}

			//

			function onWindowResize() {

				camera.aspect = window.innerWidth / window.innerHeight;
				camera.updateProjectionMatrix();

				renderer.setSize( window.innerWidth, window.innerHeight );

			}

			//

			function animate() {

				requestAnimationFrame( animate );

				var time = Date.now();

				var windStrength = Math.cos( time / 7000 ) * 20 + 40;

				windForce.set( Math.sin( time / 2000 ), Math.cos( time / 3000 ), Math.sin( time / 1000 ) );
				windForce.normalize();
				windForce.multiplyScalar( windStrength );

				simulate( time );
				render();
				stats.update();

			}

			function render() {

				var p = cloth.particles;

				for ( var i = 0, il = p.length; i < il; i ++ ) {

					var v = p[ i ].position;

					clothGeometry.attributes.position.setXYZ( i, v.x, v.y, v.z );

				}

				clothGeometry.attributes.position.needsUpdate = true;

				clothGeometry.computeVertexNormals();

				sphere.position.copy( ballPosition );

				renderer.render( scene, camera );

			}

		</script>
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</html>