11-hashing.html

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<!DOCTYPE html>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<html lang="en">
	<head>
		<title>Spatial Hashing</title>
		<style>
			body {
				font-family: verdana; 
				font-size: 15px;
			}			
			.button {
				background-color: #606060;
				border: none;
				color: white;
				padding: 10px 32px;
				font-size: 16px;
				margin: 4px 2px;
				cursor: pointer;
			}
		</style>
	</head>
	
	<body>

        <h1>Spatial Hashing</h1> 
		<button id = "buttonRun" onclick="run()" class="button">Run</button>
		<button onclick="restart()" class="button">Restart</button>
		<input type = "checkbox" onclick = "onShowColl()"> Show collisions</p>
		<span id = "particleCount">0</span> particles, 
		<span id = "ms">0.000</span> ms per frame

		<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>
			
			var threeScene;
			var renderer;
			var camera;
			var cameraControl;	

			// ------------------------------------------------------------------
			class Hash {
				constructor(spacing, maxNumObjects) 
				{
					this.spacing = spacing;
					this.tableSize = 2 * maxNumObjects;
					this.cellStart = new Int32Array(this.tableSize + 1);
					this.cellEntries = new Int32Array(maxNumObjects);
					this.queryIds = new Int32Array(maxNumObjects);
					this.querySize = 0;
				}

				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++;
								}
							}
						}
					}
				}
			};

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

			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 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];
			}	

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

			var physicsScene = 
			{
				gravity : [0.0, 0.0, 0.0],
				dt : 1.0 / 60.0,
				worldBounds :  [-1.0, 0.0, -1.0, 1.0, 2.0, 1.0],
				paused: true,
				balls: null,
			};

			function onShowColl() {
				if (physicsScene.balls)
					physicsScene.balls.showCollisions = !physicsScene.balls.showCollisions;
			}			
						
			// ------------------------------------------------------------------
			class Balls {
				constructor(radius, pos, vel, scene)
				{
					// physics data 

                    this.radius = radius;
                    this.pos = pos;
					this.prevPos = pos;
                    this.vel = vel;
					this.matrix = new THREE.Matrix4();
					this.numBalls = Math.floor(pos.length / 3);
					this.hash = new Hash(2.0 * radius, this.numBalls);
					this.showCollisions = false;

					this.normal = new Float32Array(3);

					// visual mesh

                    var geometry = new THREE.SphereGeometry( radius, 8, 8 );
                    var material = new THREE.MeshPhongMaterial();

					this.visMesh = new THREE.InstancedMesh( geometry, material, this.numBalls );
					this.visMesh.instanceMatrix.setUsage(THREE.DynamicDrawUsage); 

					this.ballColor = new THREE.Color(0xFF0000);
					this.ballCollisionColor = new THREE.Color(0xFF8000);

					var colors = new Float32Array(3 * this.numBalls);
					this.visMesh.instanceColor = new THREE.InstancedBufferAttribute(colors, 3, false, 1);
					for (var i = 0; i < this.numBalls; i++) 
						this.visMesh.setColorAt(i, this.ballColor);

                    threeScene.add(this.visMesh);

					this.updateMesh();
				}

				updateMesh()
				{
					for (var i = 0; i < this.numBalls; i++) {
						this.matrix.makeTranslation(this.pos[3 * i], this.pos[3 * i + 1], this.pos[3 * i + 2]);
						this.visMesh.setMatrixAt(i, this.matrix);
					}
					this.visMesh.instanceMatrix.needsUpdate = true;
					this.visMesh.instanceColor.needsUpdate = true;
				}
			
				simulate(dt, gravity, worldBounds)
				{
					var minDist = 2.0 * this.radius;

					// integrate

					for (var i = 0; i < this.numBalls; i++) {
						vecAdd(this.vel, i, gravity, 0, dt);
						vecCopy(this.prevPos, i, this.pos, i);
						vecAdd(this.pos, i, this.vel, i, dt);
					}

					this.hash.create(this.pos);

					// handle collisions

					for (var i = 0; i < this.numBalls; i++) {

						this.visMesh.setColorAt(i, this.ballColor);

						// world collision

						for (var dim = 0; dim < 3; dim++) {

							var nr = 3 * i + dim;
							if (this.pos[nr] < worldBounds[dim] + this.radius) {
								this.pos[nr] = worldBounds[dim] + this.radius;
								this.vel[nr] = - this.vel[nr];
								if (this.showCollisions)
									this.visMesh.setColorAt(i, this.ballCollisionColor);
							}
							else if (this.pos[nr] > worldBounds[dim + 3] - this.radius) {
								this.pos[nr] = worldBounds[dim + 3] - this.radius;
								this.vel[nr] = - this.vel[nr];
								if (this.showCollisions)
									this.visMesh.setColorAt(i, this.ballCollisionColor);
							}
						}

						//  interball collision

						this.hash.query(this.pos, i, 2.0 * this.radius);

						for (var nr = 0; nr < this.hash.querySize; nr++) {
							var j = this.hash.queryIds[nr];

							vecSetDiff(this.normal, 0, this.pos, i, this.pos, j);
							var d2 = vecLengthSquared(this.normal, 0);

							 // are the balls overlapping?

							if (d2 > 0.0 && d2 < minDist * minDist) {
								var d = Math.sqrt(d2);
								vecScale(this.normal, 0, 1.0 / d);	

								// separate the balls

								var corr = (minDist - d) * 0.5;

								vecAdd(this.pos, i, this.normal, 0, corr);
								vecAdd(this.pos, j, this.normal, 0, -corr);

								// reflect velocities along normal

								var vi = vecDot(this.vel, i, this.normal, 0);
								var vj = vecDot(this.vel, j, this.normal, 0);

								vecAdd(this.vel, i, this.normal, 0, vj - vi);
								vecAdd(this.vel, j, this.normal, 0, vi - vj);

								if (this.showCollisions)
									this.visMesh.setColorAt(i, this.ballCollisionColor);
							}
						}
					}
					this.updateMesh();
				}
			}

			// ------------------------------------------------------------------
			function initPhysics(scene) 
			{
				var radius = 0.025;

				var spacing = 3.0 * radius;
				var velRand = 0.2;

				var s = physicsScene.worldBounds;

				var numX = Math.floor((s[3] - s[0] - 2.0 * spacing) / spacing);
				var numY = Math.floor((s[4] - s[1] - 2.0 * spacing) / spacing);
				var numZ = Math.floor((s[5] - s[2] - 2.0 * spacing) / spacing);

				var pos = new Float32Array(3 * numX * numY * numZ);
				var vel = new Float32Array(3 * numX * numY * numZ);
				vel.fill(0.0);

				for (var xi = 0; xi < numX; xi++) {
					for (var yi = 0; yi < numY; yi++) {
						for (var zi = 0; zi < numZ; zi++) {
							var x = 3 * ((xi * numY + yi) * numZ + zi);
							var y = x + 1;
							var z = x + 2;
							pos[x] = s[0] + spacing + xi * spacing;
							pos[y] = s[1] + spacing + yi * spacing;
							pos[z] = s[2] + spacing + zi * spacing;

							vel[x] = -velRand + 2.0 * velRand * Math.random();
							vel[y] = -velRand + 2.0 * velRand * Math.random();
							vel[z] = -velRand + 2.0 * velRand * Math.random();
						}
					}
				}

				physicsScene.balls = new Balls(radius, pos, vel, threeScene);

				document.getElementById("particleCount").innerHTML = pos.length / 3;		

			}

			var timeFrames = 0;
			var timeSum = 0;	
						
			// ------------------------------------------------------------------
			function simulate() 
			{
				if (physicsScene.paused)
					return;

				var startTime = performance.now();					

				physicsScene.balls.simulate(physicsScene.dt, 
					physicsScene.gravity, physicsScene.worldBounds);

				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() 
			{
				threeScene = new THREE.Scene();
				
				// Lights
				
				threeScene.add( new THREE.AmbientLight( 0x505050 ) );	
				threeScene.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;
				threeScene.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;
				threeScene.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;
				threeScene.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);
				threeScene.add( helper );				
				
				// Renderer

				renderer = new THREE.WebGLRenderer();
				renderer.shadowMap.enabled = true;
				renderer.setPixelRatio( window.devicePixelRatio );
				renderer.setSize( 0.8 * window.innerWidth, 0.8 * window.innerHeight );
				window.addEventListener( 'resize', onWindowResize, false );
				container.appendChild( renderer.domElement );
				
				// Camera
						
				camera = new THREE.PerspectiveCamera( 70, window.innerWidth / window.innerHeight, 0.01, 100);
			    camera.position.set(0, 2, 4);
				camera.updateMatrixWorld();	

				threeScene.add( camera );

				cameraControl = new THREE.OrbitControls(camera, renderer.domElement);
    			cameraControl.zoomSpeed = 2.0;
    			cameraControl.panSpeed = 0.4;
			}

			function onWindowResize() {

				camera.aspect = window.innerWidth / window.innerHeight;
				camera.updateProjectionMatrix();
				renderer.setSize( window.innerWidth, window.innerHeight );
			}

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

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

			function update() {
				simulate();
				renderer.render(threeScene, camera);
				cameraControl.update();				
				
				requestAnimationFrame(update);
			}
			
			initThreeScene();
			onWindowResize();
			initPhysics();
			update();
			
		</script>
	</body>
</html>