pages/tenMinutePhysics/24-morton.html at master · matthias-research/pages · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Morton BVH Collision Detection Demo</title>
    <style>
        body { margin: 0; overflow: hidden; background-color: #000; }
        .info {
            position: absolute;
            top: 10px;
            left: 10px;
            background: rgba(0, 0, 0, 0.7);
            color: white;
            font-family: monospace;
            padding: 10px;
            font-size: 12px;
            pointer-events: none;
            z-index: 100;
            border-radius: 5px;
        }
    </style>
</head>
<body>
    <div id="container"></div>
    <div class="info">
        <h3>3D Morton BVH Collision Detection</h3>
        <p>Boxes: <span id="boxCount">0</span></p>
        <p>Collisions: <span id="collisionCount">0</span></p>
        <p>BVH Build Time: <span id="buildTime">0</span> ms</p>
        <p>Collision Check Time: <span id="checkTime">0</span> ms</p>
        <p>BVH Checks: <span id="bvhChecks">0</span></p>
        <p>FPS: <span id="fps">0</span></p>
    </div>

    <script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r128/three.min.js"></script>
    <script>
        // All function declarations first, then usage

        // ================ Constants ================
        const BOX_COUNT = 10000; // Reduced for better performance with shadows
        const WORLD_SIZE = 100;
        const MIN_BOX_SIZE = 0.5;
        const MAX_BOX_SIZE = 3;
        const MAX_SPEED = 0.5;

        // ================ Utility Functions ================

        // Morton code bit manipulation
        function expandBits(v) {
            v = (v * 0x00010001) & 0xFF0000FF;
            v = (v * 0x00000101) & 0x0F00F00F;
            v = (v * 0x00000011) & 0xC30C30C3;
            v = (v * 0x00000005) & 0x49249249;
            return v;
        }

        // Calculate 3D Morton code
        function calculateMortonCode(x, y, z) {
            // Normalize coordinates to [0,1] range based on world size
            const normalizeCoord = (val) => {
                return (val + WORLD_SIZE / 2) / WORLD_SIZE;
            };

            x = normalizeCoord(x);
            y = normalizeCoord(y);
            z = normalizeCoord(z);

            // Clamp to ensure they're in [0,1]
            x = Math.min(Math.max(x, 0.0), 1.0);
            y = Math.min(Math.max(y, 0.0), 1.0);
            z = Math.min(Math.max(z, 0.0), 1.0);

            // Scale to range [0, 1023] for 10-bit encoding
            x = Math.min(Math.floor(x * 1023), 1023);
            y = Math.min(Math.floor(y * 1023), 1023);
            z = Math.min(Math.floor(z * 1023), 1023);

            // Insert zeros between bits (3D Morton code)
            const xx = expandBits(x);
            const yy = expandBits(y);
            const zz = expandBits(z);

            // Interleave the bits
            return xx | (yy << 1) | (zz << 2);
        }

        // Check if two AABBs intersect
        function aabbIntersect(aabb1, aabb2) {
            return (
                aabb1.min.x <= aabb2.max.x && aabb1.max.x >= aabb2.min.x &&
                aabb1.min.y <= aabb2.max.y && aabb1.max.y >= aabb2.min.y &&
                aabb1.min.z <= aabb2.max.z && aabb1.max.z >= aabb2.min.z
            );
        }

        // ================ Box Class ================
        class Box {
            constructor(id) {
                this.id = id;

                // Random size
                this.width = MIN_BOX_SIZE + Math.random() * (MAX_BOX_SIZE - MIN_BOX_SIZE);
                this.height = MIN_BOX_SIZE + Math.random() * (MAX_BOX_SIZE - MIN_BOX_SIZE);
                this.depth = MIN_BOX_SIZE + Math.random() * (MAX_BOX_SIZE - MIN_BOX_SIZE);

                // Random position within 3D cube bounds
                this.position = new THREE.Vector3(
                    (Math.random() - 0.5) * WORLD_SIZE,
                    (Math.random() - 0.5) * WORLD_SIZE + WORLD_SIZE/4, // Offset upward a bit
                    (Math.random() - 0.5) * WORLD_SIZE
                );

                // Random velocity in all three dimensions
                this.velocity = new THREE.Vector3(
                    (Math.random() - 0.5) * MAX_SPEED,
                    (Math.random() - 0.5) * MAX_SPEED,
                    (Math.random() - 0.5) * MAX_SPEED
                );

                // Create Three.js mesh with improved materials
                const geometry = new THREE.BoxGeometry(this.width, this.height, this.depth);
                const material = new THREE.MeshStandardMaterial({
                    color: 0x00ff00,
                    roughness: 0.5,
                    metalness: 0.2,
                    emissive: 0x002200,
                    emissiveIntensity: 0.1
                });
                this.mesh = new THREE.Mesh(geometry, material);
                this.mesh.position.copy(this.position);

                // Enable shadows
                this.mesh.castShadow = true;
                this.mesh.receiveShadow = true;

                // Default state
                this.isColliding = false;
            }

            update() {
                // Update position based on velocity
                this.position.add(this.velocity);

                // Bounce off world boundaries in all three dimensions
                if (Math.abs(this.position.x) > WORLD_SIZE / 2 - this.width / 2) {
                    this.velocity.x *= -1;
                    this.position.x = Math.sign(this.position.x) * (WORLD_SIZE / 2 - this.width / 2);
                }

                if (Math.abs(this.position.y) > WORLD_SIZE / 2 - this.height / 2) {
                    this.velocity.y *= -1;
                    this.position.y = Math.sign(this.position.y) * (WORLD_SIZE / 2 - this.height / 2);
                }

                if (Math.abs(this.position.z) > WORLD_SIZE / 2 - this.depth / 2) {
                    this.velocity.z *= -1;
                    this.position.z = Math.sign(this.position.z) * (WORLD_SIZE / 2 - this.depth / 2);
                }

                // Update mesh position
                this.mesh.position.copy(this.position);

                // Reset collision state
                if (this.isColliding) {
                    this.mesh.material.color.set(0x00ff00);
                    this.mesh.material.emissive.set(0x002200);
                    this.isColliding = false;
                }
            }

            markCollision() {
                this.mesh.material.color.set(0xff3300);
                this.mesh.material.emissive.set(0x330000);
                this.isColliding = true;
            }

            // Get axis-aligned bounding box
            getAABB() {
                return {
                    min: new THREE.Vector3(
                        this.position.x - this.width / 2,
                        this.position.y - this.height / 2,
                        this.position.z - this.depth / 2
                    ),
                    max: new THREE.Vector3(
                        this.position.x + this.width / 2,
                        this.position.y + this.height / 2,
                        this.position.z + this.depth / 2
                    )
                };
            }

            // Check collision with another box
            checkCollision(other) {
                const aabb1 = this.getAABB();
                const aabb2 = other.getAABB();

                return (
                    aabb1.min.x <= aabb2.max.x && aabb1.max.x >= aabb2.min.x &&
                    aabb1.min.y <= aabb2.max.y && aabb1.max.y >= aabb2.min.y &&
                    aabb1.min.z <= aabb2.max.z && aabb1.max.z >= aabb2.min.z
                );
            }
        }

        // ================ BVH Node Class ================
        class BVHNode {
            constructor() {
                this.left = null;
                this.right = null;
                this.boxId = -1;  // Only leaf nodes have valid boxIds
                this.aabb = {
                    min: new THREE.Vector3(Infinity, Infinity, Infinity),
                    max: new THREE.Vector3(-Infinity, -Infinity, -Infinity)
                };
            }

            isLeaf() {
                return this.boxId !== -1;
            }
        }

        // ================ BVH Construction Functions ================
        function getSplitPos(list, begin, end) {
            // Simple middle split strategy
            return Math.floor((begin + end) / 2);
        }

        function createLeaf(boxId, box) {
            const node = new BVHNode();
            node.boxId = boxId;

            // Set AABB from box
            const aabb = box.getAABB();
            node.aabb.min.copy(aabb.min);
            node.aabb.max.copy(aabb.max);

            return node;
        }

        function createNode() {
            return new BVHNode();
        }

        function createSubTree(list, begin, end, boxes) {
            if (begin === end) {
                return createLeaf(list[begin].id, boxes[list[begin].id]);
            } else {
                const m = getSplitPos(list, begin, end);
                const node = createNode();

                node.left = createSubTree(list, begin, m, boxes);
                node.right = createSubTree(list, m + 1, end, boxes);

                // Update node's AABB to encompass children's AABBs
                node.aabb.min.x = Math.min(node.left.aabb.min.x, node.right.aabb.min.x);
                node.aabb.min.y = Math.min(node.left.aabb.min.y, node.right.aabb.min.y);
                node.aabb.min.z = Math.min(node.left.aabb.min.z, node.right.aabb.min.z);

                node.aabb.max.x = Math.max(node.left.aabb.max.x, node.right.aabb.max.x);
                node.aabb.max.y = Math.max(node.left.aabb.max.y, node.right.aabb.max.y);
                node.aabb.max.z = Math.max(node.left.aabb.max.z, node.right.aabb.max.z);

                return node;
            }
        }

        function createTree(boxes) {
            // Create list of box IDs with their Morton codes
            const list = [];
            for (let i = 0; i < boxes.length; i++) {
                const box = boxes[i];
                const center = box.position;
                const mortonCode = calculateMortonCode(center.x, center.y, center.z);
                list.push({ id: i, mortonCode: mortonCode });
            }

            // Sort by Morton code for spatial locality
            list.sort((a, b) => a.mortonCode - b.mortonCode);

            // Create the BVH tree recursively
            return createSubTree(list, 0, list.length - 1, boxes);
        }

        // ================ Collision Detection Functions ================
        // Find collisions between a box and the BVH tree
        function findCollisions(boxId, box, node, boxes, collisions, checkCount) {
            checkCount.value++;

            // If this box's AABB doesn't intersect with the node's AABB, return
            if (!aabbIntersect(box.getAABB(), node.aabb)) {
                return;
            }

            // If this is a leaf node
            if (node.isLeaf()) {
                // Don't check collisions with self
                if (node.boxId !== boxId) {
                    // Check for actual collision between boxes
                    if (box.checkCollision(boxes[node.boxId])) {
                        collisions.push({ a: boxId, b: node.boxId });
                    }
                }
                return;
            }

            // Recurse through children
            findCollisions(boxId, box, node.left, boxes, collisions, checkCount);
            findCollisions(boxId, box, node.right, boxes, collisions, checkCount);
        }

        // Check all collisions using BVH
        function checkCollisionsBVH(boxes, bvhRoot) {
            const collisions = [];
            const checkCount = { value: 0 };

            for (let i = 0; i < boxes.length; i++) {
                findCollisions(i, boxes[i], bvhRoot, boxes, collisions, checkCount);
            }

            return { collisions, checkCount: checkCount.value };
        }

        // Naive collision detection (for comparison)
        function checkCollisionsNaive(boxes) {
            const collisions = [];
            let checkCount = 0;

            for (let i = 0; i < boxes.length; i++) {
                for (let j = i + 1; j < boxes.length; j++) {
                    checkCount++;
                    if (boxes[i].checkCollision(boxes[j])) {
                        collisions.push({ a: i, b: j });
                    }
                }
            }

            return { collisions, checkCount };
        }

        // Camera rotation variables
        let cameraAngle = 0;
        const cameraRadius = 85;
        const cameraHeight = 40;

        // Function to update camera position
        function updateCamera() {
            cameraAngle += 0.001;
            camera.position.x = Math.sin(cameraAngle) * cameraRadius;
            camera.position.z = Math.cos(cameraAngle) * cameraRadius;
            camera.position.y = cameraHeight;
            camera.lookAt(0, 0, 0);
        }

        // FPS calculation
        let frameCount = 0;
        let lastTime = performance.now();

        function updateFPS() {
            const now = performance.now();
            frameCount++;

            if (now - lastTime >= 1000) {
                const fps = Math.round((frameCount * 1000) / (now - lastTime));
                document.getElementById('fps').textContent = fps;
                frameCount = 0;
                lastTime = now;
            }
        }

        // ================ Animation Loop ================
        function animate() {
            requestAnimationFrame(animate);

            // Update box positions
            for (const box of boxes) {
                box.update();
            }

            // Rebuild BVH (since boxes are moving)
            const buildStartTime = performance.now();
            const bvhRoot = createTree(boxes);
            const buildEndTime = performance.now();

            // Check collisions using BVH
            const checkStartTime = performance.now();
            const bvhResult = checkCollisionsBVH(boxes, bvhRoot);
            const checkEndTime = performance.now();

            // For comparison: naive collision checking
            // const naiveResult = checkCollisionsNaive(boxes);
            const naiveResult = { checkCount: 0 };

            // Mark colliding boxes
            const collisions = bvhResult.collisions;
            for (const collision of collisions) {
                boxes[collision.a].markCollision();
                boxes[collision.b].markCollision();
            }

            // Update stats
            document.getElementById('boxCount').textContent = boxes.length;
            document.getElementById('collisionCount').textContent = collisions.length;
            document.getElementById('buildTime').textContent = (buildEndTime - buildStartTime).toFixed(2);
            document.getElementById('checkTime').textContent = (checkEndTime - checkStartTime).toFixed(2);
            // document.getElementById('naiveChecks').textContent = naiveResult.checkCount;
            document.getElementById('bvhChecks').textContent = bvhResult.checkCount;

            // Update camera position
            updateCamera();

            // Update FPS counter
            updateFPS();

            // Render the scene
            renderer.render(scene, camera);
        }

        // ================ Scene Setup ================
        const scene = new THREE.Scene();
        scene.background = new THREE.Color(0x111111);

        // Add fog for depth perception
        scene.fog = new THREE.FogExp2(0x111111, 0.0025);

        const camera = new THREE.PerspectiveCamera(45, window.innerWidth / window.innerHeight, 0.1, 1000);
        camera.position.set(70, 40, 70);
        camera.lookAt(0, 0, 0);

        // Improved renderer with shadow maps
        const renderer = new THREE.WebGLRenderer({
            antialias: true,
            powerPreference: "high-performance"
        });
        renderer.setSize(window.innerWidth, window.innerHeight);
        renderer.setPixelRatio(window.devicePixelRatio);

        // Enable shadows in the renderer
        renderer.shadowMap.enabled = true;
        renderer.shadowMap.type = THREE.PCFSoftShadowMap; // Softer shadows

        document.getElementById('container').appendChild(renderer.domElement);

        // Enhanced Lighting Setup

        // Ambient light for base illumination
        const ambientLight = new THREE.AmbientLight(0x333333);
        scene.add(ambientLight);

        // Main directional light (sun-like) with shadows
        const mainLight = new THREE.DirectionalLight(0xffffff, 0.8);
        mainLight.position.set(50, 100, 50);
        mainLight.castShadow = true;

        // Optimize shadow map settings
        mainLight.shadow.mapSize.width = 2048;
        mainLight.shadow.mapSize.height = 2048;
        mainLight.shadow.camera.near = 0.5;
        mainLight.shadow.camera.far = 500;

        // Adjust shadow camera frustum to fit the scene
        const d = 100;
        mainLight.shadow.camera.left = -d;
        mainLight.shadow.camera.right = d;
        mainLight.shadow.camera.top = d;
        mainLight.shadow.camera.bottom = -d;

        // Add bias to reduce shadow acne
        mainLight.shadow.bias = -0.001;

        scene.add(mainLight);

        // Additional accent lights for better dimension
        const fillLight = new THREE.DirectionalLight(0x9090ff, 0.4);
        fillLight.position.set(-50, 20, -50);
        scene.add(fillLight);

        const rimLight = new THREE.DirectionalLight(0xff9090, 0.3);
        rimLight.position.set(0, -30, 100);
        scene.add(rimLight);

        // Create a floor plane to catch shadows
        const floorGeometry = new THREE.PlaneGeometry(WORLD_SIZE * 2, WORLD_SIZE * 2);
        const floorMaterial = new THREE.MeshStandardMaterial({
            color: 0x222222,
            roughness: 0.8,
            metalness: 0.2,
            side: THREE.DoubleSide
        });
        const floor = new THREE.Mesh(floorGeometry, floorMaterial);
        floor.rotation.x = Math.PI / 2;
        floor.position.y = -WORLD_SIZE / 2;
        floor.receiveShadow = true;
        scene.add(floor);

        // Create a transparent cube to visualize the 3D bounds
        const cubeGeometry = new THREE.BoxGeometry(WORLD_SIZE, WORLD_SIZE, WORLD_SIZE);
        const cubeMaterial = new THREE.MeshBasicMaterial({
            color: 0x444444,
            wireframe: true,
            transparent: true,
            opacity: 0.2
        });
        const boundingCube = new THREE.Mesh(cubeGeometry, cubeMaterial);
        scene.add(boundingCube);

        // Grid helper with better visibility
        const gridHelper = new THREE.GridHelper(WORLD_SIZE * 2, 20, 0x444444, 0x222222);
        gridHelper.position.y = -WORLD_SIZE / 2 + 0.01; // Slightly above the floor
        scene.add(gridHelper);

        // Axes helper
        const axesHelper = new THREE.AxesHelper(10);
        scene.add(axesHelper);

        // ================ Main ================
        // Create boxes
        const boxes = [];
        for (let i = 0; i < BOX_COUNT; i++) {
            const box = new Box(i);
            boxes.push(box);
            scene.add(box.mesh);
        }

        // Handle window resize
        window.addEventListener('resize', () => {
            camera.aspect = window.innerWidth / window.innerHeight;
            camera.updateProjectionMatrix();
            renderer.setSize(window.innerWidth, window.innerHeight);
        });

        // Start animation
        animate();
    </script>
</body>
</html>