pages/tenMinutePhysics/23-SAP.html at master · matthias-research/pages · GitHub

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<!DOCTYPE html>
<html>
<head>
    <style>
        body {
            margin: 0;
            overflow: hidden;
        }
        canvas {
            border: 1px solid black;
            background: #101010;
            display: block;  /* Removes small gap at bottom */
        }
        .controls {
            position: fixed;
            top: 10px;
            left: 10px;
            margin: 10px 0;
            font-family: Arial, sans-serif;
            background: rgba(255, 255, 255, 0.8);
            padding: 5px;
            border-radius: 4px;
        }
        .stats {
            font-family: monospace;
            margin: 10px 0;
        }
    </style>
</head>
<body>
    <div class="controls">
        <label>
            <input type="radio" name="algorithm" value="bruteforce"> Brute Force
        </label>
        <label>
            <input type="radio" name="algorithm" value="sweepprune" checked> Sweep and Prune
        </label>
        <span id="stats" class="stats"></span>
    </div>
    <canvas id="canvas"></canvas>
    <script>
        const canvas = document.getElementById('canvas');
        const ctx = canvas.getContext('2d');

        // Set canvas size to window size
        function resizeCanvas() {
            canvas.width = window.innerWidth;
            canvas.height = window.innerHeight;
        }

        // Initial resize
        resizeCanvas();

        // Handle window resize
        window.addEventListener('resize', resizeCanvas);

        const statsEl = document.getElementById('stats');
        let collisionChecks = 0;
        let actualCollisions = 0;

        function calculateCollision(m1, m2, x1, y1, x2, y2, vx1, vy1, vx2, vy2, r1, r2, e) {
            const dx = x2 - x1;
            const dy = y2 - y1;
            const dist = Math.sqrt(dx * dx + dy * dy);

            if (dist > r1 + r2) {
                return { vx1_new: vx1, vy1_new: vy1, vx2_new: vx2, vy2_new: vy2 };
            }

            const nx = dx / dist;
            const ny = dy / dist;

            const vrx = vx2 - vx1;  // Changed direction of relative velocity
            const vry = vy2 - vy1;

            const vn = vrx * nx + vry * ny;

            if (vn > 0) {
                return { vx1_new: vx1, vy1_new: vy1, vx2_new: vx2, vy2_new: vy2 };
            }

            const j = -(1 + e) * vn / (1/m1 + 1/m2);

            const vx1_new = vx1 - (j * nx) / m1;  // Changed sign
            const vy1_new = vy1 - (j * ny) / m1;  // Changed sign
            const vx2_new = vx2 + (j * nx) / m2;  // Changed sign
            const vy2_new = vy2 + (j * ny) / m2;  // Changed sign

            return { vx1_new, vy1_new, vx2_new, vy2_new };
        }

        class Sphere {
            constructor(x, y, vx, vy, radius) {
                this.x = x;
                this.y = y;
                this.vx = vx;
                this.vy = vy;
                this.radius = radius;
                this.mass = Math.PI * radius * radius;
                this.color = `hsl(${Math.random() * 360}, 70%, 50%)`;
            }

            get left() {
                return this.x - this.radius;
            }

            get right() {
                return this.x + this.radius;
            }

            update(dt) {
                const gravity = 980;

                // this.vy += gravity * dt;
                this.x += this.vx * dt;
                this.y += this.vy * dt;

                if (this.x - this.radius < 0) {
                    this.x = this.radius;
                    this.vx *= -1.0;
                }
                if (this.x + this.radius > canvas.width) {
                    this.x = canvas.width - this.radius;
                    this.vx *= -1.0;
                }
                if (this.y + this.radius > canvas.height) {
                    this.y = canvas.height - this.radius;
                    this.vy *= -1.0;
                }
                if (this.y - this.radius < 0) {
                    this.y = this.radius;
                    this.vy *= -1.0;
                }
            }

            draw() {
                ctx.beginPath();
                ctx.arc(this.x, this.y, this.radius, 0, Math.PI * 2);
                ctx.fillStyle = this.color;
                ctx.fill();
                ctx.closePath();
            }
        }

        function solveCollision(sphere1, sphere2) {
            collisionChecks++;

            const dx = sphere2.x - sphere1.x;
            const dy = sphere2.y - sphere1.y;
            const distance = Math.sqrt(dx * dx + dy * dy);

            if (distance < sphere1.radius + sphere2.radius) {
                actualCollisions++;

                // Calculate new velocities using provided function
                const { vx1_new, vy1_new, vx2_new, vy2_new } = calculateCollision(
                    sphere1.mass, sphere2.mass,
                    sphere1.x, sphere1.y, sphere2.x, sphere2.y,
                    sphere1.vx, sphere1.vy, sphere2.vx, sphere2.vy,
                    sphere1.radius, sphere2.radius,
                    1.0  // restitution coefficient
                );

                // Update velocities
                sphere1.vx = vx1_new;
                sphere1.vy = vy1_new;
                sphere2.vx = vx2_new;
                sphere2.vy = vy2_new;

                // Resolve overlap
                const overlap = (sphere1.radius + sphere2.radius - distance);
                const nx = dx / distance;
                const ny = dy / distance;

                const cx = overlap * nx / 2;
                const cy = overlap * ny / 2;

                sphere1.x -= cx;
                sphere1.y -= cy;
                sphere2.x += cx;
                sphere2.y += cy;
            }
        }

        function bruteForceCollisions(spheres) {
            for (let i = 0; i < spheres.length; i++) {
                for (let j = i + 1; j < spheres.length; j++) {
                    solveCollision(spheres[i], spheres[j]);
                }
            }
        }

        function sweepAndPruneCollisions(spheres) {
            const sortedSpheres = spheres.sort((a, b) => a.left - b.left);

            for (let i = 0; i < sortedSpheres.length; i++) {
                const sphere1 = sortedSpheres[i];

                for (let j = i + 1; j < sortedSpheres.length; j++) {
                    const sphere2 = sortedSpheres[j];

                    if (sphere2.left > sphere1.right) {
                        break;
                    }

                    if (Math.abs(sphere1.y - sphere2.y) <= sphere1.radius + sphere2.radius) {
                        solveCollision(sphere1, sphere2);
                    }
                }
            }
        }

        const spheres = [];
        for (let i = 0; i < 5000; i++) {
            let radius = Math.floor(Math.pow(Math.random(), 10.0) * 20 + 2);
            const x = Math.random() * (canvas.width - radius * 2) + radius;
            const y = Math.random() * (canvas.height - radius * 2) + radius;
            const vx = Math.random() * 400 - 200;
            const vy = Math.random() * 400 - 200;
            spheres.push(new Sphere(x, y, vx, vy, radius));
        }

        let lastTime = performance.now();
        function animate() {
            const currentTime = performance.now();
            const dt = Math.min((currentTime - lastTime) / 1000, 0.016);
            lastTime = currentTime;

            collisionChecks = 0;
            actualCollisions = 0;

            ctx.clearRect(0, 0, canvas.width, canvas.height);

            // Run multiple physics steps per frame
            const numSubsteps = 5;
            const subDt = dt / numSubsteps;

            const algorithm = document.querySelector('input[name="algorithm"]:checked').value;

            for (let step = 0; step < numSubsteps; step++) {
                spheres.forEach(sphere => sphere.update(subDt));

                if (algorithm === 'bruteforce') {
                    bruteForceCollisions(spheres);
                } else {
                    sweepAndPruneCollisions(spheres);
                }
            }

            // Draw all spheres
            spheres.forEach(sphere => sphere.draw());

            // Draw sweep bounds when sweep and prune is selected
            if (algorithm === 'sweepprune') {
                const sortedSpheres = [...spheres].sort((a, b) => a.left - b.left);
                ctx.strokeStyle = 'rgba(255,0,0,0.5)';
                ctx.beginPath();
                sortedSpheres.forEach(sphere => {
                    ctx.moveTo(sphere.left, 0);
                    ctx.lineTo(sphere.left, 10);
                    ctx.moveTo(sphere.right, 0);
                    ctx.lineTo(sphere.right, 10);
                });
                ctx.stroke();
            }

            // Update stats
            statsEl.textContent = `Spheres: ${spheres.length} | Checks/frame: ${collisionChecks} | Collisions/frame: ${actualCollisions}`;

            requestAnimationFrame(animate);
        }

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