Bouncing balls in a heptagon · ministral-3b-2512

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<!DOCTYPE html> <html> <head> <title>2D Physics Simulation: Rotating Heptagon with Balls</title> <style> body { margin: 0; overflow: hidden; background: #222; font-family: Arial, sans-serif; } canvas { display: block; background: #111; } .controls { position: absolute; top: 10px; left: 10px; color: white; background: rgba(0, 0, 0, 0.7); padding: 10px; border-radius: 5px; } button { margin: 5px; padding: 5px 10px; background: #4CAF50; color: white; border: none; border-radius: 3px; cursor: pointer; } button:hover { background: #45a049; } button:disabled { background: #cccccc; cursor: not-allowed; } </style> </head> <body> <div class="controls"> <button id="pauseBtn">Pause</button> <button id="resetBtn">Reset</button> </div> <canvas id="simCanvas"></canvas> <script> // Canvas setup const canvas = document.getElementById('simCanvas'); const ctx = canvas.getContext('2d'); const controls = { pauseBtn: document.getElementById('pauseBtn'), resetBtn: document.getElementById('resetBtn'), }; // Simulation parameters const WIDTH = 800; const HEIGHT = 600; // Heptagon parameters const HEPTAGON_RADIUS = 150; const HEPTAGON_CENTRE_X = WIDTH / 2; const HEPTAGON_CENTRE_Y = HEIGHT / 2; // Ball parameters const BALL_RADIUS = 12; const BALLS = 20; // Physics constants const GRAVITY = 0.2; // Reduced gravity for smoother fall const COLLISION_RESPONSE = 0.8; const FRICTION = 0.95; const ROTATION_SPEED = 2 * Math.PI / 5; // 1 rev every 5 seconds // Simulation state let balls = []; let heptagonAngle = 0; let isPaused = false; // Initialize simulation function init() { // Create balls for (let i = 0; i < BALLS; i++) { balls.push({ id: i + 1, x: HEPTAGON_CENTRE_X, y: HEPTAGON_CENTRE_Y, vx: 0, vy: 0, angle: Math.random() * Math.PI * 2, angularVelocity: (Math.random() - 0.5) * 0.5, spin: Math.random() * 2 * Math.PI, color: getColorForBall(i), }); } // Set up canvas canvas.width = WIDTH; canvas.height = HEIGHT; // Set up event listeners controls.pauseBtn.addEventListener('click', togglePause); controls.resetBtn.addEventListener('click', resetSimulation); // Start animation loop requestAnimationFrame(update); } // Toggle pause function togglePause() { isPaused = !isPaused; controls.pauseBtn.textContent = isPaused ? 'Resume' : 'Pause'; } // Reset simulation function resetSimulation() { balls.forEach(ball => { ball.x = HEPTAGON_CENTRE_X; ball.y = HEPTAGON_CENTRE_Y; ball.vx = 0; ball.vy = 0; ball.angle = Math.random() * Math.PI * 2; ball.angularVelocity = (Math.random() - 0.5) * 0.5; ball.spin = Math.random() * 2 * Math.PI; }); heptagonAngle = 0; togglePause(); // Resume after reset } // Update simulation function update(time) { if (!isPaused) { // Update heptagon angle heptagonAngle += ROTATION_SPEED; // Update balls updateBalls(time); // Draw everything draw(); } requestAnimationFrame(update); } // Update ball positions and physics function updateBalls(time) { // Update each ball balls.forEach(ball => { // Apply gravity ball.vy += GRAVITY; // Update position ball.x += ball.vx; ball.y += ball.vy; // Apply friction ball.vx *= FRICTION; ball.vy *= FRICTION; // Apply angular velocity ball.angle += ball.angularVelocity; // Check for collisions with walls checkWallCollisions(ball); // Check for collisions with other balls checkBallCollisions(ball); }); } // Check collision with heptagon walls function checkWallCollisions(ball) { const heptagonVertices = getHeptagonVertices(heptagonAngle); // Check if ball is inside the heptagon const isInside = isPointInPolygon(ball.x, ball.y, heptagonVertices); if (!isInside) { // Ball is outside; bounce it back const closestEdge = findClosestEdge(ball.x, ball.y, heptagonVertices); const normal = getEdgeNormal(closestEdge); // Apply bounce with moving wall consideration const wallVelocityX = -Math.sin(heptagonAngle) * ROTATION_SPEED; const wallVelocityY = Math.cos(heptagonAngle) * ROTATION_SPEED; // Calculate relative velocity const relativeVx = ball.vx - wallVelocityX; const relativeVy = ball.vy - wallVelocityY; // Apply bounce response const bounceFactor = COLLISION_RESPONSE * (1 + Math.abs(relativeVx) + Math.abs(relativeVy)); ball.vx -= normal.x * bounceFactor * relativeVx; ball.vy -= normal.y * bounceFactor * relativeVy; // Reposition ball to just outside the polygon const offset = 2 * BALL_RADIUS; const newX = closestEdge.x + normal.x * offset; const newY = closestEdge.y + normal.y * offset; ball.x = newX; ball.y = newY; } } // Check collisions between balls function checkBallCollisions(ball) { for (let i = 0; i < balls.length; i++) { if (ball.id !== balls[i].id) { const otherBall = balls[i]; const dx = ball.x - otherBall.x; const dy = ball.y - otherBall.y; const distance = Math.sqrt(dx * dx + dy * dy); // Check for collision if (distance < BALL_RADIUS * 2) { // Calculate collision normal const normalX = dx / distance; const normalY = dy / distance; // Apply collision response with damping const overlap = (BALL_RADIUS * 2 - distance) / 2; const impulse = COLLISION_RESPONSE * overlap; // Apply impulse to both balls ball.vx -= normalX * impulse; ball.vy -= normalY * impulse; otherBall.vx += normalX * impulse; otherBall.vy += normalY * impulse; // Rotate balls to avoid overlapping ball.x += normalX * overlap * 0.3; ball.y += normalY * overlap * 0.3; otherBall.x -= normalX * overlap * 0.3; otherBall.y -= normalY * overlap * 0.3; // Add some spin to the collision ball.angularVelocity += (Math.random() - 0.5) * 0.5; otherBall.angularVelocity += (Math.random() - 0.5) * 0.5; } } } } // Draw everything function draw() { // Clear canvas ctx.clearRect(0, 0, WIDTH, HEIGHT); // Draw heptagon const heptagonVertices = getHeptagonVertices(heptagonAngle); ctx.beginPath(); ctx.moveTo(heptagonVertices[0].x, heptagonVertices[0].y); for (let i = 1; i < heptagonVertices.length; i++) { ctx.lineTo(heptagonVertices[i].x, heptagonVertices[i].y); } ctx.lineWidth = 2; ctx.strokeStyle = '#4CAF50'; ctx.stroke(); // Draw balls balls.forEach(ball => { // Calculate rotation matrix const cosA = Math.cos(ball.angle); const sinA = Math.sin(ball.angle); // Draw ball with rotation ctx.save(); ctx.translate(ball.x, ball.y); ctx.rotate(ball.angle); // Draw ball body ctx.fillStyle = ball.color; ctx.beginPath(); ctx.arc(0, 0, BALL_RADIUS, 0, Math.PI * 2); ctx.fill(); // Draw ball number ctx.fillStyle = 'white'; ctx.font = 'bold 16px Arial'; ctx.textAlign = 'center'; ctx.textBaseline = 'middle'; ctx.fillText(ball.id.toString(), 0, 0); // Draw spin effect ctx.rotate(ball.spin); ctx.fillStyle = 'rgba(255, 255, 255, 0.3)'; ctx.beginPath(); ctx.arc(0, 0, BALL_RADIUS * 1.2, 0, Math.PI * 2); ctx.fill(); ctx.restore(); }); } // Helper functions function getHeptagonVertices(angle) { const vertices = []; for (let i = 0; i < 7; i++) { const x = HEPTAGON_CENTRE_X + HEPTAGON_RADIUS * Math.cos(angle + i * (2 * Math.PI / 7)); const y = HEPTAGON_CENTRE_Y + HEPTAGON_RADIUS * Math.sin(angle + i * (2 * Math.PI / 7)); vertices.push({x, y}); } return vertices; } function isPointInPolygon(x, y, polygon) { let inside = false; for (let i = 0, j = polygon.length - 1; i < polygon.length; j = i++) { const xi = polygon[i].x; const yi = polygon[i].y; const xj = polygon[j].x; const yj = polygon[j].y; const intersect = ((yi > y) !== (yj > y)) && (x < (xj - xi) * (y - yi) / (yj - yi) + xi); if (intersect) inside = !inside; } return inside; } function findClosestVertex(x, y, vertices) { let closest = null; let minDist = Infinity; for (const vertex of vertices) { const dx = vertex.x - x; const dy = vertex.y - y; const dist = dx * dx + dy * dy; if (dist < minDist) { minDist = dist; closest = vertex; } } return closest; } function findClosestEdge(x, y, vertices) { let closestEdge = null; let minDist = Infinity; for (let i = 0; i < vertices.length; i++) { const j = (i + 1) % vertices.length; const edge = {x: vertices[i].x, y: vertices[i].y, x2: vertices[j].x, y2: vertices[j].y}; const dist = pointToSegmentDistance(x, y, edge.x, edge.y, edge.x2, edge.y2); if (dist < minDist) { minDist = dist; closestEdge = edge; } } return closestEdge; } function getEdgeNormal(edge) { const dx = edge.x2 - edge.x; const dy = edge.y2 - edge.y; const length = Math.sqrt(dx * dx + dy * dy); if (length === 0) return {x: 0, y: 0}; const normalX = -dy / length; const normalY = dx / length; return {x: normalX, y: normalY}; } function pointToSegmentDistance(x, y, x1, y1, x2, y2) { const l2 = Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); if (l2 === 0) return Math.sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1)); const t = ((x - x1) * (x2 - x1) + (y - y1) * (y2 - y1)) / l2; t = Math.max(0, Math.min(1, t)); const closestX = x1 + t * (x2 - x1); const closestY = y1 + t * (y2 - y1); return Math.sqrt((x - closestX) * (x - closestX) + (y - closestY) * (y - closestY)); } function getColorForBall(id) { const hue = (id % 360) / 360; return `hsl(${hue * 60}, 80%, 60%)`; } // Initialize simulation init(); </script> </body> </html>

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canvas.width = WIDTH; canvas.height = HEIGHT; // Set up event listeners controls.pauseBtn.addEventListener('click', togglePause); controls.resetBtn.addEventListener('click', resetSimulation); // Start animation loop requestAnimationFrame(update); } // Toggle pause function togglePause() { isPaused = !isPaused; controls.pauseBtn.textContent = isPaused ? 'Resume' : 'Pause'; } // Reset simulation function resetSimulation() { // Reset balls to initial positions const initialRadius = 50; balls.forEach((ball, index) => { const angle = (index / BALLS) * Math.PI * 2; ball.x = HEPTAGON_CENTRE_X + Math.cos(angle) * initialRadius; ball.y = HEPTAGON_CENTRE_Y + Math.sin(angle) * initialRadius; ball.vx = 0; ball.vy = 0; ball.angle = angle; ball.angularVelocity = (Math.random() - 0.5) * 0.2; ball.spin = Math.random() * 2 * Math.PI; }); heptagonAngle = 0; togglePause(); // Resume after reset } // Update simulation function update(time) { if (!isPaused) { // Update heptagon angle heptagonAngle += ROTATION_SPEED; // Update balls updateBalls(time); // Draw everything draw(); } requestAnimationFrame(update); } // Update ball positions and physics function updateBalls(time) { // Update each ball balls.forEach(ball => { // Apply gravity ball.vy += GRAVITY; // Update position ball.x += ball.vx; ball.y += ball.vy; // Apply friction ball.vx *= FRICTION; ball.vy *= FRICTION; // Apply angular velocity ball.angle += ball.angularVelocity; // Check for collisions with walls checkWallCollisions(ball); // Check for collisions with other balls checkBallCollisions(ball); }); } // Check collision with heptagon walls function checkWallCollisions(ball) { const heptagonVertices = getHeptagonVertices(heptagonAngle); // Check if ball is inside the heptagon const isInside = isPointInPolygon(ball.x, ball.y, heptagonVertices); if (!isInside) { // Find closest edge const closestEdge = findClosestEdge(ball.x, ball.y, heptagonVertices); const normal = getEdgeNormal(closestEdge); // Apply bounce with moving wall consideration const wallVelocityX = -Math.sin(heptagonAngle) * ROTATION_SPEED; const wallVelocityY = Math.cos(heptagonAngle) * ROTATION_SPEED; // Calculate relative velocity const relativeVx = ball.vx - wallVelocityX; const relativeVy = ball.vy - wallVelocityY; // Apply bounce response with damping const bounceFactor = 0.7 * (1 + Math.abs(relativeVx) + Math.abs(relativeVy)); ball.vx -= normal.x * bounceFactor * relativeVx; ball.vy -= normal.y * bounceFactor * relativeVy; // Reposition ball to just outside the polygon const offset = 2 * BALL_RADIUS; ball.x = closestEdge.x + normal.x * offset; ball.y = closestEdge.y + normal.y * offset; } } // Check collisions between balls function checkBallCollisions(ball) { for (let i = 0; i < balls.length; i++) { if (ball.id !== balls[i].id) { const otherBall = balls[i]; const dx = ball.x - otherBall.x; const dy = ball.y - otherBall.y; const distance = Math.sqrt(dx * dx + dy * dy); // Check for collision if (distance < BALL_RADIUS * 2) { // Calculate collision normal const normalX = dx / distance; const normalY = dy / distance; // Apply collision response with damping const overlap = (BALL_RADIUS * 2 - distance) / 2; const impulse = 0.6 * overlap; // Apply impulse to both balls ball.vx -= normalX * impulse; ball.vy -= normalY * impulse; otherBall.vx += normalX * impulse; otherBall.vy += normalY * impulse; // Rotate balls to avoid overlapping ball.x += normalX * overlap * 0.2; ball.y += normalY * overlap * 0.2; otherBall.x -= normalX * overlap * 0.2; otherBall.y -= normalY * overlap * 0.2; // Add spin to the collision ball.angularVelocity += (Math.random() - 0.5) * 0.6; otherBall.angularVelocity += (Math.random() - 0.5) * 0.6; } } } } // Draw everything function draw() { // Clear canvas [158 more lines in file. Use offset=250 to continue.]

ctx.clearRect(0, 0, WIDTH, HEIGHT); // Draw heptagon const heptagonVertices = getHeptagonVertices(heptagonAngle); ctx.beginPath(); ctx.moveTo(heptagonVertices[0].x, heptagonVertices[0].y); for (let i = 1; i < heptagonVertices.length; i++) { ctx.lineTo(heptagonVertices[i].x, heptagonVertices[i].y); } // Draw heptagon outline with rotation ctx.lineWidth = 2; ctx.strokeStyle = '#4CAF50'; ctx.stroke(); // Draw heptagon fill with rotation ctx.beginPath(); ctx.moveTo(heptagonVertices[0].x, heptagonVertices[0].y); for (let i = 1; i < heptagonVertices.length; i++) { ctx.lineTo(heptagonVertices[i].x, heptagonVertices[i].y); } ctx.closePath(); ctx.fillStyle = 'rgba(76, 175, 80, 0.1)'; ctx.fill(); // Draw balls balls.forEach(ball => { // Calculate rotation matrix const cosA = Math.cos(ball.angle); const sinA = Math.sin(ball.angle); // Draw ball with rotation ctx.save(); ctx.translate(ball.x, ball.y); ctx.rotate(ball.angle); // Draw ball body ctx.fillStyle = ball.color; ctx.beginPath(); ctx.arc(0, 0, BALL_RADIUS, 0, Math.PI * 2); ctx.fill(); // Draw ball number ctx.fillStyle = 'white'; ctx.font = 'bold 16px Arial'; ctx.textAlign = 'center'; ctx.textBaseline = 'middle'; ctx.fillText(ball.id.toString(), 0, 0); // Draw spin effect ctx.rotate(ball.spin); ctx.fillStyle = 'rgba(255, 255, 255, 0.3)'; ctx.beginPath(); ctx.arc(0, 0, BALL_RADIUS * 1.2, 0, Math.PI * 2); ctx.fill(); ctx.restore(); }); } // Helper functions function getHeptagonVertices(angle) { const vertices = []; for (let i = 0; i < 7; i++) { const x = HEPTAGON_CENTRE_X + HEPTAGON_RADIUS * Math.cos(angle + i * (2 * Math.PI / 7)); const y = HEPTAGON_CENTRE_Y + HEPTAGON_RADIUS * Math.sin(angle + i * (2 * Math.PI / 7)); vertices.push({x, y}); } return vertices; } function isPointInPolygon(x, y, polygon) { let inside = false; for (let i = 0, j = polygon.length - 1; i < polygon.length; j = i++) { const xi = polygon[i].x; const yi = polygon[i].y; const xj = polygon[j].x; const yj = polygon[j].y; const intersect = ((yi > y) !== (yj > y)) && (x < (xj - xi) * (y - yi) / (yj - yi) + xi); if (intersect) inside = !inside; } return inside; } function findClosestVertex(x, y, vertices) { let closest = null; let minDist = Infinity; for (const vertex of vertices) { const dx = vertex.x - x; const dy = vertex.y - y; const dist = dx * dx + dy * dy; if (dist < minDist) { minDist = dist; closest = vertex; [58 more lines in file. Use offset=350 to continue.]

} } return closest; } function findClosestEdge(x, y, vertices) { let closestEdge = null; let minDist = Infinity; for (let i = 0; i < vertices.length; i++) { const j = (i + 1) % vertices.length; const edge = {x: vertices[i].x, y: vertices[i].y, x2: vertices[j].x, y2: vertices[j].y}; const dist = pointToSegmentDistance(x, y, edge.x, edge.y, edge.x2, edge.y2); if (dist < minDist) { minDist = dist; closestEdge = edge; } } return closestEdge; } function getEdgeNormal(edge) { const dx = edge.x2 - edge.x; const dy = edge.y2 - edge.y; const length = Math.sqrt(dx * dx + dy * dy); if (length === 0) return {x: 0, y: 0}; const normalX = -dy / length; const normalY = dx / length; return {x: normalX, y: normalY}; } function pointToSegmentDistance(x, y, x1, y1, x2, y2) { const l2 = Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); if (l2 === 0) return Math.sqrt((x - x1) * (x - x1) + (y - y1) * (y - y1)); const t = ((x - x1) * (x2 - x1) + (y - y1) * (y2 - y1)) / l2; t = Math.max(0, Math.min(1, t)); const closestX = x1 + t * (x2 - x1); const closestY = y1 + t * (y2 - y1); return Math.sqrt((x - closestX) * (x - closestX) + (y - closestY) * (y - closestY)); } function getColorForBall(id) { const hue = (id % 360) / 360; [8 more lines in file. Use offset=400 to continue.]

return `hsl(${hue * 60}, 80%, 60%)`; } // Initialize simulation init(); </script> </body> </html>

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// Set up canvas canvas.width = WIDTH; canvas.height = HEIGHT; // Set up event listeners controls.pauseBtn.addEventListener('click', togglePause); controls.resetBtn.addEventListener('click', resetSimulation); // Start animation loop requestAnimationFrame(update); } // Toggle pause function togglePause() { isPaused = !isPaused; controls.pauseBtn.textContent = isPaused ? 'Resume' : 'Pause'; } // Reset simulation function resetSimulation() { // Reset balls to initial positions with initial velocity const initialRadius = 50; balls.forEach((ball, index) => { const angle = (index / BALLS) * Math.PI * 2; ball.x = HEPTAGON_CENTRE_X + Math.cos(angle) * initialRadius; ball.y = HEPTAGON_CENTRE_Y + Math.sin(angle) * initialRadius; ball.vx = 0; ball.vy = 0.5; ball.angle = angle; ball.angularVelocity = (Math.random() - 0.5) * 0.2; ball.spin = Math.random() * 2 * Math.PI; }); heptagonAngle = 0; togglePause(); // Resume after reset } // Update simulation function update(time) { if (!isPaused) { // Update heptagon angle heptagonAngle += ROTATION_SPEED; // Update balls updateBalls(time); // Draw everything draw(); } requestAnimationFrame(update); } // Update ball positions and physics function updateBalls(time) { // Update each ball balls.forEach(ball => { // Apply gravity ball.vy += GRAVITY; // Update position ball.x += ball.vx; ball.y += ball.vy; // Apply friction ball.vx *= FRICTION; ball.vy *= FRICTION; // Apply angular velocity ball.angle += ball.angularVelocity; // Check for collisions with walls checkWallCollisions(ball); // Check for collisions with other balls checkBallCollisions(ball); }); } // Check collision with heptagon walls function checkWallCollisions(ball) { const heptagonVertices = getHeptagonVertices(heptagonAngle); // Check if ball is inside the heptagon const isInside = isPointInPolygon(ball.x, ball.y, heptagonVertices); if (!isInside) { // Find closest edge const closestEdge = findClosestEdge(ball.x, ball.y, heptagonVertices); const normal = getEdgeNormal(closestEdge); // Apply bounce with moving wall consideration const wallVelocityX = -Math.sin(heptagonAngle) * ROTATION_SPEED; const wallVelocityY = Math.cos(heptagonAngle) * ROTATION_SPEED; // Calculate relative velocity const relativeVx = ball.vx - wallVelocityX; const relativeVy = ball.vy - wallVelocityY; // Apply bounce response with damping const bounceFactor = 0.7 * (1 + Math.abs(relativeVx) + Math.abs(relativeVy)); ball.vx -= normal.x * bounceFactor * relativeVx; ball.vy -= normal.y * bounceFactor * relativeVy; // Reposition ball to just outside the polygon const offset = 2 * BALL_RADIUS; ball.x = closestEdge.x + normal.x * offset; ball.y = closestEdge.y + normal.y * offset; } } // Check collisions between balls function checkBallCollisions(ball) { for (let i = 0; i < balls.length; i++) { if (ball.id !== balls[i].id) { const otherBall = balls[i]; const dx = ball.x - otherBall.x; const dy = ball.y - otherBall.y; const distance = Math.sqrt(dx * dx + dy * dy); // Check for collision if (distance < BALL_RADIUS * 2) { // Calculate collision normal const normalX = dx / distance; const normalY = dy / distance; // Apply collision response with damping const overlap = (BALL_RADIUS * 2 - distance) / 2; const impulse = 0.6 * overlap; // Apply impulse to both balls ball.vx -= normalX * impulse; ball.vy -= normalY * impulse; otherBall.vx += normalX * impulse; otherBall.vy += normalY * impulse; // Rotate balls to avoid overlapping ball.x += normalX * overlap * 0.2; ball.y += normalY * overlap * 0.2; otherBall.x -= normalX * overlap * 0.2; otherBall.y -= normalY * overlap * 0.2; // Add spin to the collision ball.angularVelocity += (Math.random() - 0.5) * 0.6; otherBall.angularVelocity += (Math.random() - 0.5) * 0.6; } } } } // Draw everything [144 more lines in file. Use offset=250 to continue.]

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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Pause Reset","images":"attached"}

Successfully wrote to /tmp/job-VcDlv9/index.html

Frame 1, +0ms

[Browser image supplied to model]

{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Pause Reset","images":"attached"}

Successfully wrote to /tmp/job-VcDlv9/index.html

Frame 1, +0ms

[Browser image supplied to model]

{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Pause Reset","images":"attached"}