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} lastMouseX = currentMouseX; lastMouseY = currentMouseY; }); canvas.addEventListener('mouseup', () => { isDragging = false; }); // Touch interaction canvas.addEventListener('touchstart', (e) => { e.preventDefault(); isDragging = true; lastMouseX = e.touches[0].clientX / canvas.width * RESOLUTION; lastMouseY = e.touches[0].clientY / canvas.height * RESOLUTION; addDensity(lastMouseX, lastMouseY, 0.1); }); canvas.addEventListener('touchmove', (e) => { e.preventDefault(); if (!isDragging) return; const currentMouseX = e.touches[0].clientX / canvas.width * RESOLUTION; const currentMouseY = e.touches[0].clientY / canvas.height * RESOLUTION; const dx = currentMouseX - lastMouseX; const dy = currentMouseY - lastMouseY; const distance = Math.sqrt(dx * dx + dy * dy); if (distance > 0) { const strength = 0.05; addForce(lastMouseX, lastMouseY, strength * dx / distance); addForce(lastMouseX, lastMouseY, strength * dy / distance); const steps = Math.max(1, Math.floor(distance / 2)); const stepX = dx / steps; const stepY = dy / steps; for (let i = 0; i < steps; i++) { const posX = lastMouseX + i * stepX; const posY = lastMouseY + i * stepY; addDensity(posX, posY, 0.05); } } lastMouseX = currentMouseX; lastMouseY = currentMouseY; }); canvas.addEventListener('touchend', () => { isDragging = false; }); // Render function function render() { // Scale canvas to match resolution const scaleX = canvas.width / RESOLUTION; const scaleY = canvas.height / RESOLUTION; // Clear canvas ctx.fillStyle = 'rgba(0, 0, 0, 0.1)'; ctx.fillRect(0, 0, canvas.width, canvas.height); // Draw fluid velocity (optional: visualize flow) ctx.strokeStyle = 'rgba(255, 255, 255, 0.1)'; ctx.lineWidth = 1; for (let y = 1; y < RESOLUTION; y++) { for (let x = 1; x < RESOLUTION; x++) { const index = getIndex(x, y); const vx = velocityX[index]; const vy = velocityY[index]; const px = x * scaleX; const py = y * scaleY; const nx = (x + vx) * scaleX; const ny = (y + vy) * scaleY; ctx.beginPath(); ctx.moveTo(px, py); ctx.lineTo(nx, ny); ctx.stroke(); } } // Draw particles

diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field project(velocityX, velocityY); // Diffuse velocity again diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field again project(velocityX, velocityY); // Swap buffers for (let y = 0; y < RESOLUTION; y++) { for (let x = 0; x < RESOLUTION; x++) { const index = getIndex(x, y); oldVelocityX[index] = velocityX[index]; oldVelocityY[index] = velocityY[index]; } } } // Update particles based on fluid velocity function updateParticles() { for (let i = 0; i < particles.length; i++) { const p = particles[i]; // Sample velocity at particle position const x = p.x; const y = p.y; // Bilinear interpolation for velocity const vx = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityX ); const vy = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityY ); // Update particle position p.x += vx * 0.1; p.y += vy * 0.1; // Boundary conditions if (p.x < 0) p.x = 0; if (p.x > RESOLUTION - 1) p.x = RESOLUTION - 1; if (p.y < 0) p.y = 0; if (p.y > RESOLUTION - 1) p.y = RESOLUTION - 1; } } // Add density at a position function addDensity(x, y, amount) { const index = getIndex(Math.floor(x), Math.floor(y)); density[index] += amount; } // Diffuse density function diffuseDensity() { diffuse(density, density, DIFFUSE_ITERATIONS); } // Mouse interaction let isDragging = false; let lastMouseX = 0; let lastMouseY = 0; canvas.addEventListener('mousedown', (e) => { isDragging = true; lastMouseX = e.clientX / canvas.width * RESOLUTION; lastMouseY = e.clientY / canvas.height * RESOLUTION; addDensity(lastMouseX, lastMouseY, 0.1); }); canvas.addEventListener('mousemove', (e) => { if (!isDragging) return; const currentMouseX = e.clientX / canvas.width * RESOLUTION; const currentMouseY = e.clientY / canvas.height * RESOLUTION; // Add force along the direction of the mouse movement const dx = currentMouseX - lastMouseX; const dy = currentMouseY - lastMouseY; const distance = Math.sqrt(dx * dx + dy * dy); if (distance > 0) { const strength = 0.05; addForce(lastMouseX, lastMouseY, strength * dx / distance); addForce(lastMouseX, lastMouseY, strength * dy / distance); // Add density along the path const steps = Math.max(1, Math.floor(distance / 2)); const stepX = dx / steps; const stepY = dy / steps; for (let i = 0; i < steps; i++) { const posX = lastMouseX + i * stepX; const posY = lastMouseY + i * stepY; addDensity(posX, posY, 0.05); } [87 more lines in file. Use offset=300 to continue.]

for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); const a = field[index]; const b = (oldField[index + 1] - oldField[index - 1]) * 0.5; const c = (oldField[index + RESOLUTION] - oldField[index - RESOLUTION]) * 0.5; field[index] = (a + hSquare * (b * b + c * c)) / (1 + 2 * hSquare); } } // Copy back for (let y = 0; y < RESOLUTION; y++) { for (let x = 0; x < RESOLUTION; x++) { const index = getIndex(x, y); oldField[index] = field[index]; } } } } // Velocity function function velocity(field, oldField, iterations) { const h = 1.0 / RESOLUTION; for (let iter = 0; iter < iterations; iter++) { for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); const p = field[index]; const a = oldField[index]; const b = (oldField[index + 1] - oldField[index - 1]) * h; const c = (oldField[index + RESOLUTION] - oldField[index - RESOLUTION]) * h; field[index] = (a - 0.5 * h * (p * b + c)) / (1 + h * h); } } // Copy back for (let y = 0; y < RESOLUTION; y++) { for (let x = 0; x < RESOLUTION; x++) { const index = getIndex(x, y); oldField[index] = field[index]; } } } } // Add force to velocity function addForce(x, y, strength) { const index = getIndex(Math.floor(x), Math.floor(y)); velocityX[index] += strength; velocityY[index] += strength; } // Project velocity field to enforce divergence-free condition function project(fieldX, fieldY) { const h = 1.0 / RESOLUTION; // Compute divergence const div = new Float32Array(RESOLUTION * RESOLUTION); for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); div[index] = -rac{1}{h} * ( (fieldX[index + 1] - fieldX[index - 1]) * 0.5 + (fieldY[index + RESOLUTION] - fieldY[index - RESOLUTION]) * 0.5 ); } } // Compute pressure const pressure = new Float32Array(RESOLUTION * RESOLUTION); for (let iter = 0; iter < 20; iter++) { for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); pressure[index] = ( div[index] + pressure[index + 1] + pressure[index - 1] + pressure[index + RESOLUTION] + pressure[index - RESOLUTION] ) / 4; } } } // Subtract pressure gradient for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); fieldX[index] -= 0.5 * h * (pressure[index + 1] - pressure[index - 1]); fieldY[index] -= 0.5 * h * (pressure[index + RESOLUTION] - pressure[index - RESOLUTION]); } } } // Update fluid simulation function updateFluid() { // Add external forces (e.g., mouse drag) // This will be handled in the mouse event handler // Diffuse velocity diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field project(velocityX, velocityY); // Diffuse velocity again diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field again project(velocityX, velocityY); // Swap buffers for (let y = 0; y < RESOLUTION; y++) { for (let x = 0; x < RESOLUTION; x++) { const index = getIndex(x, y); oldVelocityX[index] = velocityX[index]; oldVelocityY[index] = velocityY[index]; } } } // Update particles based on fluid velocity function updateParticles() { for (let i = 0; i < particles.length; i++) { const p = particles[i]; // Sample velocity at particle position const x = p.x; const y = p.y; // Bilinear interpolation for velocity const vx = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityX ); const vy = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityY ); // Update particle position p.x += vx * 0.1; p.y += vy * 0.1; // Boundary conditions if (p.x < 0) p.x = 0; if (p.x > RESOLUTION - 1) p.x = RESOLUTION - 1; if (p.y < 0) p.y = 0; if (p.y > RESOLUTION - 1) p.y = RESOLUTION - 1; } } [137 more lines in file. Use offset=250 to continue.]

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// Project velocity field to enforce divergence-free condition function project(fieldX, fieldY) { const h = 1.0 / RESOLUTION; // Compute divergence const div = new Float32Array(RESOLUTION * RESOLUTION); for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); div[index] = -rac{1}{h} * ( [227 more lines in file. Use offset=160 to continue.]

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} } // Add force to velocity function addForce(x, y, strength) { const index = getIndex(Math.floor(x), Math.floor(y)); velocityX[index] += strength; velocityY[index] += strength; } // Project velocity field to enforce divergence-free condition function project(fieldX, fieldY) { const h = 1.0 / RESOLUTION; // Compute divergence const div = new Float32Array(RESOLUTION * RESOLUTION); for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); div[index] = -rac{1}{h} * ( [227 more lines in file. Use offset=160 to continue.]

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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>Fluid Simulation</title> <style> body { margin: 0; padding: 0; overflow: hidden; background-color: #111; font-family: Arial, sans-serif; } canvas { display: block; width: 100vw; height: 100vh; } #info { position: absolute; top: 10px; left: 10px; color: white; font-size: 14px; background-color: rgba(0, 0, 0, 0.5); padding: 5px 10px; border-radius: 5px; } </style> </head> <body> <canvas id="canvas"></canvas> <div id="info">Fluid Simulation - Drag to add dye</div> <script> // Fluid simulation constants const RESOLUTION = 128; // Resolution of the grid const VISCOSITY = 0.1; // Fluid viscosity const DIFFUSE_ITERATIONS = 20; // Diffusion iterations const VELOCITY_ITERATIONS = 20; // Velocity iterations const PARTICLE_COUNT = 500; // Number of dye particles const PARTICLE_SIZE = 2; // Size of dye particles // Canvas setup const canvas = document.getElementById('canvas'); const ctx = canvas.getContext('2d'); const info = document.getElementById('info'); // Resize canvas to full screen function resizeCanvas() { canvas.width = window.innerWidth; canvas.height = window.innerHeight; } window.addEventListener('resize', resizeCanvas); resizeCanvas(); // Fluid simulation data structures const density = new Float32Array(RESOLUTION * RESOLUTION); const velocityX = new Float32Array(RESOLUTION * RESOLUTION); const velocityY = new Float32Array(RESOLUTION * RESOLUTION); const oldVelocityX = new Float32Array(RESOLUTION * RESOLUTION); const oldVelocityY = new Float32Array(RESOLUTION * RESOLUTION); // Dye particles const particles = []; for (let i = 0; i < PARTICLE_COUNT; i++) { particles.push({ x: Math.random() * RESOLUTION, y: Math.random() * RESOLUTION, color: `hsl(${Math.random() * 60 + 240}, 100%, 50%)` }); } // Helper functions function getIndex(x, y) { return y * RESOLUTION + x; } function linearInterpolation(x0, x1, x, value0, value1) { return value0 + (x - x0) * (value1 - value0) / (x1 - x0); } function bilinearInterpolation(x0, y0, x1, y1, x, y, value) { const a = value[getIndex(Math.floor(x0), Math.floor(y0))]; const b = value[getIndex(Math.floor(x1), Math.floor(y0))]; const c = value[getIndex(Math.floor(x0), Math.floor(y1))]; const d = value[getIndex(Math.floor(x1), Math.floor(y1))]; const top = linearInterpolation(x0, x1, x, a, b); const bottom = linearInterpolation(x0, x1, x, c, d); return linearInterpolation(y0, y1, y, top, bottom); } // Diffusion function function diffuse(field, oldField, iterations) { const h = 1.0 / RESOLUTION; const hSquare = h * h; for (let iter = 0; iter < iterations; iter++) { for (let y = 1; y < RESOLUTION - 1; y++) { [286 more lines in file. Use offset=101 to continue.]

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// Add density at a position function addDensity(x, y, amount) { const index = getIndex(Math.floor(x), Math.floor(y)); density[index] += amount; } // Diffuse density function diffuseDensity() { diffuse(density, density, DIFFUSE_ITERATIONS); [127 more lines in file. Use offset=260 to continue.]

diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field project(velocityX, velocityY); // Diffuse velocity again diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field again project(velocityX, velocityY); // Swap buffers for (let y = 0; y < RESOLUTION; y++) { for (let x = 0; x < RESOLUTION; x++) { const index = getIndex(x, y); oldVelocityX[index] = velocityX[index]; oldVelocityY[index] = velocityY[index]; } } } // Update particles based on fluid velocity function updateParticles() { for (let i = 0; i < particles.length; i++) { const p = particles[i]; // Sample velocity at particle position const x = p.x; const y = p.y; // Bilinear interpolation for velocity const vx = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityX ); const vy = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityY ); // Update particle position p.x += vx * 0.1; p.y += vy * 0.1; // Boundary conditions if (p.x < 0) p.x = 0; if (p.x > RESOLUTION - 1) p.x = RESOLUTION - 1; if (p.y < 0) p.y = 0; if (p.y > RESOLUTION - 1) p.y = RESOLUTION - 1; } } [137 more lines in file. Use offset=250 to continue.]

} } // Subtract pressure gradient for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); fieldX[index] -= 0.5 * h * (pressure[index + 1] - pressure[index - 1]); fieldY[index] -= 0.5 * h * (pressure[index + RESOLUTION] - pressure[index - RESOLUTION]); } } } // Update fluid simulation function updateFluid() { // Add external forces (e.g., mouse drag) // This will be handled in the mouse event handler // Diffuse velocity diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field project(velocityX, velocityY); // Diffuse velocity again diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field again project(velocityX, velocityY); // Swap buffers for (let y = 0; y < RESOLUTION; y++) { for (let x = 0; x < RESOLUTION; x++) { const index = getIndex(x, y); oldVelocityX[index] = velocityX[index]; oldVelocityY[index] = velocityY[index]; } } } // Update particles based on fluid velocity function updateParticles() { for (let i = 0; i < particles.length; i++) { const p = particles[i]; // Sample velocity at particle position const x = p.x; const y = p.y; [157 more lines in file. Use offset=230 to continue.]

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for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); pressure[index] = ( div[index] + pressure[index + 1] + pressure[index - 1] + pressure[index + RESOLUTION] + pressure[index - RESOLUTION] ) / 4; } [207 more lines in file. Use offset=180 to continue.]

(fieldX[index + 1] - fieldX[index - 1]) * 0.5 + (fieldY[index + RESOLUTION] - fieldY[index - RESOLUTION]) * 0.5 ); } } // Compute pressure const pressure = new Float32Array(RESOLUTION * RESOLUTION); for (let iter = 0; iter < 20; iter++) { for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); pressure[index] = ( div[index] + pressure[index + 1] + pressure[index - 1] + pressure[index + RESOLUTION] + pressure[index - RESOLUTION] ) / 4; } [207 more lines in file. Use offset=180 to continue.]

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// Project velocity field to enforce divergence-free condition function project(fieldX, fieldY) { const h = 1.0 / RESOLUTION; // Compute divergence const div = new Float32Array(RESOLUTION * RESOLUTION); for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); div[index] = -rac{1}{h} * ( [227 more lines in file. Use offset=160 to continue.]

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} } // Add force to velocity function addForce(x, y, strength) { const index = getIndex(Math.floor(x), Math.floor(y)); velocityX[index] += strength; velocityY[index] += strength; } // Project velocity field to enforce divergence-free condition function project(fieldX, fieldY) { const h = 1.0 / RESOLUTION; // Compute divergence const div = new Float32Array(RESOLUTION * RESOLUTION); for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); div[index] = -rac{1}{h} * ( (fieldX[index + 1] - fieldX[index - 1]) * 0.5 + (fieldY[index + RESOLUTION] - fieldY[index - RESOLUTION]) * 0.5 ); } } // Compute pressure const pressure = new Float32Array(RESOLUTION * RESOLUTION); for (let iter = 0; iter < 20; iter++) { for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); pressure[index] = ( div[index] + pressure[index + 1] + pressure[index - 1] + pressure[index + RESOLUTION] + pressure[index - RESOLUTION] ) / 4; } } } // Subtract pressure gradient for (let y = 1; y < RESOLUTION - 1; y++) { for (let x = 1; x < RESOLUTION - 1; x++) { const index = getIndex(x, y); fieldX[index] -= (pressure[index + 1] - pressure[index - 1]); fieldY[index] -= (pressure[index + RESOLUTION] - pressure[index - RESOLUTION]); } } } // Update fluid simulation function updateFluid() { // Add external forces (e.g., mouse drag) // This will be handled in the mouse event handler // Diffuse velocity diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field project(velocityX, velocityY); // Diffuse velocity again diffuse(velocityX, oldVelocityX, VELOCITY_ITERATIONS); diffuse(velocityY, oldVelocityY, VELOCITY_ITERATIONS); // Project velocity field again project(velocityX, velocityY); // Swap buffers for (let y = 0; y < RESOLUTION; y++) { for (let x = 0; x < RESOLUTION; x++) { const index = getIndex(x, y); oldVelocityX[index] = velocityX[index]; oldVelocityY[index] = velocityY[index]; } } } // Update particles based on fluid velocity function updateParticles() { for (let i = 0; i < particles.length; i++) { const p = particles[i]; // Sample velocity at particle position const x = p.x; const y = p.y; // Bilinear interpolation for velocity const vx = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityX ); const vy = bilinearInterpolation( x, y, x + 1, y + 1, x, y, velocityY ); // Update particle position [147 more lines in file. Use offset=240 to continue.]

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