Fluid simulation · mercury-2
Create a real-time fluid simulation on a full-screen canvas where dragging the mouse pushes swirling colored dye through the fluid.
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transcript · 2 messages
Create a real-time fluid simulation on a full-screen canvas where dragging the mouse pushes swirling colored dye through the fluid.
**index.html** (written with a single `write` call) ```html <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <title>Real‑time Fluid Simulation</title> <style> html, body { margin:0; padding:0; overflow:hidden; background:#000; } canvas { display:block; } </style> </head> <body> <canvas id="c"></canvas> <script> (() => { const canvas = document.getElementById('c'); const ctx = canvas.getContext('2d'); // Resize to full screen const resize = () => { canvas.width = window.innerWidth; canvas.height = window.innerHeight; }; window.addEventListener('resize', resize); resize(); // Fluid simulation parameters const N = 128; // grid resolution (N x N) const size = (N + 2) * (N + 2); const dt = 0.1; // time step const diff = 0.0001; // diffusion rate const visc = 0.0001; // viscosity const force = 5.0; // mouse force magnitude const source = 100; // dye amount per mouse move // Helper to map 2D to 1D index const IX = (i, j) => i + (N + 2) * j; // Fluid fields const u = new Float32Array(size); const v = new Float32Array(size); const uPrev = new Float32Array(size); const vPrev = new Float32Array(size); const dens = new Float32Array(size); const densPrev = new Float32Array(size); // Linear solver (Gauss‑Seidel) const linSolve = (b, x, x0, a, c) => { const iter = 4; for (let k = 0; k < iter; k++) { for (let j = 1; j <= N; j++) { for (let i = 1; i <= N; i++) { x[IX(i,j)] = (x0[IX(i,j)] + a * (x[IX(i-1,j)] + x[IX(i+1,j)] + x[IX(i,j-1)] + x[IX(i,j+1)])) / c; } } setBnd(b, x); } }; // Set boundary conditions const setBnd = (b, x) => { for (let i = 1; i <= N; i++) { x[IX(i,0)] = b===1 ? -x[IX(i,1)] : x[IX(i,1)]; x[IX(i,N+1)] = b===1 ? -x[IX(i,N)] : x[IX(i,N)]; x[IX(0,i)] = b===2 ? -x[IX(1,i)] : x[IX(1,i)]; x[IX(N+1,i)] = b===2 ? -x[IX(N,i)] : x[IX(N,i)]; } x[IX(0,0)] = 0.5 * (x[IX(1,0)] + x[IX(0,1)]); x[IX(0,N+1)] = 0.5 * (x[IX(1,N+1)] + x[IX(0,N)]); x[IX(N+1,0)] = 0.5 * (x[IX(N,0)] + x[IX(N+1,1)]); x[IX(N+1,N+1)] = 0.5 * (x[IX(N,N+1)] + x[IX(N+1,N)]); }; // Diffusion step const diffuse = (b, x, x0, diff) => { const a = dt * diff * N * N; linSolve(b, x, x0, a, 1 + 4 * a); }; // Advection step const advect = (b, d, d0, u, v) => { const dt0 = dt * N; for (let j = 1; j <= N; j++) { for (let i = 1; i <= N; i++) { let x = i - dt0 * u[IX(i,j)]; let y = j - dt0 * v[IX(i,j)]; if (x < 0.5) x = 0.5; if (x > N + 0.5) x = N + 0.5; const i0 = Math.floor(x); const i1 = i0 + 1; if (y < 0.5) y = 0.5; if (y > N + 0.5) y = N + 0.5; const j0 = Math.floor(y); const j1 = j0 + 1; const s1 = x - i0; const s0 = 1 - s1; const t1 = y - j0; const t0 = 1 - t1; d[IX(i,j)] = s0 * (t0 * d0[IX(i0,j0)] + t1 * d0[IX(i0,j1)]) + s1 * (t0 * d0[IX(i1,j0)] + t1 * d0[IX(i1,j1)]); } } setBnd(b, d); }; // Projection step (make velocity field divergence‑free) const project = (u, v, p, div) => { for (let j = 1; j <= N; j++) { for (let i = 1; i <= N; i++) { div[IX(i,j)] = -0.5 * (u[IX(i+1,j)] - u[IX(i-1,j)] + v[IX(i,j+1)] - v[IX(i,j-1)]) / N; p[IX(i,j)] = 0; } } setBnd(0, div); setBnd(0, p); linSolve(0, p, div, 1, 4); for (let j = 1; j <= N; j++) { for (let i = 1; i <= N; i++) { u[IX(i,j)] -= 0.5 * N * (p[IX(i+1,j)] - p[IX(i-1,j)]); v[IX(i,j)] -= 0.5 * N * (p[IX(i,j+1)] - p[IX(i,j-1)]); } } setBnd(1, u); setBnd(2, v); }; // Velocity step const velStep = (u, v, u0, v0, visc) => { addSource(u, u0); addSource(v, v0); [u0, u] = [u, u0]; [v0, v] = [v, v0]; diffuse(1, u, u0, visc); diffuse(2, v, v0, visc); project(u, v, u0, v0); [u0, u] = [u, u0]; [v0, v] = [v, v0]; advect(1, u, u0, u0, v0); advect(2, v, v0, u0, v0); project(u, v, u0, v0); }; // Density step const densStep = (x, x0, u, v, diff) => { addSource(x, x0); [x0, x] = [x, x0]; diffuse(0, x, x0, diff); [x0, x] = [x, x0]; advect(0, x, x0, u, v); }; // Add source to a field const addSource = (x, s) => { for (let i = 0; i < size; i++) x[i] += dt * s[i]; }; // Mouse interaction let mouseDown = false; let lastX = 0, lastY = 0; canvas.addEventListener('mousedown', e => { mouseDown = true; const rect = canvas.getBoundingClientRect(); lastX = e.clientX - rect.left; lastY = e.clientY - rect.top; }); canvas.addEventListener('mouseup', () => mouseDown = false); canvas.addEventListener('mouseleave', () => mouseDown = false); canvas.addEventListener('mousemove', e => { if (!mouseDown) return; const rect = canvas.getBoundingClientRect(); const x = e.clientX - rect.left; const y = e.clientY - rect.top; const i = Math.floor((x / canvas.width) * N) + 1; const j = Math.floor((y / canvas.height) * N) + 1; const i0 = Math.floor((lastX / canvas.width) * N) + 1; const j0 = Math.floor((lastY / canvas.height) * N) + 1; const dx = x - lastX; const dy = y - lastY; const idx = IX(i, j); uPrev[idx] += force * dx; vPrev[idx] += force * dy; densPrev[idx] += source; lastX = x; lastY = y; }); // Rendering const render = () => { const img = ctx.createImageData(canvas.width, canvas.height); const data = img.data; const cellW = canvas.width / N; const cellH = canvas.height / N; for (let j = 1; j <= N; j++) { for (let i = 1; i <= N; i++) { const d = dens[IX(i, j)]; const hue = (Math.atan2(v[IX(i,j)], u[IX(i,j)]) * 180 / Math.PI + 360) % 360; const sat = Math.min(1, d); const rgb = hslToRgb(hue / 360, sat, 0.5); const x0 = Math.floor((i - 1) * cellW); const y0 = Math.floor((j - 1) * cellH); for (let yy = 0; yy < cellH; yy++) { const yPos = y0 + yy; if (yPos >= canvas.height) break; for (let xx = 0; xx < cellW; xx++) { const xPos = x0 + xx; if (xPos >= canvas.width) break; const p = (yPos * canvas.width + xPos) * 4; data[p] = rgb[0]; data[p+1] = rgb[1]; data[p+2] = rgb[2]; data[p+3] = 255; } } } } ctx.putImageData(img, 0, 0); }; // HSL → RGB helper (0‑1 inputs) const hslToRgb = (h, s, l) => { let r, g, b; if (s === 0) { r = g = b = l; } else { const hue2rgb = (p, q, t) => { if (t < 0) t += 1; if (t > 1) t -= 1; if (t < 1/6) return p + (q - p) * 6 * t; if (t < 1/2) return q; if (t < 2/3) return p + (q - p) * (2/3 - t) * 6; return p; }; const q = l < 0.5 ? l * (1 + s) : l + s - l * s; const p = 2 * l - q; r = hue2rgb(p, q, h + 1/3); g = hue2rgb(p, q, h); b = hue2rgb(p, q, h - 1/3); } return [Math.round(r*255), Math.round(g*255), Math.round(b*255)]; }; // Main loop const step = () => { velStep(u, v, uPrev, vPrev, visc); densStep(dens, densPrev, u, v, diff); // Clear previous sources uPrev.fill(0); vPrev.fill(0); densPrev.fill(0); render(); requestAnimationFrame(step); }; requestAnimationFrame(step); })(); </script> </body> </html> ```
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