回答編集履歴
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調整
answer
CHANGED
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@@ -1,4 +1,369 @@
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流体シミュレーションは普通はライブラリにまかせることが多いでしょう。
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自力でやるのであれば[ナビエ–ストークス方程式](https://ja.wikipedia.org/wiki/%E3%83%8A%E3%83%93%E3%82%A8%E2%80%93%E3%82%B9%E3%83%88%E3%83%BC%E3%82%AF%E3%82%B9%E6%96%B9%E7%A8%8B%E5%BC%8F)を利用することです。
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なお完全な物理シミュレーションは負荷が高いのでスパコンの世界になります。
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-
個人が趣味でやるレベルであればある程度簡略化して疑似処理でやるしかないと思います。
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個人が趣味でやるレベルであればある程度簡略化して疑似処理でやるしかないと思います。
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# 参考
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「ライブラリになしのjavascriptで流体シミュレーション書いてよチャッピー」とお願いしたらサンプルを書いてくれました。
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マウスクリックで染料投入、マウスムーブで流体シミュレーションです。参考までに
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```HTML
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<canvas id="canvas" width="600" height="600"></canvas>
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<script>
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const canvas = document.getElementById("canvas");
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const ctx = canvas.getContext("2d");
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const N = 100;
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const SIZE = N * N;
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const dt = 0.1;
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const viscosity = 0.00001;
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const pressureIterations = 30;
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const u = new Float32Array(SIZE);
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const v = new Float32Array(SIZE);
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const uPrev = new Float32Array(SIZE);
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const vPrev = new Float32Array(SIZE);
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const pressure = new Float32Array(SIZE);
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const pressurePrev = new Float32Array(SIZE);
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const divergence = new Float32Array(SIZE);
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const density = new Float32Array(SIZE);
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const densityPrev = new Float32Array(SIZE);
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function IX(x, y) {
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return x + y * N;
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}
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function setBoundary(field, type) {
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for (let i = 1; i < N - 1; i++) {
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field[IX(i, 0)] =
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type === 2
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? -field[IX(i, 1)]
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: field[IX(i, 1)];
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field[IX(i, N - 1)] =
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type === 2
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? -field[IX(i, N - 2)]
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: field[IX(i, N - 2)];
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field[IX(0, i)] =
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type === 1
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? -field[IX(1, i)]
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: field[IX(1, i)];
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field[IX(N - 1, i)] =
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type === 1
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? -field[IX(N - 2, i)]
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: field[IX(N - 2, i)];
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}
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field[IX(0, 0)] =
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0.5 * (
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field[IX(1, 0)] +
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field[IX(0, 1)]
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);
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field[IX(0, N - 1)] =
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0.5 * (
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field[IX(1, N - 1)] +
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field[IX(0, N - 2)]
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);
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field[IX(N - 1, 0)] =
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0.5 * (
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field[IX(N - 2, 0)] +
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field[IX(N - 1, 1)]
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);
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field[IX(N - 1, N - 1)] =
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0.5 * (
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field[IX(N - 2, N - 1)] +
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field[IX(N - 1, N - 2)]
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);
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}
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function diffuse(field, source, diff, dt, boundaryType) {
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const a = dt * diff * (N - 2) * (N - 2);
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for (let k = 0; k < 20; k++) {
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for (let y = 1; y < N - 1; y++) {
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for (let x = 1; x < N - 1; x++) {
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const i = IX(x, y);
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field[i] =
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(
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source[i] +
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a * (
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field[IX(x - 1, y)] +
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field[IX(x + 1, y)] +
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field[IX(x, y - 1)] +
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field[IX(x, y + 1)]
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)
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)
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/
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(1 + 4 * a);
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}
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}
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setBoundary(field, boundaryType);
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}
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}
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function advect(
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field,
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source,
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uVelocity,
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vVelocity,
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dt,
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boundaryType
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) {
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const dt0 = dt * (N - 2);
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for (let y = 1; y < N - 1; y++) {
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for (let x = 1; x < N - 1; x++) {
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const i = IX(x, y);
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let px = x - dt0 * uVelocity[i];
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let py = y - dt0 * vVelocity[i];
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if (px < 0.5) px = 0.5;
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if (px > N - 1.5) px = N - 1.5;
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if (py < 0.5) py = 0.5;
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111
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if (py > N - 1.5) py = N - 1.5;
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const x0 = Math.floor(px);
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const x1 = x0 + 1;
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const y0 = Math.floor(py);
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const y1 = y0 + 1;
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const sx = px - x0;
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const sy = py - y0;
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const i00 = IX(x0, y0);
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const i10 = IX(x1, y0);
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const i01 = IX(x0, y1);
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const i11 = IX(x1, y1);
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field[i] =
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(1 - sy) *
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(
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(1 - sx) * source[i00] +
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sx * source[i10]
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)
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+
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sy *
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(
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(1 - sx) * source[i01] +
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sx * source[i11]
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);
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}
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}
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setBoundary(field, boundaryType);
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}
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function project(u, v, pressure, divergence) {
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for (let y = 1; y < N - 1; y++) {
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for (let x = 1; x < N - 1; x++) {
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const i = IX(x, y);
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divergence[i] =
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-0.5 * (
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u[IX(x + 1, y)] -
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u[IX(x - 1, y)] +
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v[IX(x, y + 1)] -
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v[IX(x, y - 1)]
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) / N;
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pressure[i] = 0;
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}
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}
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setBoundary(divergence, 0);
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setBoundary(pressure, 0);
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for (let k = 0; k < pressureIterations; k++) {
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for (let y = 1; y < N - 1; y++) {
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for (let x = 1; x < N - 1; x++) {
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const i = IX(x, y);
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pressure[i] =
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(
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160
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divergence[i] +
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pressure[IX(x - 1, y)] +
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pressure[IX(x + 1, y)] +
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pressure[IX(x, y - 1)] +
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pressure[IX(x, y + 1)]
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165
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) / 4;
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}
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}
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setBoundary(pressure, 0);
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}
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for (let y = 1; y < N - 1; y++) {
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for (let x = 1; x < N - 1; x++) {
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const i = IX(x, y);
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u[i] -=
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0.5 *
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N *
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(
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pressure[IX(x + 1, y)] -
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pressure[IX(x - 1, y)]
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);
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180
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v[i] -=
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0.5 *
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N *
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(
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184
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pressure[IX(x, y + 1)] -
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pressure[IX(x, y - 1)]
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+
);
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}
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}
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setBoundary(u, 1);
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setBoundary(v, 2);
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}
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192
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function velocityStep() {
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uPrev.set(u);
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vPrev.set(v);
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diffuse(
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u,
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197
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uPrev,
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198
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viscosity,
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199
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dt,
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200
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1
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201
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+
);
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202
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diffuse(
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v,
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204
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vPrev,
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205
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viscosity,
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206
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dt,
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207
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2
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208
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);
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209
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+
project(
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210
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u,
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211
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v,
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212
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pressure,
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213
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+
divergence
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214
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+
);
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215
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uPrev.set(u);
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216
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vPrev.set(v);
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217
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+
advect(
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218
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u,
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219
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uPrev,
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220
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+
uPrev,
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221
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+
vPrev,
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222
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+
dt,
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223
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1
|
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224
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+
);
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225
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+
advect(
|
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226
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+
v,
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227
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+
vPrev,
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228
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+
uPrev,
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229
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+
vPrev,
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230
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+
dt,
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231
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+
2
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232
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+
);
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233
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project(
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234
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u,
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235
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v,
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236
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pressure,
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237
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+
divergence
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238
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+
);
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239
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+
}
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240
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+
function densityStep() {
|
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241
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+
densityPrev.set(density);
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242
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+
diffuse(
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243
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density,
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244
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+
densityPrev,
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245
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+
0.00001,
|
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246
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+
dt,
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247
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+
0
|
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248
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+
);
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249
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densityPrev.set(density);
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250
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+
advect(
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251
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density,
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252
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+
densityPrev,
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253
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+
u,
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254
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+
v,
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255
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+
dt,
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256
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0
|
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257
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+
);
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258
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+
}
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259
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+
let mouseX = 50;
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260
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+
let mouseY = 50;
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261
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+
let previousMouseX = 50;
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262
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+
let previousMouseY = 50;
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263
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+
let mouseDown = false;
|
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264
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+
canvas.addEventListener("mousemove", function(e) {
|
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265
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+
const rect = canvas.getBoundingClientRect();
|
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266
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+
mouseX =
|
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267
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+
(e.clientX - rect.left)
|
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268
|
+
/ rect.width
|
|
269
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+
* N;
|
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270
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+
mouseY =
|
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271
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+
(e.clientY - rect.top)
|
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272
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+
/ rect.height
|
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273
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+
* N;
|
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274
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+
});
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275
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+
canvas.addEventListener("mousedown", function() {
|
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276
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mouseDown = true;
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277
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+
});
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278
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+
canvas.addEventListener("mouseup", function() {
|
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279
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+
mouseDown = false;
|
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280
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+
});
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281
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+
canvas.addEventListener("mouseleave", function() {
|
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282
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+
mouseDown = false;
|
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283
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+
});
|
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284
|
+
function addMouseForce() {
|
|
285
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+
const x = Math.floor(mouseX);
|
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286
|
+
const y = Math.floor(mouseY);
|
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287
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+
if (
|
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288
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+
x < 2 ||
|
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289
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+
x >= N - 2 ||
|
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290
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+
y < 2 ||
|
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291
|
+
y >= N - 2
|
|
292
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+
) {
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293
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+
return;
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294
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+
}
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295
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+
const dx = mouseX - previousMouseX;
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296
|
+
const dy = mouseY - previousMouseY;
|
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297
|
+
const radius = 4;
|
|
298
|
+
for (let yy = -radius; yy <= radius; yy++) {
|
|
299
|
+
for (let xx = -radius; xx <= radius; xx++) {
|
|
300
|
+
const px = x + xx;
|
|
301
|
+
const py = y + yy;
|
|
302
|
+
if (
|
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303
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+
px < 1 ||
|
|
304
|
+
px >= N - 1 ||
|
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305
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+
py < 1 ||
|
|
306
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+
py >= N - 1
|
|
307
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+
) {
|
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308
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+
continue;
|
|
309
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+
}
|
|
310
|
+
const distance =
|
|
311
|
+
Math.sqrt(xx * xx + yy * yy);
|
|
312
|
+
if (distance > radius) {
|
|
313
|
+
continue;
|
|
314
|
+
}
|
|
315
|
+
const strength =
|
|
316
|
+
1 - distance / radius;
|
|
317
|
+
const i = IX(px, py);
|
|
318
|
+
u[i] += dx * 5 * strength;
|
|
319
|
+
v[i] += dy * 5 * strength;
|
|
320
|
+
if (mouseDown) {
|
|
321
|
+
density[i] += 5 * strength;
|
|
322
|
+
}
|
|
323
|
+
}
|
|
324
|
+
}
|
|
325
|
+
previousMouseX = mouseX;
|
|
326
|
+
previousMouseY = mouseY;
|
|
327
|
+
}
|
|
328
|
+
const image =
|
|
329
|
+
ctx.createImageData(
|
|
330
|
+
canvas.width,
|
|
331
|
+
canvas.height
|
|
332
|
+
);
|
|
333
|
+
function render() {
|
|
334
|
+
const pixels = image.data;
|
|
335
|
+
for (let py = 0; py < canvas.height; py++) {
|
|
336
|
+
for (let px = 0; px < canvas.width; px++) {
|
|
337
|
+
const x =
|
|
338
|
+
Math.floor(
|
|
339
|
+
px / canvas.width * N
|
|
340
|
+
);
|
|
341
|
+
const y =
|
|
342
|
+
Math.floor(
|
|
343
|
+
py / canvas.height * N
|
|
344
|
+
);
|
|
345
|
+
const d =
|
|
346
|
+
Math.min(
|
|
347
|
+
255,
|
|
348
|
+
density[IX(x, y)] * 255
|
|
349
|
+
);
|
|
350
|
+
const index =
|
|
351
|
+
(px + py * canvas.width) * 4;
|
|
352
|
+
pixels[index] = d;
|
|
353
|
+
pixels[index + 1] = d * 0.15;
|
|
354
|
+
pixels[index + 2] = d * 0.15;
|
|
355
|
+
pixels[index + 3] = 255;
|
|
356
|
+
}
|
|
357
|
+
}
|
|
358
|
+
ctx.putImageData(image, 0, 0);
|
|
359
|
+
}
|
|
360
|
+
function update() {
|
|
361
|
+
addMouseForce();
|
|
362
|
+
velocityStep();
|
|
363
|
+
densityStep();
|
|
364
|
+
render();
|
|
365
|
+
requestAnimationFrame(update);
|
|
366
|
+
}
|
|
367
|
+
update();
|
|
368
|
+
</script>
|
|
369
|
+
```
|