Baseline render running

2025-11-04 02:20:36 -05:00 · 2023-06-26 01:56:33 +00:00
parent 8e1c7725c1
commit 0a7323a8c9
8 changed files with 760 additions and 0 deletions
--- a/posts/2023/06/flam3/0-utility.tsx
+++ b/posts/2023/06/flam3/0-utility.tsx
@ -0,0 +1,36 @@
+import React, { useEffect, useRef } from "react";
+
+export type renderFn = (image: ImageData) => void;
+
+export const Canvas: React.FC<{ f: renderFn }> = ({ f }) => {
+  const canvasRef = useRef<HTMLCanvasElement | null>(null);
+  let image: ImageData | null = null;
+  useEffect(() => {
+    if (canvasRef.current) {
+      const canvas = canvasRef.current;
+      const ctx = canvas.getContext("2d");
+
+      if (!ctx) {
+        return;
+      }
+
+      if (
+        !image ||
+        image.width !== canvas.width ||
+        image.height !== canvas.height
+      ) {
+        image = ctx.createImageData(canvas.width, canvas.height);
+      }
+
+      f(image);
+
+      ctx.putImageData(image, 0, 0);
+    }
+  });
+
+  return <canvas ref={canvasRef} width={600} height={600} />;
+};
+
+export function randomInteger(min: number, max: number) {
+  return Math.floor(Math.random() * (max - min)) + min;
+}
--- a/posts/2023/06/flam3/1-gasket.ts
+++ b/posts/2023/06/flam3/1-gasket.ts
@ -0,0 +1,61 @@
+import { randomInteger, renderFn } from "./0-utility";
+
+const ITER = 100_000;
+
+function plot(x: number, y: number, image: ImageData) {
+  // A trivial `plot` implementation would take the range [-1, 1],
+  // shift it to [0, 2], then scale by the width or height
+  // as appropriate:
+  //  pixelX = Math.floor((x + 1) * image.width / 2)
+  //  pixelY = Math.floor((y + 1) * image.height / 2)
+  //
+  // However, that produces a mirror image (across both X and Y)
+  // from the paper. We'll invert X and Y to compensate.
+  // Second, because the gasket solution only contains points in
+  // the range [0, 1), the naive plot above would waste 75% of
+  // the pixels available. We'll keep the shift by 1 (to compensate
+  // for mirroring X and Y), but scale by the full image width or
+  // height so we'll plot the specific quadrant we care about.
+  var pixelX = Math.floor((-x + 1) * image.width);
+  var pixelY = Math.floor((-y + 1) * image.height);
+
+  // Now translate the (x, y) pixel coordinates to a buffer index
+  // and paint it black:
+  const index = pixelY * (image.width * 4) + pixelX * 4;
+
+  image.data[index + 0] = 0;
+  image.data[index + 1] = 0;
+  image.data[index + 2] = 0;
+  image.data[index + 3] = 0xff;
+}
+
+type Xform = (x: number, y: number) => [number, number];
+
+export const gasket: renderFn = (image) => {
+  const F: Xform[] = [
+    (x, y) => {
+      return [x / 2, y / 2];
+    },
+    (x, y) => {
+      return [(x + 1) / 2, y / 2];
+    },
+    (x, y) => {
+      return [x / 2, (y + 1) / 2];
+    },
+  ];
+
+  let x = Math.random() * 2 - 1;
+  let y = Math.random() * 2 - 1;
+
+  // Heuristic for iteration count
+  const iter = image.height * image.width;
+
+  for (var i = 0; i < iter; i++) {
+    const Fi = randomInteger(0, F.length);
+    [x, y] = F[Fi](x, y);
+
+    if (i >= 20) {
+      plot(x, y, image);
+    }
+  }
+};
--- a/posts/2023/06/flam3/2-variations.ts
+++ b/posts/2023/06/flam3/2-variations.ts
@ -0,0 +1,142 @@
+import { randomInteger } from "./0-utility";
+
+type Variation = (x: number, y: number) => [number, number];
+
+const r = (x: number, y: number) => {
+  return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
+};
+const theta = (x: number, y: number) => {
+  return Math.atan2(x, y);
+};
+
+const linear: Variation = (x, y) => {
+  return [x, y];
+};
+
+const swirl: Variation = (x, y) => {
+  const r2 = Math.pow(r(x, y), 2);
+  const sinR2 = Math.sin(r2);
+  const cosR2 = Math.cos(r2);
+
+  return [x * sinR2 - y * cosR2, x * cosR2 + y * sinR2];
+};
+
+const polar: Variation = (x, y) => {
+  return [theta(x, y) / Math.PI, r(x, y) - 1];
+};
+
+const disc: Variation = (x, y) => {
+  const thetaOverPi = theta(x, y) / Math.PI;
+  const piR = Math.PI * r(x, y);
+  return [thetaOverPi * Math.sin(piR), thetaOverPi * Math.cos(piR)];
+};
+
+const variations = [linear, swirl, polar, disc];
+
+class Coefs {
+  constructor(
+    public readonly a: number,
+    public readonly b: number,
+    public readonly c: number,
+    public readonly d: number,
+    public readonly e: number,
+    public readonly f: number
+  ) {}
+}
+
+class Transform {
+  constructor(
+    public readonly weight: number,
+    public readonly coefs: Coefs,
+    // Assumes that we have a blend for each variation
+    public readonly blend: number[]
+  ) {}
+
+  apply(x: number, y: number) {
+    const variationX = this.coefs.a * x + this.coefs.b * y + this.coefs.c;
+    const variationY = this.coefs.d * x + this.coefs.e * y + this.coefs.f;
+
+    var transformX = 0;
+    var transformY = 0;
+    this.blend.forEach((blend, i) => {
+      const [perVarX, perVarY] = variations[i](variationX, variationY);
+      transformX += blend * perVarX;
+      transformY += blend * perVarY;
+    });
+
+    return [transformX, transformY];
+  }
+}
+
+function plot(x: number, y: number, image: ImageData) {
+  const pixelX = Math.floor(((x + 2) * image.width) / 4);
+  const pixelY = Math.floor(((y + 2) * image.height) / 4);
+
+  if (
+    pixelX < 0 ||
+    pixelX > image.width ||
+    pixelY < 0 ||
+    pixelY > image.height
+  ) {
+    return;
+  }
+
+  const index = pixelY * (image.width * 4) + pixelX * 4;
+
+  image.data[index + 0] = 0;
+  image.data[index + 1] = 0;
+  image.data[index + 2] = 0;
+  image.data[index + 3] = 0xff;
+}
+
+function render(transforms: Transform[], image: ImageData) {
+  const weightSum = transforms.reduce((val, xform) => val + xform.weight, 0);
+
+  var x = Math.random() * 2 - 1;
+  var y = Math.random() * 2 - 1;
+
+  const iter = 100_000;
+  for (var i = 0; i < iter; i++) {
+    // Find the tranform we're operating on
+
+    /*
+        var f = Math.random() * weightSum;
+
+        var transform = transforms[0];
+        transforms.forEach((xform, j) => {
+            if (f > 0 && f < xform.weight) {
+                console.log(`xform=${j}`);
+                transform = xform;
+                f -= xform.weight;
+            }
+        });
+        */
+    // HACK: Currently assuming weights are equal
+    const transform = transforms[randomInteger(0, transforms.length)];
+
+    // Play the chaos game
+    [x, y] = transform.apply(x, y);
+
+    if (i > 20) {
+      plot(x, y, image);
+    }
+  }
+}
+
+export function renderBaseline(image: ImageData) {
+  return render(
+    [
+      new Transform(
+        0.5,
+        new Coefs(0.982996, 0, -0.219512, 0, 0.982996, -0.1875),
+        [1, 0, 0, -0.934]
+      ),
+      new Transform(
+        0.5,
+        new Coefs(0.966511, -0.256624, 0.050305, 0.256624, 0.966511, -0.235518),
+        [0, 0.156, 0.778, 0]
+      ),
+    ],
+    image
+  );
+}
--- a/posts/2023/06/flam3/baseline.bak
+++ b/posts/2023/06/flam3/baseline.bak
@ -0,0 +1,230 @@
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+</Flames>
--- a/posts/2023/06/flam3/index.tsx
+++ b/posts/2023/06/flam3/index.tsx
@ -0,0 +1,20 @@
+import React from "react";
+import Blog from "../../../LayoutBlog";
+
+import { Canvas } from "./0-utility";
+import { gasket } from "./1-gasket";
+import { renderBaseline } from "./2-variations";
+
+export default function () {
+  const Layout = Blog({
+    title: "The fractal flame algorithm",
+    description: "Explaining the paper",
+    published: "2023-06-25",
+  });
+  return (
+    <Layout>
+      <Canvas f={gasket} />
+      <Canvas f={renderBaseline} />
+    </Layout>
+  );
+}
--- a/posts/2023/06/flam3/renders.flame
+++ b/posts/2023/06/flam3/renders.flame
@ -0,0 +1,40 @@
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+</flame>
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