Get full post/final xform working

This commit is contained in:
Bradlee Speice 2023-07-01 04:38:15 +00:00
parent 68c0b26015
commit 4bcc321c4b
7 changed files with 399 additions and 184 deletions

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@ -1,142 +0,0 @@
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
);
}

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@ -0,0 +1,189 @@
export type Variation = (
x: number,
y: number,
transformCoefs: Coefs
) => [number, number];
export type Coefs = {
a: number;
b: number;
c: number;
d: number;
e: number;
f: number;
};
function r(x: number, y: number) {
return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
}
function theta(x: number, y: number) {
return Math.atan2(x, y);
}
function omega(): number {
return Math.random() > 0.5 ? Math.PI : 0;
}
export const linear: Variation = (x, y) => [x, y];
export const julia: Variation = (x, y) => {
const sqrtR = Math.sqrt(r(x, y));
return [
sqrtR * Math.cos(theta(x, y) / 2 + omega()),
sqrtR * Math.sin(theta(x, y) / 2 + omega()),
];
};
export const popcorn: Variation = (x, y, transformCoefs) => {
return [
x + transformCoefs.c * Math.sin(Math.tan(3 * y)),
y + transformCoefs.f * Math.sin(Math.tan(3 * x)),
];
};
export const pdj: (
pdjA: number,
pdjB: number,
pdjC: number,
pdjD: number
) => Variation = (pdjA, pdjB, pdjC, pdjD) => {
return (x, y) => [
Math.sin(pdjA * y) - Math.cos(pdjB * x),
Math.sin(pdjC * x) - Math.cos(pdjD * y),
];
};
export class Transform {
constructor(
public readonly coefs: Coefs,
public readonly variations: [number, Variation][]
) {}
apply(x: number, y: number) {
const xformX = this.coefs.a * x + this.coefs.b * y + this.coefs.c;
const xformY = this.coefs.d * x + this.coefs.e * y + this.coefs.f;
var [curX, curY] = [0, 0];
this.variations.forEach(([blend, variation]) => {
const [varX, varY] = variation(xformX, xformY, this.coefs);
curX += blend * varX;
curY += blend * varY;
});
return [curX, curY];
}
}
export function weightedChoice<T>(choices: [number, T][]) {
const weightSum = choices.reduce(
(current, [weight, _t]) => current + weight,
0
);
var choice = Math.random() * weightSum;
for (var i = 0; i < choices.length; i++) {
const [weight, t] = choices[i];
if (choice < weight) {
return t;
}
choice -= weight;
}
throw "unreachable";
}
export 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;
}
export class Flame {
constructor(public readonly transforms: [number, Transform][]) {}
render(quality: number, image: ImageData) {
var x = Math.random() * 2 - 1;
var y = Math.random() * 2 - 1;
const iter = quality * (image.width * image.height);
for (var i = 0; i < iter; i++) {
const transform = weightedChoice(this.transforms);
// Play the chaos game
[x, y] = transform.apply(x, y);
if (i > 20) {
plot(x, y, image);
}
}
}
}
export const transform1Coefs: Coefs = {
a: -1.381068,
b: -1.381068,
c: 0,
d: 1.381068,
e: -1.381068,
f: 0,
};
export const transform1Weight = 0.56453495;
export const transform2Coefs: Coefs = {
a: 0.031393,
b: 0.031367,
c: 0,
d: -0.031367,
e: 0.031393,
f: 0,
};
export const transform2Weight = 0.013135;
export const transform3Coefs: Coefs = {
a: 1.51523,
b: -3.048677,
c: 0.724135,
d: 0.740356,
e: -1.455964,
f: -0.362059,
};
export const transform3Pdj = [1.09358, 2.13048, 2.54127, 2.37267];
export const transform3Weight = 0.42233;
export function renderBaseline(image: ImageData) {
const transform1 = new Transform(transform1Coefs, [[1, julia]]);
const transform2 = new Transform(transform2Coefs, [
[1, linear],
[1, popcorn],
]);
const [pdjA, pdjB, pdjC, pdjD] = transform3Pdj;
const transform3 = new Transform(transform3Coefs, [
[1, pdj(pdjA, pdjB, pdjC, pdjD)],
]);
const flame = new Flame([
[transform1Weight, transform1],
[transform2Weight, transform2],
[transform3Weight, transform3],
]);
flame.render(1, image);
}

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@ -0,0 +1,79 @@
import {
Coefs,
Variation,
Flame,
Transform,
linear,
julia,
popcorn,
pdj,
transform1Coefs,
transform1Weight,
transform2Coefs,
transform2Weight,
transform3Coefs,
transform3Pdj,
transform3Weight,
} from "./2a-variations";
export class TransformPost extends Transform {
constructor(
coefs: Coefs,
variations: [number, Variation][],
public readonly post: Coefs
) {
super(coefs, variations);
}
apply(x: number, y: number): [number, number] {
const [transformX, transformY] = super.apply(x, y);
return [
transformX * this.post.a + transformY * this.post.b + this.post.c,
transformX * this.post.d + transformY * this.post.e + this.post.f,
];
}
}
export function variationPost(coefs: Coefs, variation: Variation): Variation {
return (x, y, transformCoefs) => {
const [varX, varY] = variation(x, y, transformCoefs);
return [
varX * coefs.a + varY * coefs.b + coefs.c,
varX * coefs.d + varY * coefs.e + coefs.f,
];
};
}
export const transform2Post: Coefs = {
a: 1,
b: 0,
c: 0.241352,
d: 0,
e: 1,
f: 0.271521,
};
export function renderPost(image: ImageData) {
const transform1 = new Transform(transform1Coefs, [[1, julia]]);
const transform2 = new TransformPost(
transform2Coefs,
[
[1, linear],
[1, popcorn],
],
transform2Post
);
const [pdjA, pdjB, pdjC, pdjD] = transform3Pdj;
const transform3 = new Transform(transform3Coefs, [
[1, pdj(pdjA, pdjB, pdjC, pdjD)],
]);
const flame = new Flame([
[transform1Weight, transform1],
[transform2Weight, transform2],
[transform3Weight, transform3],
]);
flame.render(1, image);
}

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@ -0,0 +1,86 @@
import {
Coefs,
Flame,
Transform,
linear,
julia,
popcorn,
pdj,
transform1Coefs,
transform1Weight,
transform2Coefs,
transform2Weight,
transform3Coefs,
transform3Pdj,
transform3Weight,
weightedChoice,
plot,
} from "./2a-variations";
import { TransformPost, transform2Post } from "./2b-post";
export class FlameFinal extends Flame {
constructor(
transforms: [number, Transform][],
public readonly final: Transform
) {
super(transforms);
}
render(quality: number, image: ImageData) {
var x = Math.random() * 2 - 1;
var y = Math.random() * 2 - 1;
const iter = quality * (image.width * image.height);
for (var i = 0; i < iter; i++) {
const transform = weightedChoice(this.transforms);
[x, y] = transform.apply(x, y);
// This line is the only thing that changes:
[x, y] = this.final.apply(x, y);
if (i > 20) {
plot(x, y, image);
}
}
}
}
export const finalCoefs: Coefs = {
a: 2,
b: 0,
c: 0,
d: 0,
e: 2,
f: 0,
};
export function renderFinal(image: ImageData) {
const transform1 = new Transform(transform1Coefs, [[1, julia]]);
const transform2 = new TransformPost(
transform2Coefs,
[
[1, linear],
[1, popcorn],
],
transform2Post
);
const [pdjA, pdjB, pdjC, pdjD] = transform3Pdj;
const transform3 = new Transform(transform3Coefs, [
[1, pdj(pdjA, pdjB, pdjC, pdjD)],
]);
const transformFinal = new Transform(finalCoefs, [[1, julia]]);
const flame = new FlameFinal(
[
[transform1Weight, transform1],
[transform2Weight, transform2],
[transform3Weight, transform3],
],
transformFinal
);
flame.render(1, image);
}

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@ -1,9 +1,10 @@
import React from "react";
import Blog from "../../../LayoutBlog";
import { Canvas } from "./0-utility";
import { gasket } from "./1-gasket";
import { renderBaseline } from "./2-variations";
import { renderBaseline } from "./2a-variations";
import { renderPost } from "./2b-post";
import { renderFinal } from "./2c-final";
export default function () {
const Layout = Blog({
@ -15,6 +16,8 @@ export default function () {
<Layout>
<Canvas f={gasket} />
<Canvas f={renderBaseline} />
<Canvas f={renderPost} />
<Canvas f={renderFinal} />
</Layout>
);
}

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@ -81,6 +81,7 @@
<xform weight="0.422330042096567" color="0" pdj="1" coefs="1.51523 0.740356 -3.048677 -1.455964 0.724135 -0.362059" pdj_a="1.09358" pdj_b="2.13048" pdj_c="2.54127" pdj_d="2.37267" />
<xform weight="0.564534951145298" color="0" julia="1" coefs="-1.381068 1.381068 -1.381068 -1.381068 0 0" />
<xform weight="0.0131350067581356" color="0" linear="1" popcorn="1" coefs="0.031393 -0.031367 0.031367 0.031393 0 0" post="1 0 0 1 0.241352 0.271521" />
<finalxform color="0" symmetry="1" julia="1" coefs="2 0 0 2 0 0" />
<palette count="256" format="RGB">
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</palette>
</flame>
</Flames>

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@ -1,43 +1,4 @@
<Flames name="variations">
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<xform weight="0.564534951145298" color="0" julia="1" coefs="-1.381068 1.381068 -1.381068 -1.381068 0 0" />
<xform weight="0.0131350067581356" color="0" linear="1" popcorn="1" coefs="0.031393 -0.031367 0.031367 0.031393 0 0" />
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</flame>
<flame name="post xform" version="Apophysis 2.08 beta" size="600 600" center="0 0" scale="150" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
<xform weight="0.422330042096567" color="0" pdj="1" coefs="1.51523 0.740356 -3.048677 -1.455964 0.724135 -0.362059" pdj_a="1.09358" pdj_b="2.13048" pdj_c="2.54127" pdj_d="2.37267" />
<xform weight="0.564534951145298" color="0" julia="1" coefs="-1.381068 1.381068 -1.381068 -1.381068 0 0" />
@ -117,4 +78,43 @@
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</flame>
<flame name="baseline" version="Apophysis 2.08 beta" size="600 600" center="0 0" scale="150" oversample="1" filter="0.2" quality="1" background="0 0 0" brightness="4" gamma="4" >
<xform weight="0.422330042096567" color="0" pdj="1" coefs="1.51523 0.740356 -3.048677 -1.455964 0.724135 -0.362059" pdj_a="1.09358" pdj_b="2.13048" pdj_c="2.54127" pdj_d="2.37267" />
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