Cipal
Adapted from a CFDG program contextfreeart.org/gallery2/#design/276
Cipal by Ferma, April 30th, 2006
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// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(1);
// Global code will be evaluated once.
const turtle = new Turtle();
const polygons = Polygons();
turtle.penup();
/////////////////////////////////////////////////////
const Mat2D = class {
constructor (m) { this.m = m; }
rotate (v) {
const rad = Math.PI * v / 180;
const cos = Math.cos(rad);
const sin = Math.sin(rad);
return new Mat2D([
cos * this.m[0] + sin * this.m[2],
cos * this.m[1] + sin * this.m[3],
cos * this.m[2] - sin * this.m[0],
cos * this.m[3] - sin * this.m[1],
this.m[4],
this.m[5]
]);
}
translate (x, y = 0) {
return new Mat2D([
this.m[0],
this.m[1],
this.m[2],
this.m[3],
this.m[4] + x * this.m[0] + y * this.m[2],
this.m[5] + x * this.m[1] + y * this.m[3]
]);
}
scale (x = 1, y = x) {
return new Mat2D([
this.m[0] * x,
this.m[1] * x,
this.m[2] * y,
this.m[3] * y,
this.m[4],
this.m[5]
]);
}
flip (v) {
const rad = Math.PI * v / 180;
const x = Math.cos(rad);
const y = Math.sin(rad);
const n = 1 / (x * x + y * y);
const b00 = (x * x - y * y) / n;
const b01 = 2 * x * y / n;
const b10 = 2 * x * y / n;
const b11 = (y * y - x * x) / n;
return new Mat2D([
b00 * this.m[0] + b01 * this.m[2],
b00 * this.m[1] + b01 * this.m[3],
b10 * this.m[0] + b11 * this.m[2],
b10 * this.m[1] + b11 * this.m[3],
this.m[4],
this.m[5]
]);
}
tooSmall () {
const x = this.m[0] * this.m[0] + this.m[1] * this.m[1];
const y = this.m[2] * this.m[2] + this.m[3] * this.m[3];
return x < minSize || y < minSize;
}
transform (x, y) {
const m0 = this.m[0] * zoom;
const m1 = this.m[1] * zoom;
const m2 = this.m[2] * zoom;
const m3 = this.m[3] * zoom;
const m4 = this.m[4] * zoom - ox;
const m5 = this.m[5] * zoom - oy;
return [
m0 * x + m2 * y + m4,
m1 * x + m3 * y + m5
];
}
boundingBox (box) {
const p0 = this.transform(-0.5, -0.5);
const p1 = this.transform(0.5, -0.5);
const p2 = this.transform(0.5, 0.5);
const p3 = this.transform(-0.5, 0.5);
const minx = Math.min(p0[0], p1[0], p2[0], p3[0]);
const maxx = Math.max(p0[0], p1[0], p2[0], p3[0]);
const miny = Math.min(p0[1], p1[1], p2[1], p3[1]);
const maxy = Math.max(p0[1], p1[1], p2[1], p3[1]);
if (minx < box[0]) box[0] = minx; else if (maxx > box[2]) box[2] = maxx;
if (miny < box[1]) box[1] = miny; else if (maxy > box[3]) box[3] = maxy;
}
};
///////////////////////////////////////////////////////
const minSize = 0.01;
const shapes = [];
let zoom = 1, ox = 0, oy = 0;
const box = [100, 100, -100, -100];
const rect = (m, a = 0, s = 0) => {
m.boundingBox(box);
m.m[6] = a;
m.m[7] = s;
shapes.push(m);
};
const draw = m => {
const p = polygons.create();
const p0 = m.transform(-0.5, -0.5);
const p1 = m.transform(0.5, -0.5);
const p2 = m.transform(0.5, 0.5);
const p3 = m.transform(-0.5, 0.5);
p.addPoints(p0, p1, p2, p3);
p.addOutline(0);
if (m.m[7] !== 0) p.addHatching(m.m[6], m.m[7]);
polygons.draw(turtle, p);
};
const scale = (w, h, margin = 0.9) => {
zoom = Math.min(
margin * w / (box[2] - box[0]),
margin * h / (box[3] - box[1])
);
ox = (box[0] + box[2]) * 0.5 * zoom;
oy = (box[3] + box[1]) * 0.5 * zoom;
};
////////////////////////////////////////////////////
const branch = m => {
if (m.tooSmall() === true) return;
const r = Math.random() * 12.1;
switch (true) {
case r <= 0.4:
branch(m.scale(0.5).rotate(5));
return branch(m.scale(0.97).rotate(-0.9));
case r <= 1.3:
return branch(m.flip(50));
case r <= 2.3:
return branch(m.flip(20));
case r <= 4.1:
return branch(m.flip(99));
case r <= 8.1:
rect(m);
return branch(m.translate(0, -1).scale(0.99).rotate(-1));
default:
rect(m, Math.atan2(-m.m[3], m.m[2]), 0.1);
return branch(m.translate(0, -0.5).rotate(-1));
}
}
/////////////////// render scene //////////////////////////////
branch(new Mat2D([1, 0, 0, -1, 0, 0]));
scale(200, 200, 0.95);
// The walk function will be called until it returns false.
function walk(i) {
const m = shapes.pop();
if (!m) return false;
draw(m);
return true;
}
////////////////////////////////////////////////////////////////
// reinder's occlusion code parts from "Cubic space division #2"
// Optimizations and code clean-up by ge1doot
////////////////////////////////////////////////////////////////
function Polygons() {
const polygonList = [];
const linesDrawn = [];
const Polygon = class {
constructor() {
this.cp = []; // clip path: array of [x,y] pairs
this.dp = []; // 2d line to draw
this.aabb = []; // AABB bounding box
}
addPoints(...points) {
for (let i = 0; i < points.length; i++) this.cp.push(points[i]);
this.aabb = this.AABB();
}
addOutline(s = 0) {
for (let i = s, l = this.cp.length; i < l; i++) {
this.dp.push(this.cp[i], this.cp[(i + 1) % l]);
}
}
draw(t) {
if (this.dp.length === 0) return;
for (let i = 0, l = this.dp.length; i < l; i+=2) {
const d0 = this.dp[i];
const d1 = this.dp[i + 1];
const line_hash =
Math.min(d0[0], d1[0]).toFixed(2) + "-" +
Math.max(d0[0], d1[0]).toFixed(2) + "-" +
Math.min(d0[1], d1[1]).toFixed(2) + "-" +
Math.max(d0[1], d1[1]).toFixed(2);
if (!linesDrawn[line_hash]) {
t.penup();
t.goto(d0);
t.pendown();
t.goto(d1);
linesDrawn[line_hash] = true;
}
}
}
AABB() {
let xmin = 2000;
let xmax = -2000;
let ymin = 2000;
let ymax = -2000;
for (let i = 0, l = this.cp.length; i < l; i++) {
const x = this.cp[i][0];
const y = this.cp[i][1];
if (x < xmin) xmin = x;
if (x > xmax) xmax = x;
if (y < ymin) ymin = y;
if (y > ymax) ymax = y;
}
// Bounding box: center x, center y, half w, half h
return [
(xmin + xmax) * 0.5,
(ymin + ymax) * 0.5,
(xmax - xmin) * 0.5,
(ymax - ymin) * 0.5
];
}
addHatching(a, d) {
const tp = new Polygon();
tp.cp.push(
[this.aabb[0] - this.aabb[2], this.aabb[1] - this.aabb[3]],
[this.aabb[0] + this.aabb[2], this.aabb[1] - this.aabb[3]],
[this.aabb[0] + this.aabb[2], this.aabb[1] + this.aabb[3]],
[this.aabb[0] - this.aabb[2], this.aabb[1] + this.aabb[3]]
);
const dx = Math.sin(a) * d, dy = Math.cos(a) * d;
const cx = Math.sin(a) * 200, cy = Math.cos(a) * 200;
for (let i = 0.5; i < 150 / d; i++) {
tp.dp.push([dx * i + cy, dy * i - cx], [dx * i - cy, dy * i + cx]);
tp.dp.push([-dx * i + cy, -dy * i - cx], [-dx * i - cy, -dy * i + cx]);
}
tp.boolean(this, false);
for (let i = 0, l = tp.dp.length; i < l; i++) this.dp.push(tp.dp[i]);
}
inside(p) {
// find number of i ntersection points from p to far away
const p1 = [0.1, -1000];
let int = 0;
for (let i = 0, l = this.cp.length; i < l; i++) {
if ( (p[0]-this.cp[i][0])**2 + (p[1]-this.cp[i][1])**2 <= 0.01) return false;
if (
this.vec2_find_segment_intersect(
p,
p1,
this.cp[i],
this.cp[(i + 1) % l]
) !== false
) {
int++;
}
}
return int & 1;
}
boolean(p, diff = true) {
// polygon diff algorithm
const ndp = [];
for (let i = 0, l = this.dp.length; i < l; i+=2) {
const ls0 = this.dp[i];
const ls1 = this.dp[i + 1];
// find all intersections with clip path
const int = [];
for (let j = 0, cl = p.cp.length; j < cl; j++) {
const pint = this.vec2_find_segment_intersect(
ls0,
ls1,
p.cp[j],
p.cp[(j + 1) % cl]
);
if (pint !== false) {
int.push(pint);
}
}
if (int.length === 0) {
// 0 intersections, inside or outside?
if (diff === !p.inside(ls0)) {
ndp.push(ls0, ls1);
}
} else {
int.push(ls0, ls1);
// order intersection points on line ls.p1 to ls.p2
const cmpx = ls1[0] - ls0[0];
const cmpy = ls1[1] - ls0[1];
for (let i = 0, len = int.length; i < len; i++) {
let j = i;
const item = int[j];
for (
const db = (item[0] - ls0[0]) * cmpx + (item[1] - ls0[1]) * cmpy;
j > 0 && (int[j - 1][0] - ls0[0]) * cmpx + (int[j - 1][1] - ls0[1]) * cmpy < db;
j--
) int[j] = int[j - 1];
int[j] = item;
}
for (let j = 0; j < int.length - 1; j++) {
if (
(int[j][0] - int[j + 1][0]) ** 2 + (int[j][1] - int[j + 1][1]) ** 2 >= 0.01
) {
if (
diff ===
!p.inside([
(int[j][0] + int[j + 1][0]) / 2,
(int[j][1] + int[j + 1][1]) / 2
])
) {
ndp.push(int[j], int[j + 1]);
}
}
}
}
}
this.dp = ndp;
return this.dp.length > 0;
}
//port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs
vec2_find_segment_intersect(l1p1, l1p2, l2p1, l2p2) {
const d = (l2p2[1] - l2p1[1]) * (l1p2[0] - l1p1[0]) - (l2p2[0] - l2p1[0]) * (l1p2[1] - l1p1[1]);
if (d === 0) return false;
const n_a = (l2p2[0] - l2p1[0]) * (l1p1[1] - l2p1[1]) - (l2p2[1] - l2p1[1]) * (l1p1[0] - l2p1[0]);
const n_b = (l1p2[0] - l1p1[0]) * (l1p1[1] - l2p1[1]) - (l1p2[1] - l1p1[1]) * (l1p1[0] - l2p1[0]);
const ua = n_a / d;
const ub = n_b / d;
if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) {
return [
l1p1[0] + ua * (l1p2[0] - l1p1[0]),
l1p1[1] + ua * (l1p2[1] - l1p1[1])
];
}
return false;
}
};
return {
create() {
return new Polygon();
},
draw(turtle, p) {
let vis = true;
for (let j = 0; j < polygonList.length; j++) {
const p1 = polygonList[j];
// AABB overlapping test - still O(N2) but very fast
if (
Math.abs(p1.aabb[0] - p.aabb[0]) - (p.aabb[2] + p1.aabb[2]) < 0 &&
Math.abs(p1.aabb[1] - p.aabb[1]) - (p.aabb[3] + p1.aabb[3]) < 0
) {
if (p.boolean(p1) === false) {
vis = false;
break;
}
}
}
if (vis) {
p.draw(turtle);
polygonList.push(p);
}
}
};
}