### a world of worlds

Based on alphabet03 by jconstant, September 5th, 2014
contextfreeart.org/gallery2/#design/3506

```// 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;
this.type = 0;
}
rotate (v) {
const rad = Math.PI * v / 180;
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]
]);
}
size () {
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 Math.sqrt(Math.max(x, y));
}
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, 0);
const p1 = this.transform(0.5, 0);
const p2 = this.transform(0.5, -0.5);
const p3 = this.transform(0, -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 shapes =  [];
let zoom = 1, ox = 0, oy = 0;
const box = [0, 0, 0, 0];
const shape  = (t, m, o, a, s) => {
m.boundingBox(box);
m.m[6] = a;
m.m[7] = s;
m.m[8] = o;
m.type = t;
shapes.push(m);
};
const rect     = (m, o = 1, a = 0, s = 0) => shape(1, m, o, a, s);
const circle   = (m, o = 1, a = 0, s = 0) => shape(2, m, o, a, s);
const triangle = (m, o = 1, a = 0, s = 0) => shape(3, m, o, a, s);
const draw = shape => {
const p = polygons.create();
let p0, p1, p2, p3;
switch (shape.type) {
case 1:
// rectangle
p0 = shape.transform(-0.5, -0.5);
p1 = shape.transform(0.5, -0.5);
p2 = shape.transform(0.5, 0.5);
p3 = shape.transform(-0.5, 0.5);
if (shape.m[7] !== 0) p.addHatching(shape.m[6], shape.m[7]);
polygons.draw(turtle, p);
break;
case 2:
// circle
for (let a = Math.PI / 36; a <= 2 * Math.PI; a += Math.PI / 36) {
p.addPoints(shape.transform(Math.cos(a) * 0.5, -Math.sin(a) * 0.5));
}
if (shape.m[7] !== 0) p.addHatching(shape.m[6], shape.m[7]);
polygons.draw(turtle, p);
break;
case 3:
// triangle
p0 = shape.transform(0, 0.577350269);
p1 = shape.transform(0.5, -0.28867513);
p2 = shape.transform(-0.5, -0.28867513);
if (shape.m[7] !== 0) p.addHatching(shape.m[6], shape.m[7]);
polygons.draw(turtle, p);
break;
}
}
const scale = (margin = 0.95) => {
zoom = Math.min(
margin * 200 / (box[2] - box[0]),
margin * 200 / (box[3] - box[1])
);
ox = (box[0] + box[2]) * 0.5 * zoom;
oy = (box[3] + box[1]) * 0.5 * zoom;
};
//
//
//
//
/////////////////////////CFDG ///////////////////////////
const minSize = 0.0075;
const FRACT = m => {
if (m.size() < minSize) return;
const r = Math.random() * 3;
switch (true) {
case r <= 1:
if (m.size() > 0.01) rect(m.translate(-0.05, 0.05), 0, -Math.PI/4, 0.2);
rect(m);
FRACT(m.translate(0, .355).scale(.205));
FRACT(m.translate(-.355, .355).scale(.51));
return FRACT(m.translate(.355, .355).scale(.51));
case r <= 2:
if (m.size() > 0.01) circle(m.translate(-0.05, 0.05), 0, -Math.PI/4, 0.2);
circle(m);
FRACT(m.translate(0, .325).scale(.215));
FRACT(m.translate(-.325, .325).scale(.55));
return FRACT(m.translate(.325, .325).scale(.55));
default:
if (m.size() > 0.01) triangle(m.translate(-0.05, 0.05), 0, -Math.PI/4, 0.2);
triangle(m);
FRACT(m.translate(0, .315).scale(.225));
FRACT(m.translate(-.315, -.225).scale(.50));
return FRACT(m.translate(.315, -.225).scale(.50));
}
}

/////////////////// render scene //////////////////////////////
//
//
//
//
FRACT(new Mat2D([1, 0, 0, -1, 0, 0]));
scale(0.95);
shapes.sort((a, b) => b.size() - a.size());

// The walk function will be called until it returns false.
function walk(i) {
const m = shapes.pop();
if (!m) {
const p = polygons.create();
p.addPoints([-100, -100], [100, -100], [100, 100], [-100, 100]);
polygons.draw(turtle, p);
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 Polygon = class {
constructor() {
this.cp = [];       // clip path: array of [x,y] pairs
this.dp = [];       // 2d line to draw
this.aabb = [];     // AABB bounding box
}
for (let i = 0; i < points.length; i++) this.cp.push(points[i]);
this.aabb = this.AABB();
}
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];
t.penup();
t.goto(d0);
t.pendown();
t.goto(d1);
}
}
AABB() {
let xmin = 2000;
let xmax = -2000;
let ymin = 2000;
let ymax = -2000;
for (const cp of this.cp) {
const x = cp[0];
const y = cp[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
];
}
a += Math.PI / 2;
const tp = new Polygon();
const x = this.aabb[0], y = this.aabb[1];
const w = this.aabb[2], h = this.aabb[3];
const l = Math.sqrt((w * 2) ** 2 + (h * 2) ** 2) * 0.5;
tp.cp.push([x - w, y - h], [x + w, y - h], [x + w, y + h], [x - w, y + h]);
const cx = Math.sin(a) * l, cy = Math.cos(a) * l;
let px = x - Math.cos(a) * l;
let py = y - Math.sin(a) * l;
for (let i = 0; i < l * 2; i += d) {
tp.dp.push([px + cx, py - cy], [px - cx, py + cy]);
px += Math.cos(a) * d;
py += Math.sin(a) * d;
}
tp.boolean(this, false);
for (const dp of tp.dp) this.dp.push(dp);
}
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 <= 0.001) 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);
}
}
};
}
```