a world of worlds

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

Created by ge1doot on 2019/2/11
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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;
        this.type = 0;
    }
    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]
    	]);
	}
	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);
            p.addPoints(p0, p1, p2, p3);
            if (shape.m[8] === 1) p.addOutline(0);
            if (shape.m[7] !== 0) p.addHatching(shape.m[6], shape.m[7]);
            polygons.draw(turtle, p);
            break;
        case 2:
            // circle
    		p.addPoints(shape.transform(0.5, 0));
    		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[8] === 1) p.addOutline(0);
    		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);
            p.addPoints(p0, p1, p2);
            if (shape.m[8] === 1) p.addOutline(0);
            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]);
        p.addHatching(0, 2);
        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
		}
		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];
				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
    		];
    	}
    	addHatching(a, d) {
    	    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);
			}
		}
	};
}