The Pythagoras Tree

The Pythagoras tree

Created by ge1doot on 2019/1/27
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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();
const Matrix = 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 Matrix([
    		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 Matrix([
    		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]
    	]);
    }
};
const push = (m) => {
    if (m[4] - 0.5 * m[0] < box[0]) box[0] = m[4] - 0.5 * m[0];
	else if (m[4] + 0.5 * m[0] > box[2]) box[2] = m[4] + 0.5 * m[0];
	if (m[5] + 0.5 * m[3] < box[1]) box[1] = m[5] + 0.5 * m[3];
	else if (m[5] - 0.5 * m[3] > box[3]) box[3] = m[5] - 0.5 * m[3];
	shapes.push(m);
}; 
const SQUARE = (m, size, a = 0, s = 0) => {
	m[6] = size;
	m[7] = a;
	m[8] = s;
	push(m);
};
const transform = (x, y, m) => {
	const m0 = m[0] * zoom;
	const m1 = m[1] * zoom;
	const m2 = m[2] * zoom;
	const m3 = m[3] * zoom;
	const m4 = m[4] * zoom - ox;
	const m5 = m[5] * zoom - oy;
	return [
        m0 * x + m2 * y + m4, 
        m1 * x + m3 * y + m5
	];
};
const scale = (margin = 0.9) => {
	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;
};
const draw = () => {
	if (!shapes.length) return false;
	const m = shapes.pop();
	const p = polygons.create();
	const p0 = transform(0, 0, m);
	const p1 = transform(m[6], 0, m);
	const p2 = transform(m[6], m[6], m);
	const p3 = transform(0, m[6], m);
	p.addPoints(p0, p1, p2, p3);
	if (m[8] !== 0) p.addHatching(m[7], m[8]);
	p.addOutline(0);
	polygons.draw(turtle, p);
	return true;
}
///////////////////// Pytagoras Tree ///////////////////////
const branch = (m, size, angle) => {
	SQUARE(m.m, Math.abs(size));
	if (size < 0.75) return;
	const v1 = size * Math.cos(angle * Math.PI / 180);
	const v2 = size * Math.sin(angle * Math.PI / 180);
	branch(m.translate(size, 0).rotate(angle).translate(-v1, -v1), v1, angle + (Math.random() - Math.random()) * 15);
    branch(m.rotate(angle - 90).translate(0, -v2), v2, angle + (Math.random() - Math.random()) * 15);
};
///////////////////////////////////////////////////////////////////
let zoom = 0, ox = 0, oy = 0;
const box = [100, 100, -100, -100];
const shapes = [];
const size = 200 / 7;
const m = new Matrix([1, 0, 0, 1, 0, 0]);
branch(m, size, 15 + Math.random() * 60);
scale(0.97);
// The walk function will be called until it returns false.
function walk(i) {
    return draw();
}

////////////////////////////////////////////////////////////////
// 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) {
				t.penup();
				t.goto(this.dp[i]);
				t.pendown();
				t.goto(this.dp[i + 1]);
			}
		}
		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
			// if even your outside
			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 (narrow phase)
			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);
			}
		}
	};
}