Torus

A quite famous torus.
I have combined code from @flockaroo (turtletoy.net/turtle/2dc4806767) and the cleaned-up version of my own occlusion code by @ge1doot (turtletoy.net/turtle/c2cf454d80).

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// Torus. Created by Reinder Nijhoff 2019
// @reindernijhoff
//
// https://turtletoy.net/turtle/90e6288a6b
//
// I have combined code from @flockaroo (https://turtletoy.net/turtle/2dc4806767)
// and the cleaned up version of my own occlusion code by @ge1doot
// (https://turtletoy.net/turtle/c2cf454d80).
//

const turtle = new Slowpoke();
const polygons = Polygons();
const faces = [];
const nth = 120;
const nph = 40;
const radius_0 = 70;
const radius_1 = 55;
const radius_2 = 55;
const proj_xy_scale = 80;
const camera_z = 65;
const near = 5;

class Face {
    constructor (p0, p1, p2, p3, d) {
        this.p0 = p0;
        this.p1 = p1;
        this.p2 = p2;
        this.p3 = p3;
        this.dark = d;
    }
	draw () {
		const p = polygons.create();
		p.addPoints(this.p0, this.p1, this.p3, this.p2);
		p.addSegments(
		    this.p0, this.p1,
		    this.p2, this.p3
	    );
		if (this.dark) {
			p.addHatching(-Math.PI / 4, 1);
		}
		polygons.draw(turtle, p);
	}
};

for (let i = 0; i < nth; i++) {
	for (let j = 0; j < nph; j++) {
		let p0 = getTorusPoint(i, j, radius_0, radius_1, radius_2, nph, nth);
		let p1 = getTorusPoint(i + 1, j, radius_0, radius_1, radius_2, nph, nth);
		let p2 = getTorusPoint(i, j + 1, radius_0, radius_1, radius_2, nph, nth);
		let p3 = getTorusPoint(i + 1, j + 1, radius_0, radius_1, radius_2, nph, nth);

		p0 = project(p0);
		p1 = project(p1);
		p2 = project(p2);
		p3 = project(p3);

		if (p0[2] > near && p1[2] > near && p2[2] > near && p3[2] > near) {
			const face = new Face(p0, p1, p2, p3, j & 1);
			faces.push(face);
		}
	}
}

faces.sort((a, b) => a.p0[2] - b.p0[2]);

function walk(i) {
	faces[i].draw();
	return i < faces.length - 1;
}

function project(p) {
	p[1] += camera_z;
	return [p[0] / p[1] * proj_xy_scale, p[2] / p[1] * proj_xy_scale, p[1]];
}

function getTorusPoint(i, j, R, r1, r2, nph, nth) {
	const th = i / nth * Math.PI * 2.0;
	const ph = j / nph * Math.PI * 2.0 + th;
	return [
		(R + r1 * Math.cos(th)) * Math.cos(ph),
		(R + r1 * Math.cos(th)) * Math.sin(ph),
		r2 * Math.sin(th)
	];
}



////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/a5befa1f8d
////////////////////////////////////////////////////////////////

function Polygons() {
	const polygonList = [];
	const Polygon = class {
		constructor() {
			this.cp = [];       // clip path: array of [x,y] pairs
			this.dp = [];       // 2d lines [x0,y0],[x1,y1] to draw
			this.aabb = [];     // AABB bounding box
		}
		addPoints(...points) {
		    // add point to clip path and update bounding box
		    let xmin = 1e5, xmax = -1e5, ymin = 1e5, ymax = -1e5;
			(this.cp = [...this.cp, ...points]).forEach( p => {
				xmin = Math.min(xmin, p[0]), xmax = Math.max(xmax, p[0]);
				ymin = Math.min(ymin, p[1]), ymax = Math.max(ymax, p[1]);
			});
		    this.aabb = [(xmin+xmax)/2, (ymin+ymax)/2, (xmax-xmin)/2, (ymax-ymin)/2];
		}
		addSegments(...points) {
		    // add segments (each a pair of points)
		    points.forEach(p => this.dp.push(p));
		}
		addOutline() {
			for (let i = 0, l = this.cp.length; i < l; i++) {
				this.dp.push(this.cp[i], this.cp[(i + 1) % l]);
			}
		}
		draw(t) {
			for (let i = 0, l = this.dp.length; i < l; i+=2) {
				t.jump(this.dp[i]), t.goto(this.dp[i + 1]);
			}
		}
		addHatching(a, d) {
			const tp = new Polygon();
			tp.cp.push([-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);
			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);
			this.dp = [...this.dp, ...tp.dp];
		}
		inside(p) {
			let int = 0; // find number of i ntersection points from p to far away
			for (let i = 0, l = this.cp.length; i < l; i++) {
				if (this.segment_intersect(p, [0.1, -1000], this.cp[i], this.cp[(i + 1) % l])) {
					int++;
				}
			}
			return int & 1; // if even your outside
		}
		boolean(p, diff = true) {
		    // bouding box optimization by ge1doot.
		    if (Math.abs(this.aabb[0] - p.aabb[0]) - (p.aabb[2] + this.aabb[2]) >= 0 &&
				Math.abs(this.aabb[1] - p.aabb[1]) - (p.aabb[3] + this.aabb[3]) >= 0) return this.dp.length > 0;
				
			// 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.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];
					int.sort( (a,b) =>  (a[0] - ls0[0]) * cmpx + (a[1] - ls0[1]) * cmpy - 
					                    (b[0] - ls0[0]) * cmpx - (b[1] - ls0[1]) * cmpy);
					 
					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 >= 0.001) {
							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]);
							}
						}
					}
				}
			}
			return (this.dp = ndp).length > 0;
		}
		//port of http://paulbourke.net/geometry/pointlineplane/Helpers.cs
		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 {
		list: () => polygonList,
		create: () => new Polygon(),
		draw: (turtle, p, addToVisList=true) => {
			for (let j = 0; j < polygonList.length && p.boolean(polygonList[j]); j++);
			p.draw(turtle);
			if (addToVisList) polygonList.push(p);
		}
	};
}

////////////////////////////////////////////////////////////////
// Slowpoke utility code. Created by Reinder Nijhoff 2019
// https://turtletoy.net/turtle/cfe9091ad8
////////////////////////////////////////////////////////////////

function Slowpoke(x, y) {
    const linesDrawn = {};
    class Slowpoke extends Turtle {
        goto(x, y) {
            const p = Array.isArray(x) ? [...x] : [x, y];
            if (this.isdown()) {
                const o = [this.x(), this.y()];
                const h1 = o[0].toFixed(2)+'_'+p[0].toFixed(2)+o[1].toFixed(2)+'_'+p[1].toFixed(2);
                const h2 = p[0].toFixed(2)+'_'+o[0].toFixed(2)+p[1].toFixed(2)+'_'+o[1].toFixed(2);
                if (linesDrawn[h1] || linesDrawn[h2]) {
                    super.up();
                    super.goto(p);
                    super.down();
                    return;
                }
                linesDrawn[h1] = linesDrawn[h2] = true;
            } 
            super.goto(p);
        }
    }
    return new Slowpoke(x,y);
}