cubes

3D cubes test
using reinder's occlusion code parts from "Cubic space division #2"

Created by ge1doot on 2019/1/20
142
2

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// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(0.66);

// Global code will be evaluated once.
const turtle = new Turtle();
turtle.penup();
const polygons = Polygons();

const cubes = [];
const Point = class {
    constructor (x, y, z) {
		this.x = x;
		this.y = y;
		this.z = z;
		this.xp = 0;
		this.yp = 0;
	}
    project (angle) {
		const x = this.x;
		const y = this.y;
		const z = this.z;
		const xy = angle.cx * y - angle.sx * z;
		const xz = angle.sx * y + angle.cx * z;
		const yz = angle.cy * xz - angle.sy * x;
		const yx = angle.sy * xz + angle.cy * x;
		const scale = 0.65 * fov / (fov + yz);
		this.xp = yx * scale;
		this.yp = xy * scale;
		return yz;
	}
};
const Face = class {
    constructor (p0, p1, p2, p3) {
		this.p0 = p0;
		this.p1 = p1;
		this.p2 = p2;
		this.p3 = p3;
	}
	project(angle) {
		this.p0.project(angle);
		this.p1.project(angle);
		this.p2.project(angle);
		this.p3.project(angle);
	}
	draw() {
		if (((this.p1.yp - this.p0.yp) / (this.p1.xp - this.p0.xp) < (this.p2.yp - this.p0.yp) / (this.p2.xp - this.p0.xp) ^ this.p0.xp < this.p1.xp == this.p0.xp > this.p2.xp)) {
    	    const p = polygons.create();
    	    p.addPoints(
    	        [this.p0.xp, this.p0.yp],
                [this.p1.xp, this.p1.yp],
                [this.p2.xp, this.p2.yp],
                [this.p3.xp, this.p3.yp]
            );
            p.addOutline(0);
            polygons.draw(turtle, p);
		}
	}
};
const Cube = class {
    constructor (x, y, z, w, h, p) {
        p /= 2;
        w /= 2;
        h /= 2;
        this.z = 0;
        this.points = [
    		new Point(x - w, y - h, z - p),
    		new Point(x + w, y - h, z - p),
    		new Point(x + w, y + h, z - p),
    		new Point(x - w, y + h, z - p),
    		new Point(x - w, y - h, z + p),
    		new Point(x + w, y - h, z + p),
    		new Point(x + w, y + h, z + p),
    		new Point(x - w, y + h, z + p)
    	];
    	const c = this.points;
    	this.faces = [
    		new Face(c[0], c[1], c[2], c[3]),
    		new Face(c[0], c[4], c[5], c[1]),
    		new Face(c[3], c[2], c[6], c[7]),
    		new Face(c[0], c[3], c[7], c[4]),
    		new Face(c[1], c[5], c[6], c[2]),
    		new Face(c[5], c[4], c[7], c[6])
    	];
    	cubes.push(this);
    }
    project (angle) {
        this.z = 0;
        for (const p of this.points) this.z += p.project(angle);
        
    }
    draw() {
        for (const f of this.faces) f.draw();
    }
};
const fov = 300;
const rx = 2 * Math.random() - 1;
const ry = 2 * Math.random() - 1;
const angle = {
    cx: Math.cos(rx),
    sx: Math.sin(rx),
    cy: Math.cos(ry),
    sy: Math.sin(ry)
};
for (let x = - 4; x <= 4; x++) {
    for (let y = - 4; y <= 4; y++) {
        for (let z = - 4; z <= 4; z++) {
            new Cube(x * 20, y * 20, z * 20, 15, 15, 15);
        }
    }
}
for (let c of cubes) c.project(angle);
cubes.sort((a, b) => a.z - b.z);
for (let c of cubes) c.draw();

////////////////////////////////////////////////////////////////
// reinder's occlusion code parts from "Cubic space division #2"
// AABB optimized version 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();
		}
		addSegments(...points) {
		    for (let i = 0; i < points.length; i++) this.dp.push(points[i]);
		}
		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]);
			}
		}
		createPoly(x, y, c, r, a) {
			this.cp.length = 0;
			for (let i = 0; i < c; i++) {
				this.cp.push([
					x + Math.sin(i * Math.PI * 2 / c + a) * r,
					y + Math.cos(i * Math.PI * 2 / c + a) * r
				]);
			}
			this.aabb = this.AABB();
		}
		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
			// if even your outside
			const p1 = [0.1, -1000];
			let int = 0;
			for (let i = 0, l = this.cp.length; i < l; i++) {
				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 {
		list() {
			return polygonList;
		},
		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);
			}
		}
	};
}