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// You can find the Turtle API reference here: https://turtletoy.net/syntax
Canvas.setpenopacity(0.6);
const turtle = new Turtle();
turtle.penup();
const polygons = Polygons();
const cube = [];
///////////////////////////////////
const ax = Math.random() - 0.5;
const ay = Math.random() - 0.5;
const fov = 250;
const zoom = 0.2;
///////////////////////////////////
const angle = {
cx: Math.cos(ax),
sx: Math.sin(ax),
cy: Math.cos(ay),
sy: Math.sin(ay)
}
const Point = class {
constructor (x, y, z) {
this.x = x;
this.y = y;
this.z = z;
this.xp = 0;
this.yp = 0;
this.scale = 0;
}
project (cube, 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;
this.scale = fov / (fov + yz);
this.xp = yx * this.scale * zoom;
this.yp = xy * this.scale * zoom;
if (yz < -fov) cube.visible = false;
}
};
const Cube = class {
constructor (x, y, z, w, h, p) {
this.visible = true;
this.coord = [
new Point(x - w, y - h, z),
new Point(x + w, y - h, z),
new Point(x + w, y + h, z),
new Point(x - w, y + h, z),
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.coord;
this.faces = [
[c[0], c[1], c[2], c[3], 0],
[c[0], c[4], c[5], c[1], 0],
[c[3], c[2], c[6], c[7], 0],
[c[0], c[3], c[7], c[4], 1],
[c[1], c[5], c[6], c[2], 1],
[c[5], c[4], c[7], c[6], 0]
];
}
project () {
for (let i = 0; i < 8; i++) {
this.coord[i].project(this, angle);
}
for (let f = 0; f < 6; f++) {
const p = this.faces[f];
if (this.visible && ((p[1].yp - p[0].yp) / (p[1].xp - p[0].xp) < (p[2].yp - p[0].yp) / (p[2].xp - p[0].xp) ^ p[0].xp < p[1].xp == p[0].xp > p[2].xp)) {
const poly = polygons.create();
poly.addPoints([p[0].xp, p[0].yp], [p[1].xp, p[1].yp], [p[2].xp, p[2].yp], [p[3].xp, p[3].yp]);
if (p[4]) {
const a = Math.atan2(-p[0].yp + p[1].yp, p[0].xp - p[1].xp);
poly.addHatching(a, Math.min(1, Math.max(0.1, p[0].scale * 0.1)));
}
poly.addOutline(0);
polygons.draw(turtle, poly);
}
}
}
};
// create cubes structure
const r = (d0, d1) => Math.round(Math.random() * (d1 - d0) + d0);
let w = 50;
for (let z = 400; z > -400; z -= 20) {
cube.push(
new Cube(
r(-w, w), r(-w, w), z,
r(2, 30), r(2, 30), r(2, 180)
)
);
if (z > -100 && z < 100) {
for (let i = 0; i < 4; i++) {
cube.push(
new Cube(
r(-400, 400), r(-w, w), z,
r(2, 80), r(2, 30), r(2, 30)
)
);
cube.push(
new Cube(
r(-w, w), r(-400, 400), z,
r(2, 30), r(2, 80), r(2, 30)
)
);
}
}
}
cube.forEach(c => c.project());
////////////////////////////////////////////////////////////////
// reinder's occlusion code parts from "Cubic space division #2"
// Optimizations and code clean-up 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();
}
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];
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) {
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(t, 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(t);
polygonList.push(p);
}
}
};
}