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