Triangulation 🔺
Delaunay triangulation with some hatching
#triangulation
Log in to post a comment.
const seed = 250; // min=1, max=500, step=1
const size = 100; // min=50, max=150, step=5
const amount = 200; // min=10, max=1000, step=5
const hatching = 0.5; // min=0.0, max=1.0, step=0.05
const outlines = 0.5; // min=0.0, max=1.0, step=0.05
const density = 0.85; // min=0, max=1, step=0.05
const uniform = 0.8; // min=0, max=1, step=0.05
const destroyed = 0.1; // min=0, max=1, step=0.05
const shape = 2; // min=0, max=3, step=1 (Raw, Square, Rounded, Round)
const turtle = new Turtle();
const polygons = new Polygons();
const random = new Random(seed);
const delaunay = new Delaunay();
const sizeSqrt = Math.ceil(Math.sqrt(amount));
function walk(step = 0) {
if (step === 0) {
let input = [...Array(amount).keys()].map(p => [
-size + ((p % sizeSqrt) / sizeSqrt) * size * 2,
-size + ((p / sizeSqrt | 0) / sizeSqrt) * size * 2,
]);
random.shuffle(input);
input = input.filter(p => random.next() > destroyed / 2);
input = input.filter(p => random.next() > destroyed / 2);
input = input.filter(p => random.next() > destroyed / 2);
input = input.filter(p => random.next() > destroyed / 2);
input = input.filter(p => random.next() > destroyed / 2);
if (shape == 1) {
input.unshift([-size,-size]);
input.unshift([size,-size]);
input.unshift([size,size]);
input.unshift([-size,size]);
} else if (shape == 2 || shape == 3) {
input = input.filter(p => p[0] * p[0] + p[1] * p[1] < (size * size));
const total = Math.max(amount - input.length, 20);
if (shape == 3) for(let i=0;i<total;i++) {
const a = i/total*Math.PI*2;
input.unshift([Math.sin(a)*size,Math.cos(a)*size]);
}
}
const spread = (1 - uniform) * size / 2;
input.forEach(p => {
const r = (shape == 0) ? random.next() : Math.max(0, Math.min(1, 1 - (p[0] * p[0] + p[1] * p[1]) / (size * size)))
p[0] += random.range(-spread, spread) * r;
p[1] += random.range(-spread, spread) * r;
})
random.shuffle(input);
delaunay.compute(input);
}
let idx = step * 3;
let { indices, points } = delaunay;
let p0 = points[indices[idx + 0]];
let p1 = points[indices[idx + 1]];
let p2 = points[indices[idx + 2]];
if (!p0 || !p1 || !p2) return false;
const angle = Math.atan2(p0[1]-p1[1]-p2[1], p0[0]-p1[0]-p2[0]);
if (outlines === 1 && hatching === 0) {
if (random.next() < density) {
turtle.jump(p0);
turtle.goto(p1);
turtle.goto(p2);
turtle.goto(p0);
}
} else {
const triangle = polygons.create();
triangle.addPoints(p0, p1, p2);
if (random.next() < outlines) triangle.addOutline();
if (random.next() < hatching) triangle.addHatching(angle, (0.25 + (idx / indices.length) * 1.5) * lerp(1.0, 0.75, Math.min(amount, 1000) / 1000));
if (random.next() < density) polygons.draw(turtle, triangle);
}
return true;
}
function add2(p, v) { return [p[0] + v[0], p[1] + v[1]]; }
function scl2(p, x, y = x) { return [p[0] * x, p[1] * y]; }
function lerp(a,b,t) { return a + (b-a) * t; }
function Delaunay() {
// Ported from some output of my old Haxe project
class Delaunay {
constructor() { }
compute(points) {
this.points = points;
let t = 0, n=0, c=0;
let s = points.length;
if (s < 3) return null;
let e = 1e9;
points.push([0, -e]);
points.push([e, e]);
points.push([-e, e]);
this.indices = [points.length - 3, points.length - 2, points.length - 1];
this.circles = [0, 0, e];
for (let h = [], t = 0, n = 0, c = 0, r = 0; r < s; ) {
let l = r++, p = 0;
if (0 < this.indices.length)
for (;;) {
let d = points[l];
let a = this.circles[p] - d[0];
let o = this.circles[p + 1] - d[1];
let f = this.circles[p + 2] > a * a + o * o;
if (
(f &&
((t = this.indices[p]),
(n = this.indices[p + 1]),
(c = this.indices[p + 2]),
h.push(t),
h.push(n),
h.push(n),
h.push(c),
h.push(c),
h.push(t),
this.indices.splice(p, 3),
this.circles.splice(p, 3),
(p -= 3)),
!((p += 3) < this.indices.length))
)
break;
}
let u = 0;
if (0 < h.length)
for (;;) {
let g = u + 2;
if (g < h.length)
for (;;) {
if (
(h[u] == h[g] && h[u + 1] == h[g + 1]) ||
(h[u + 1] == h[g] && h[u] == h[g + 1])
) {
if ((h.splice(g, 2), h.splice(u, 2), (g -= 2), (u -= 2) < 0))
break;
if (g < 0) break;
}
if (!((g += 2) < h.length)) break;
}
if (!((u += 2) < h.length)) break;
}
let v = 0;
if (0 < h.length)
for (;;) {
this.indices.push(h[v]);
this.indices.push(h[v + 1]);
this.indices.push(l);
let x = points[h[v]],
y = points[h[v + 1]],
b = points[l],
k = y[0] - x[0],
T = y[1] - x[1],
m = b[0] - x[0],
j = b[1] - x[1],
q = k * (x[0] + y[0]) + T * (x[1] + y[1]),
w = m * (x[0] + b[0]) + j * (x[1] + b[1]),
z = 2 * (k * (b[1] - y[1]) - T * (b[0] - y[0])),
A = (j * q - T * w) / z;
this.circles.push(A);
let B = (k * w - m * q) / z;
if (
(this.circles.push(B),
(A -= x[0]),
(B -= x[1]),
this.circles.push(A * A + B * B),
!((v += 2) < h.length))
)
break;
}
for (; 0 != h.length; ) h.pop();
}
(t = points.length - 3), (n = points.length - 2), (c = points.length - 1);
let C = 0;
if (0 < this.indices.length)
for (;;) {
if (
this.indices[C] == t ||
this.indices[C] == n ||
this.indices[C] == c ||
this.indices[C + 1] == t ||
this.indices[C + 1] == n ||
this.indices[C + 1] == c ||
this.indices[C + 2] == t ||
this.indices[C + 2] == n ||
this.indices[C + 2] == c
) {
if (
(this.indices.splice(C, 3),
(C -= 3),
(C += 3) < this.indices.length)
)
continue;
break;
}
if (!((C += 3) < this.indices.length)) break;
}
return points.pop(), points.pop(), points.pop(), this.indices;
}
}
return new Delaunay();
}
// Seeded random - Mulberry32
function Random(seed) {
class Random {
constructor(seed) {
this.seed = seed;
}
next() {
var t = this.seed += 0x6D2B79F5;
t = Math.imul(t ^ t >>> 15, t | 1);
t ^= t + Math.imul(t ^ t >>> 7, t | 61);
return ((t ^ t >>> 14) >>> 0) / 4294967296;
}
range(from, to) {
var r = this.next();
return from + (to - from) * r;
}
either(a = 0, b = 1, chance = 0.5) {
return this.next() > chance ? a : b;
}
shuffle(arr) {
for (let i = arr.length - 1; i > 0; i--) {
const j = Math.floor(this.next() * (i + 1));
[arr[i], arr[j]] = [arr[j], arr[i]];
}
return arr;
}
}
return new Random(seed);
}
////////////////////////////////////////////////////////////////
// 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);
}
};
}