Lloyd’s Algorithm With Velocities / Job van der Zwan

Delaunator = {

const EPSILON = Math.pow(2, -52);

const EDGE_STACK = new Uint32Array(512);

class Delaunator {

static from(points, getX = defaultGetX, getY = defaultGetY) {

const n = points.length;

const coords = new Float64Array(n * 2);

for (let i = 0; i < n; i++) {

const p = points[i];

coords[2 * i] = getX(p);

coords[2 * i + 1] = getY(p);

}

return new Delaunator(coords);

}

constructor(coords) {

const n = coords.length >> 1;

if (n > 0 && typeof coords[0] !== 'number') throw new Error('Expected coords to contain numbers.');

this.coords = coords;

// arrays that will store the triangulation graph

const maxTriangles = Math.max(2 * n - 5, 0);

this._triangles = new Uint32Array(maxTriangles * 3);

this._halfedges = new Int32Array(maxTriangles * 3);

// temporary arrays for tracking the edges of the advancing convex hull

this._hashSize = Math.ceil(Math.sqrt(n));

this._hullPrev = new Uint32Array(n); // edge to prev edge

this._hullNext = new Uint32Array(n); // edge to next edge

this._hullTri = new Uint32Array(n); // edge to adjacent triangle

this._hullHash = new Int32Array(this._hashSize).fill(-1); // angular edge hash

// temporary arrays for sorting points

this._ids = new Uint32Array(n);

this._dists = new Float64Array(n);

this.update();

}

update() {

const {coords, _hullPrev: hullPrev, _hullNext: hullNext, _hullTri: hullTri, _hullHash: hullHash} = this;

const n = coords.length >> 1;

// populate an array of point indices; calculate input data bbox

let minX = Infinity;

let minY = Infinity;

let maxX = -Infinity;

let maxY = -Infinity;

for (let i = 0; i < n; i++) {

const x = coords[2 * i];

const y = coords[2 * i + 1];

if (x < minX) minX = x;

if (y < minY) minY = y;

if (x > maxX) maxX = x;

if (y > maxY) maxY = y;

this._ids[i] = i;

}

const cx = (minX + maxX) / 2;

const cy = (minY + maxY) / 2;

let minDist = Infinity;

let i0, i1, i2;

// pick a seed point close to the center

for (let i = 0; i < n; i++) {

const d = dist(cx, cy, coords[2 * i], coords[2 * i + 1]);

if (d < minDist) {

i0 = i;

minDist = d;

}

const i0x = coords[2 * i0];

const i0y = coords[2 * i0 + 1];

minDist = Infinity;

// find the point closest to the seed

for (let i = 0; i < n; i++) {

if (i === i0) continue;

const d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1]);

if (d < minDist && d > 0) {

i1 = i;

minDist = d;

}

let i1x = coords[2 * i1];

let i1y = coords[2 * i1 + 1];

let minRadius = Infinity;

// find the third point which forms the smallest circumcircle with the first two

for (let i = 0; i < n; i++) {

if (i === i0 || i === i1) continue;

const r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1]);

if (r < minRadius) {

i2 = i;

minRadius = r;

}

let i2x = coords[2 * i2];

let i2y = coords[2 * i2 + 1];

if (minRadius === Infinity) {

// order collinear points by dx (or dy if all x are identical)

// and return the list as a hull

for (let i = 0; i < n; i++) {

this._dists[i] = (coords[2 * i] - coords[0]) || (coords[2 * i + 1] - coords[1]);

}

quicksort(this._ids, this._dists, 0, n - 1);

const hull = new Uint32Array(n);

let j = 0;

for (let i = 0, d0 = -Infinity; i < n; i++) {

const id = this._ids[i];

if (this._dists[id] > d0) {

hull[j++] = id;

d0 = this._dists[id];

}

this.hull = hull.subarray(0, j);

this.triangles = new Uint32Array(0);

this.halfedges = new Uint32Array(0);

return;

}

// swap the order of the seed points for counter-clockwise orientation

if (orient(i0x, i0y, i1x, i1y, i2x, i2y)) {

const i = i1;

const x = i1x;

const y = i1y;

i1 = i2;

i1x = i2x;

i1y = i2y;

i2 = i;

i2x = x;

i2y = y;

}

const center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y);

this._cx = center.x;

this._cy = center.y;

for (let i = 0; i < n; i++) {

this._dists[i] = dist(coords[2 * i], coords[2 * i + 1], center.x, center.y);

}

// sort the points by distance from the seed triangle circumcenter

quicksort(this._ids, this._dists, 0, n - 1);

// set up the seed triangle as the starting hull

this._hullStart = i0;

let hullSize = 3;

hullNext[i0] = hullPrev[i2] = i1;

hullNext[i1] = hullPrev[i0] = i2;

hullNext[i2] = hullPrev[i1] = i0;

hullTri[i0] = 0;

hullTri[i1] = 1;

hullTri[i2] = 2;

hullHash.fill(-1);

hullHash[this._hashKey(i0x, i0y)] = i0;

hullHash[this._hashKey(i1x, i1y)] = i1;

hullHash[this._hashKey(i2x, i2y)] = i2;

this.trianglesLen = 0;

this._addTriangle(i0, i1, i2, -1, -1, -1);

for (let k = 0, xp, yp; k < this._ids.length; k++) {

const i = this._ids[k];

const x = coords[2 * i];

const y = coords[2 * i + 1];

// skip near-duplicate points

if (k > 0 && Math.abs(x - xp) <= EPSILON && Math.abs(y - yp) <= EPSILON) continue;

xp = x;

yp = y;

// skip seed triangle points

if (i === i0 || i === i1 || i === i2) continue;

// find a visible edge on the convex hull using edge hash

let start = 0;

for (let j = 0, key = this._hashKey(x, y); j < this._hashSize; j++) {

start = hullHash[(key + j) % this._hashSize];

if (start !== -1 && start !== hullNext[start]) break;

}

start = hullPrev[start];

let e = start, q;

while (q = hullNext[e], !orient(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1])) {

e = q;

if (e === start) {

e = -1;

break;

}

if (e === -1) continue; // likely a near-duplicate point; skip it

// add the first triangle from the point

let t = this._addTriangle(e, i, hullNext[e], -1, -1, hullTri[e]);

// recursively flip triangles from the point until they satisfy the Delaunay condition

hullTri[i] = this._legalize(t + 2);

hullTri[e] = t; // keep track of boundary triangles on the hull

hullSize++;

// walk forward through the hull, adding more triangles and flipping recursively

let n = hullNext[e];

while (q = hullNext[n], orient(x, y, coords[2 * n], coords[2 * n + 1], coords[2 * q], coords[2 * q + 1])) {

t = this._addTriangle(n, i, q, hullTri[i], -1, hullTri[n]);

hullTri[i] = this._legalize(t + 2);

hullNext[n] = n; // mark as removed

hullSize--;

n = q;

}

// walk backward from the other side, adding more triangles and flipping

if (e === start) {

while (q = hullPrev[e], orient(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1])) {

t = this._addTriangle(q, i, e, -1, hullTri[e], hullTri[q]);

this._legalize(t + 2);

hullTri[q] = t;

hullNext[e] = e; // mark as removed

hullSize--;

e = q;

}

// update the hull indices

this._hullStart = hullPrev[i] = e;

hullNext[e] = hullPrev[n] = i;

hullNext[i] = n;

// save the two new edges in the hash table

hullHash[this._hashKey(x, y)] = i;

hullHash[this._hashKey(coords[2 * e], coords[2 * e + 1])] = e;

}

this.hull = new Uint32Array(hullSize);

for (let i = 0, e = this._hullStart; i < hullSize; i++) {

this.hull[i] = e;

e = hullNext[e];

}

// trim typed triangle mesh arrays

this.triangles = this._triangles.subarray(0, this.trianglesLen);

this.halfedges = this._halfedges.subarray(0, this.trianglesLen);

}

_hashKey(x, y) {

return Math.floor(pseudoAngle(x - this._cx, y - this._cy) * this._hashSize) % this._hashSize;

}

_legalize(a) {

const {_triangles: triangles, _halfedges: halfedges, coords} = this;

let i = 0;

let ar = 0;

// recursion eliminated with a fixed-size stack

while (true) {

const b = halfedges[a];

/* if the pair of triangles doesn't satisfy the Delaunay condition

* (p1 is inside the circumcircle of [p0, pl, pr]), flip them,

* then do the same check/flip recursively for the new pair of triangles

*

* pl pl

* /||\ / \

* al/ || \bl al/ \a

* / || \ / \

* / a||b \ flip /___ar___\

* p0\ || /p1 => p0\---bl---/p1

* \ || / \ /

* ar\ || /br b\ /br

* \||/ \ /

* pr pr

*/

const a0 = a - a % 3;

ar = a0 + (a + 2) % 3;

if (b === -1) { // convex hull edge

if (i === 0) break;

a = EDGE_STACK[--i];

continue;

}

const b0 = b - b % 3;

const al = a0 + (a + 1) % 3;

const bl = b0 + (b + 2) % 3;

const p0 = triangles[ar];

const pr = triangles[a];

const pl = triangles[al];

const p1 = triangles[bl];

const illegal = inCircle(

coords[2 * p0], coords[2 * p0 + 1],

coords[2 * pr], coords[2 * pr + 1],

coords[2 * pl], coords[2 * pl + 1],

coords[2 * p1], coords[2 * p1 + 1]);

if (illegal) {

triangles[a] = p1;

triangles[b] = p0;

const hbl = halfedges[bl];

// edge swapped on the other side of the hull (rare); fix the halfedge reference

if (hbl === -1) {

let e = this._hullStart;

do {

if (this._hullTri[e] === bl) {

this._hullTri[e] = a;

break;

}

e = this._hullPrev[e];

} while (e !== this._hullStart);

}

this._link(a, hbl);

this._link(b, halfedges[ar]);

this._link(ar, bl);

const br = b0 + (b + 1) % 3;

// don't worry about hitting the cap: it can only happen on extremely degenerate input

if (i < EDGE_STACK.length) {

EDGE_STACK[i++] = br;

}

} else {

if (i === 0) break;

a = EDGE_STACK[--i];

}

return ar;

}

_link(a, b) {

this._halfedges[a] = b;

if (b !== -1) this._halfedges[b] = a;

}

// add a new triangle given vertex indices and adjacent half-edge ids

_addTriangle(i0, i1, i2, a, b, c) {

const t = this.trianglesLen;

this._triangles[t] = i0;

this._triangles[t + 1] = i1;

this._triangles[t + 2] = i2;

this._link(t, a);

this._link(t + 1, b);

this._link(t + 2, c);

this.trianglesLen += 3;

return t;

}

// monotonically increases with real angle, but doesn't need expensive trigonometry

function pseudoAngle(dx, dy) {

const p = dx / (Math.abs(dx) + Math.abs(dy));

return (dy > 0 ? 3 - p : 1 + p) / 4; // [0..1]

}

function dist(ax, ay, bx, by) {

const dx = ax - bx;

const dy = ay - by;

return dx * dx + dy * dy;

}

function orient(px, py, qx, qy, rx, ry) {

return (qy - py) * (rx - qx) - (qx - px) * (ry - qy) < 0;

}

function inCircle(ax, ay, bx, by, cx, cy, px, py) {

const dx = ax - px;

const dy = ay - py;

const ex = bx - px;

const ey = by - py;

const fx = cx - px;

const fy = cy - py;

const ap = dx * dx + dy * dy;

const bp = ex * ex + ey * ey;

const cp = fx * fx + fy * fy;

return dx * (ey * cp - bp * fy) -

dy * (ex * cp - bp * fx) +

ap * (ex * fy - ey * fx) < 0;

}

function circumradius(ax, ay, bx, by, cx, cy) {

const dx = bx - ax;

const dy = by - ay;

const ex = cx - ax;

const ey = cy - ay;

const bl = dx * dx + dy * dy;

const cl = ex * ex + ey * ey;

const d = 0.5 / (dx * ey - dy * ex);

const x = (ey * bl - dy * cl) * d;

const y = (dx * cl - ex * bl) * d;

return x * x + y * y;

}

function circumcenter(ax, ay, bx, by, cx, cy) {

const dx = bx - ax;

const dy = by - ay;

const ex = cx - ax;

const ey = cy - ay;

const bl = dx * dx + dy * dy;

const cl = ex * ex + ey * ey;

const d = 0.5 / (dx * ey - dy * ex);

const x = ax + (ey * bl - dy * cl) * d;

const y = ay + (dx * cl - ex * bl) * d;

return {x, y};

}

function quicksort(ids, dists, left, right) {

if (right - left <= 20) {

for (let i = left + 1; i <= right; i++) {

const temp = ids[i];

const tempDist = dists[temp];

let j = i - 1;

while (j >= left && dists[ids[j]] > tempDist) ids[j + 1] = ids[j--];

ids[j + 1] = temp;

}

} else {

const median = (left + right) >> 1;

let i = left + 1;

let j = right;

swap(ids, median, i);

if (dists[ids[left]] > dists[ids[right]]) swap(ids, left, right);

if (dists[ids[i]] > dists[ids[right]]) swap(ids, i, right);

if (dists[ids[left]] > dists[ids[i]]) swap(ids, left, i);

const temp = ids[i];

const tempDist = dists[temp];

while (true) {

do i++; while (dists[ids[i]] < tempDist);

do j--; while (dists[ids[j]] > tempDist);

if (j < i) break;

swap(ids, i, j);

}

ids[left + 1] = ids[j];

ids[j] = temp;

if (right - i + 1 >= j - left) {

quicksort(ids, dists, i, right);

quicksort(ids, dists, left, j - 1);

} else {

quicksort(ids, dists, left, j - 1);

quicksort(ids, dists, i, right);

}

function swap(arr, i, j) {

const tmp = arr[i];

arr[i] = arr[j];

arr[j] = tmp;

}

function defaultGetX(p) {

return p[0];

}

function defaultGetY(p) {

return p[1];

}

return Delaunator;

}

class Voronoi {

constructor(delaunay, [xmin, ymin, xmax, ymax] = [0, 0, 960, 500]) {

if (!((xmax = +xmax) >= (xmin = +xmin)) || !((ymax = +ymax) >= (ymin = +ymin))) throw new Error("invalid bounds");

const {points, hull, triangles} = this.delaunay = delaunay;

const circumcenters = this.circumcenters = new Float64Array(triangles.length / 3 * 2);

const vectors = this.vectors = new Float64Array(points.length * 2);

this.xmax = xmax, this.xmin = xmin;

this.ymax = ymax, this.ymin = ymin;

// Compute circumcenters.

for (let i = 0, j = 0, n = triangles.length; i < n; i += 3, j += 2) {

const t1 = triangles[i] * 2;

const t2 = triangles[i + 1] * 2;

const t3 = triangles[i + 2] * 2;

const x1 = points[t1];

const y1 = points[t1 + 1];

const x2 = points[t2];

const y2 = points[t2 + 1];

const x3 = points[t3];

const y3 = points[t3 + 1];

const a2 = x1 - x2;

const a3 = x1 - x3;

const b2 = y1 - y2;

const b3 = y1 - y3;

const d1 = x1 * x1 + y1 * y1;

const d2 = d1 - x2 * x2 - y2 * y2;

const d3 = d1 - x3 * x3 - y3 * y3;

const ab = (a3 * b2 - a2 * b3) * 2;

// degenerate case (2 points)

if (!ab) {

circumcenters[j] = (x1 + x3) / 2 + 1e8 * b3;

circumcenters[j + 1] = (y1 + y3) / 2 - 1e8 * a3;

} else {

circumcenters[j] = (b2 * d3 - b3 * d2) / ab;

circumcenters[j + 1] = (a3 * d2 - a2 * d3) / ab;

}

// Compute exterior cell rays.

let h = hull[hull.length - 1];

let p0, p1 = h * 4;

let x0, x1 = points[2 * h];

let y0, y1 = points[2 * h + 1];

for (let i = 0; i < hull.length; ++i) {

h = hull[i];

p0 = p1, x0 = x1, y0 = y1;

p1 = h * 4, x1 = points[2 * h], y1 = points[2 * h + 1];

vectors[p0 + 2] = vectors[p1] = y0 - y1;

vectors[p0 + 3] = vectors[p1 + 1] = x1 - x0;

}

render(context) {

const buffer = context == null ? context = new Path : undefined;

const {delaunay: {halfedges, inedges, hull}, circumcenters, vectors} = this;

if (hull.length <= 1) return null;

for (let i = 0, n = halfedges.length; i < n; ++i) {

const j = halfedges[i];

if (j < i) continue;

const ti = Math.floor(i / 3) * 2;

const tj = Math.floor(j / 3) * 2;

const xi = circumcenters[ti];

const yi = circumcenters[ti + 1];

const xj = circumcenters[tj];

const yj = circumcenters[tj + 1];

this._renderSegment(xi, yi, xj, yj, context);

}

let h0, h1 = hull[hull.length - 1];

for (let i = 0; i < hull.length; ++i) {

h0 = h1, h1 = hull[i];

const t = Math.floor(inedges[h1] / 3) * 2;

const x = circumcenters[t];

const y = circumcenters[t + 1];

const v = h0 * 4;

const p = this._project(x, y, vectors[v + 2], vectors[v + 3]);

if (p) this._renderSegment(x, y, p[0], p[1], context);

}

return buffer && buffer.value();

}

renderBounds(context) {

const buffer = context == null ? context = new Path : undefined;

context.rect(this.xmin, this.ymin, this.xmax - this.xmin, this.ymax - this.ymin);

return buffer && buffer.value();

}

renderCell(i, context) {

const buffer = context == null ? context = new Path : undefined;

const points = this._clip(i);

if (points === null) return;

context.moveTo(points[0], points[1]);

for (let i = 2, n = points.length; i < n; i += 2) {

context.lineTo(points[i], points[i + 1]);

}

context.closePath();

return buffer && buffer.value();

}

*cellPolygons() {

const {delaunay: {points}} = this;

for (let i = 0, n = points.length / 2; i < n; ++i) {

const cell = this.cellPolygon(i);

if (cell) yield cell;

}

cellPolygon(i) {

const polygon = new Polygon;

this.renderCell(i, polygon);

return polygon.value();

}

_renderSegment(x0, y0, x1, y1, context) {

let S;

const c0 = this._regioncode(x0, y0);

const c1 = this._regioncode(x1, y1);

if (c0 === 0 && c1 === 0) {

context.moveTo(x0, y0);

context.lineTo(x1, y1);

} else if (S = this._clipSegment(x0, y0, x1, y1, c0, c1)) {

context.moveTo(S[0], S[1]);

context.lineTo(S[2], S[3]);

}

contains(i, x, y) {

if ((x = +x, x !== x) || (y = +y, y !== y)) return false;

return this.delaunay._step(i, x, y) === i;

}

_cell(i) {

const {circumcenters, delaunay: {inedges, halfedges, triangles}} = this;

const e0 = inedges[i];

if (e0 === -1) return null; // coincident point

const points = [];

let e = e0;

do {

const t = Math.floor(e / 3);

points.push(circumcenters[t * 2], circumcenters[t * 2 + 1]);

e = e % 3 === 2 ? e - 2 : e + 1;

if (triangles[e] !== i) break; // bad triangulation

e = halfedges[e];

} while (e !== e0 && e !== -1);

return points;

}

_clip(i) {

// degenerate case (1 valid point: return the box)

if (i === 0 && this.delaunay.hull.length === 1) {

return [this.xmax, this.ymin, this.xmax, this.ymax, this.xmin, this.ymax, this.xmin, this.ymin];

}

const points = this._cell(i);

if (points === null) return null;

const {vectors: V} = this;

const v = i * 4;

return V[v] || V[v + 1]

? this._clipInfinite(i, points, V[v], V[v + 1], V[v + 2], V[v + 3])

: this._clipFinite(i, points);

}

_clipFinite(i, points) {

const n = points.length;

let P = null;

let x0, y0, x1 = points[n - 2], y1 = points[n - 1];

let c0, c1 = this._regioncode(x1, y1);

let e0, e1;

for (let j = 0; j < n; j += 2) {

x0 = x1, y0 = y1, x1 = points[j], y1 = points[j + 1];

c0 = c1, c1 = this._regioncode(x1, y1);

if (c0 === 0 && c1 === 0) {

e0 = e1, e1 = 0;

if (P) P.push(x1, y1);

else P = [x1, y1];

} else {

let S, sx0, sy0, sx1, sy1;

if (c0 === 0) {

if ((S = this._clipSegment(x0, y0, x1, y1, c0, c1)) === null) continue;

[sx0, sy0, sx1, sy1] = S;

} else {

if ((S = this._clipSegment(x1, y1, x0, y0, c1, c0)) === null) continue;

[sx1, sy1, sx0, sy0] = S;

e0 = e1, e1 = this._edgecode(sx0, sy0);

if (e0 && e1) this._edge(i, e0, e1, P, P.length);

if (P) P.push(sx0, sy0);

else P = [sx0, sy0];

}

e0 = e1, e1 = this._edgecode(sx1, sy1);

if (e0 && e1) this._edge(i, e0, e1, P, P.length);

if (P) P.push(sx1, sy1);

else P = [sx1, sy1];

}

if (P) {

e0 = e1, e1 = this._edgecode(P[0], P[1]);

if (e0 && e1) this._edge(i, e0, e1, P, P.length);

} else if (this.contains(i, (this.xmin + this.xmax) / 2, (this.ymin + this.ymax) / 2)) {

return [this.xmax, this.ymin, this.xmax, this.ymax, this.xmin, this.ymax, this.xmin, this.ymin];

}

return P;

}

_clipSegment(x0, y0, x1, y1, c0, c1) {

while (true) {

if (c0 === 0 && c1 === 0) return [x0, y0, x1, y1];

if (c0 & c1) return null;

let x, y, c = c0 || c1;

if (c & 0b1000) x = x0 + (x1 - x0) * (this.ymax - y0) / (y1 - y0), y = this.ymax;

else if (c & 0b0100) x = x0 + (x1 - x0) * (this.ymin - y0) / (y1 - y0), y = this.ymin;

else if (c & 0b0010) y = y0 + (y1 - y0) * (this.xmax - x0) / (x1 - x0), x = this.xmax;

else y = y0 + (y1 - y0) * (this.xmin - x0) / (x1 - x0), x = this.xmin;

if (c0) x0 = x, y0 = y, c0 = this._regioncode(x0, y0);

else x1 = x, y1 = y, c1 = this._regioncode(x1, y1);

}

_clipInfinite(i, points, vx0, vy0, vxn, vyn) {

let P = Array.from(points), p;

if (p = this._project(P[0], P[1], vx0, vy0)) P.unshift(p[0], p[1]);

if (p = this._project(P[P.length - 2], P[P.length - 1], vxn, vyn)) P.push(p[0], p[1]);

if (P = this._clipFinite(i, P)) {

for (let j = 0, n = P.length, c0, c1 = this._edgecode(P[n - 2], P[n - 1]); j < n; j += 2) {

c0 = c1, c1 = this._edgecode(P[j], P[j + 1]);

if (c0 && c1) j = this._edge(i, c0, c1, P, j), n = P.length;

}

} else if (this.contains(i, (this.xmin + this.xmax) / 2, (this.ymin + this.ymax) / 2)) {

P = [this.xmin, this.ymin, this.xmax, this.ymin, this.xmax, this.ymax, this.xmin, this.ymax];

}

return P;

}

_edge(i, e0, e1, P, j) {

while (e0 !== e1) {

let x, y;

switch (e0) {

case 0b0101: e0 = 0b0100; continue; // top-left

case 0b0100: e0 = 0b0110, x = this.xmax, y = this.ymin; break; // top

case 0b0110: e0 = 0b0010; continue; // top-right

case 0b0010: e0 = 0b1010, x = this.xmax, y = this.ymax; break; // right

case 0b1010: e0 = 0b1000; continue; // bottom-right

case 0b1000: e0 = 0b1001, x = this.xmin, y = this.ymax; break; // bottom

case 0b1001: e0 = 0b0001; continue; // bottom-left

case 0b0001: e0 = 0b0101, x = this.xmin, y = this.ymin; break; // left

}

if ((P[j] !== x || P[j + 1] !== y) && this.contains(i, x, y)) {

P.splice(j, 0, x, y), j += 2;

}

return j;

}

_project(x0, y0, vx, vy) {

let t = Infinity, c, x, y;

if (vy < 0) { // top

if (y0 <= this.ymin) return null;

if ((c = (this.ymin - y0) / vy) < t) y = this.ymin, x = x0 + (t = c) * vx;

} else if (vy > 0) { // bottom

if (y0 >= this.ymax) return null;

if ((c = (this.ymax - y0) / vy) < t) y = this.ymax, x = x0 + (t = c) * vx;

}

if (vx > 0) { // right

if (x0 >= this.xmax) return null;

if ((c = (this.xmax - x0) / vx) < t) x = this.xmax, y = y0 + (t = c) * vy;

} else if (vx < 0) { // left

if (x0 <= this.xmin) return null;

if ((c = (this.xmin - x0) / vx) < t) x = this.xmin, y = y0 + (t = c) * vy;

}

return [x, y];

}

_edgecode(x, y) {

return (x === this.xmin ? 0b0001

: x === this.xmax ? 0b0010 : 0b0000)

| (y === this.ymin ? 0b0100

: y === this.ymax ? 0b1000 : 0b0000);

}

_regioncode(x, y) {

return (x < this.xmin ? 0b0001

: x > this.xmax ? 0b0010 : 0b0000)

| (y < this.ymin ? 0b0100

: y > this.ymax ? 0b1000 : 0b0000);

}

Delaunay = {

const tau = 2 * Math.PI;

function pointX(p) {

return p[0];

}

function pointY(p) {

return p[1];

}

function area(hull, points) {

let n = hull.length, x0, y0,

x1 = points[2 * hull[n - 1]],

y1 = points[2 * hull[n - 1] + 1],

area = 0;

for (let i = 0; i < n; i ++) {

x0 = x1, y0 = y1;

x1 = points[2 * hull[i]];

y1 = points[2 * hull[i] + 1];

area += y0 * x1 - x0 * y1;

}

return area / 2;

}

function jitter(x, y, r) {

return [x + Math.sin(x + y) * r, y + Math.cos(x - y) * r];

}

class Delaunay {

constructor(points) {

let d = new Delaunator(points),

a = area(d.hull, points);

if (a < 1e-10 && d.hull && d.hull.length > 2) {

this.collinear = Int32Array.from({length: points.length/2}, (_,i) => i)

.sort((i, j) => points[2 * i] - points[2 * j] || points[2 * i + 1] - points[2 * j + 1]); // for exact neighbors

const e = this.collinear[0], f = this.collinear[this.collinear.length - 1],

bounds = [ points[2 * e], points[2 * e + 1], points[2 * f], points[2 * f + 1] ],

r = 1e-8 * Math.sqrt((bounds[3] - bounds[1])**2 + (bounds[2] - bounds[0])**2);

for (let i = 0, n = points.length / 2; i < n; ++i) {

const p = jitter(points[2 * i], points[2 * i + 1], r);

points[2 * i] = p[0];

points[2 * i + 1] = p[1];

}

d = new Delaunator(points);

}

this._delaunator = d;

this.inedges = new Int32Array(points.length / 2);

this._hullIndex = new Int32Array(points.length / 2);

this.points = this._delaunator.coords;

this._init();

}

update() {

this._delaunator.update();

this._init();

}

_init() {

const halfedges = this.halfedges = this._delaunator.halfedges;

const hull = this.hull = this._delaunator.hull;

const triangles = this.triangles = this._delaunator.triangles;

const inedges = this.inedges.fill(-1);

const hullIndex = this._hullIndex.fill(-1);

// Compute an index from each point to an (arbitrary) incoming halfedge

// Used to give the first neighbor of each point; for this reason,

// on the hull we give priority to exterior halfedges

for (let e = 0, n = halfedges.length; e < n; ++e) {

const p = triangles[e % 3 === 2 ? e - 2 : e + 1];

if (halfedges[e] === -1 || inedges[p] === -1) inedges[p] = e;

}

for (let i = 0, n = hull.length; i < n; ++i) {

hullIndex[hull[i]] = i;

}

// degenerate case: 1 or 2 (distinct) points

if (hull.length <= 2 && hull.length > 0) {

this.triangles = new Int32Array(3).fill(-1);

this.halfedges = new Int32Array(3).fill(-1);

this.triangles[0] = hull[0];

this.triangles[1] = hull[1];

this.triangles[2] = hull[1];

inedges[hull[0]] = 1;

if (hull.length === 2) inedges[hull[1]] = 0;

}

voronoi(bounds) {

return new Voronoi(this, bounds);

}

*neighbors(i) {

const {inedges, hull, _hullIndex, halfedges, triangles} = this;

// degenerate case with several collinear points

if (this.collinear) {

const l = this.collinear.indexOf(i);

if (l > 0) yield this.collinear[l - 1];

if (l < this.collinear.length - 1) yield this.collinear[l + 1];

return;

}

const e0 = inedges[i];

if (e0 === -1) return; // coincident point

let e = e0, p0 = -1;

do {

yield p0 = triangles[e];

e = e % 3 === 2 ? e - 2 : e + 1;

if (triangles[e] !== i) return; // bad triangulation

e = halfedges[e];

if (e === -1) {

const p = hull[(_hullIndex[i] + 1) % hull.length];

if (p !== p0) yield p;

return;

}

} while (e !== e0);

}

find(x, y, i = 0) {

if ((x = +x, x !== x) || (y = +y, y !== y)) return -1;

const i0 = i;

let c;

while ((c = this._step(i, x, y)) >= 0 && c !== i && c !== i0) i = c;

return c;

}

_step(i, x, y) {

const {inedges, points} = this;

if (inedges[i] === -1 || !points.length) return (i + 1) % (points.length >> 1);

let c = i;

let dc = (x - points[i * 2]) ** 2 + (y - points[i * 2 + 1]) ** 2;

for (const t of this.neighbors(i)) {

const dt = (x - points[t * 2]) ** 2 + (y - points[t * 2 + 1]) ** 2;

if (dt < dc) dc = dt, c = t;

}

return c;

}

render(context) {

const buffer = context == null ? context = new Path : undefined;

const {points, halfedges, triangles} = this;

for (let i = 0, n = halfedges.length; i < n; ++i) {

const j = halfedges[i];

if (j < i) continue;

const ti = triangles[i] * 2;

const tj = triangles[j] * 2;

context.moveTo(points[ti], points[ti + 1]);

context.lineTo(points[tj], points[tj + 1]);

}

this.renderHull(context);

return buffer && buffer.value();

}

renderPoints(context, r = 2) {

const buffer = context == null ? context = new Path : undefined;

const {points} = this;

for (let i = 0, n = points.length; i < n; i += 2) {

const x = points[i], y = points[i + 1];

context.moveTo(x + r, y);

context.arc(x, y, r, 0, tau);

}

return buffer && buffer.value();

}

renderHull(context) {

const buffer = context == null ? context = new Path : undefined;

const {hull, points} = this;

const h = hull[0] * 2, n = hull.length;

context.moveTo(points[h], points[h + 1]);

for (let i = 1; i < n; ++i) {

const h = 2 * hull[i];

context.lineTo(points[h], points[h + 1]);

}

context.closePath();

return buffer && buffer.value();

}

hullPolygon() {

const polygon = new Polygon;

this.renderHull(polygon);

return polygon.value();

}

renderTriangle(i, context) {

const buffer = context == null ? context = new Path : undefined;

const {points, triangles} = this;

const t0 = triangles[i *= 3] * 2;

const t1 = triangles[i + 1] * 2;

const t2 = triangles[i + 2] * 2;

context.moveTo(points[t0], points[t0 + 1]);

context.lineTo(points[t1], points[t1 + 1]);

context.lineTo(points[t2], points[t2 + 1]);

context.closePath();

return buffer && buffer.value();

}

*trianglePolygons() {

const {triangles} = this;

for (let i = 0, n = triangles.length / 3; i < n; ++i) {

yield this.trianglePolygon(i);

}

trianglePolygon(i) {

const polygon = new Polygon;

this.renderTriangle(i, polygon);

return polygon.value();

}

Delaunay.from = function(points, fx = pointX, fy = pointY, that) {

return new Delaunay("length" in points

? flatArray(points, fx, fy, that)

: Float64Array.from(flatIterable(points, fx, fy, that)));

};

function flatArray(points, fx, fy, that) {

const n = points.length;

const array = new Float64Array(n * 2);

for (let i = 0; i < n; ++i) {

const p = points[i];

array[i * 2] = fx.call(that, p, i, points);

array[i * 2 + 1] = fy.call(that, p, i, points);

}

return array;

}

function* flatIterable(points, fx, fy, that) {

let i = 0;

for (const p of points) {

yield fx.call(that, p, i, points);

yield fy.call(that, p, i, points);

++i;

}

return Delaunay;

}

class Polygon {

constructor() {

this._ = [];

}

moveTo(x, y) {

this._.push([x, y]);

}

closePath() {

this._.push(this._[0].slice());

}

lineTo(x, y) {

this._.push([x, y]);

}

value() {

return this._.length ? this._ : null;

}

Path = {

const epsilon = 1e-6;

class Path {

constructor() {

this._x0 = this._y0 = // start of current subpath

this._x1 = this._y1 = null; // end of current subpath

this._ = "";

}

moveTo(x, y) {

this._ += `M${this._x0 = this._x1 = +x},${this._y0 = this._y1 = +y}`;

}

closePath() {

if (this._x1 !== null) {

this._x1 = this._x0, this._y1 = this._y0;

this._ += "Z";

}

lineTo(x, y) {

this._ += `L${this._x1 = +x},${this._y1 = +y}`;

}

arc(x, y, r) {

x = +x, y = +y, r = +r;

const x0 = x + r;

const y0 = y;

if (r < 0) throw new Error("negative radius");

if (this._x1 === null) this._ += `M${x0},${y0}`;

else if (Math.abs(this._x1 - x0) > epsilon || Math.abs(this._y1 - y0) > epsilon) this._ += "L" + x0 + "," + y0;

if (!r) return;

this._ += `A${r},${r},0,1,1,${x - r},${y}A${r},${r},0,1,1,${this._x1 = x0},${this._y1 = y0}`;

}

rect(x, y, w, h) {

this._ += `M${this._x0 = this._x1 = +x},${this._y0 = this._y1 = +y}h${+w}v${+h}h${-w}Z`;

}

value() {

return this._ || null;

}

return Path;

}

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