File: /var/dev/math/ui/node_modules/d3-delaunay/dist/d3-delaunay.js
// https://github.com/d3/d3-delaunay v6.0.4 Copyright 2018-2021 Observable, Inc., 2021 Mapbox
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
typeof define === 'function' && define.amd ? define(['exports'], factory) :
(global = typeof globalThis !== 'undefined' ? globalThis : global || self, factory(global.d3 = global.d3 || {}));
}(this, (function (exports) { 'use strict';
const epsilon$1 = 1.1102230246251565e-16;
const splitter = 134217729;
const resulterrbound = (3 + 8 * epsilon$1) * epsilon$1;
// fast_expansion_sum_zeroelim routine from oritinal code
function sum(elen, e, flen, f, h) {
let Q, Qnew, hh, bvirt;
let enow = e[0];
let fnow = f[0];
let eindex = 0;
let findex = 0;
if ((fnow > enow) === (fnow > -enow)) {
Q = enow;
enow = e[++eindex];
} else {
Q = fnow;
fnow = f[++findex];
}
let hindex = 0;
if (eindex < elen && findex < flen) {
if ((fnow > enow) === (fnow > -enow)) {
Qnew = enow + Q;
hh = Q - (Qnew - enow);
enow = e[++eindex];
} else {
Qnew = fnow + Q;
hh = Q - (Qnew - fnow);
fnow = f[++findex];
}
Q = Qnew;
if (hh !== 0) {
h[hindex++] = hh;
}
while (eindex < elen && findex < flen) {
if ((fnow > enow) === (fnow > -enow)) {
Qnew = Q + enow;
bvirt = Qnew - Q;
hh = Q - (Qnew - bvirt) + (enow - bvirt);
enow = e[++eindex];
} else {
Qnew = Q + fnow;
bvirt = Qnew - Q;
hh = Q - (Qnew - bvirt) + (fnow - bvirt);
fnow = f[++findex];
}
Q = Qnew;
if (hh !== 0) {
h[hindex++] = hh;
}
}
}
while (eindex < elen) {
Qnew = Q + enow;
bvirt = Qnew - Q;
hh = Q - (Qnew - bvirt) + (enow - bvirt);
enow = e[++eindex];
Q = Qnew;
if (hh !== 0) {
h[hindex++] = hh;
}
}
while (findex < flen) {
Qnew = Q + fnow;
bvirt = Qnew - Q;
hh = Q - (Qnew - bvirt) + (fnow - bvirt);
fnow = f[++findex];
Q = Qnew;
if (hh !== 0) {
h[hindex++] = hh;
}
}
if (Q !== 0 || hindex === 0) {
h[hindex++] = Q;
}
return hindex;
}
function estimate(elen, e) {
let Q = e[0];
for (let i = 1; i < elen; i++) Q += e[i];
return Q;
}
function vec(n) {
return new Float64Array(n);
}
const ccwerrboundA = (3 + 16 * epsilon$1) * epsilon$1;
const ccwerrboundB = (2 + 12 * epsilon$1) * epsilon$1;
const ccwerrboundC = (9 + 64 * epsilon$1) * epsilon$1 * epsilon$1;
const B = vec(4);
const C1 = vec(8);
const C2 = vec(12);
const D = vec(16);
const u = vec(4);
function orient2dadapt(ax, ay, bx, by, cx, cy, detsum) {
let acxtail, acytail, bcxtail, bcytail;
let bvirt, c, ahi, alo, bhi, blo, _i, _j, _0, s1, s0, t1, t0, u3;
const acx = ax - cx;
const bcx = bx - cx;
const acy = ay - cy;
const bcy = by - cy;
s1 = acx * bcy;
c = splitter * acx;
ahi = c - (c - acx);
alo = acx - ahi;
c = splitter * bcy;
bhi = c - (c - bcy);
blo = bcy - bhi;
s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
t1 = acy * bcx;
c = splitter * acy;
ahi = c - (c - acy);
alo = acy - ahi;
c = splitter * bcx;
bhi = c - (c - bcx);
blo = bcx - bhi;
t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
_i = s0 - t0;
bvirt = s0 - _i;
B[0] = s0 - (_i + bvirt) + (bvirt - t0);
_j = s1 + _i;
bvirt = _j - s1;
_0 = s1 - (_j - bvirt) + (_i - bvirt);
_i = _0 - t1;
bvirt = _0 - _i;
B[1] = _0 - (_i + bvirt) + (bvirt - t1);
u3 = _j + _i;
bvirt = u3 - _j;
B[2] = _j - (u3 - bvirt) + (_i - bvirt);
B[3] = u3;
let det = estimate(4, B);
let errbound = ccwerrboundB * detsum;
if (det >= errbound || -det >= errbound) {
return det;
}
bvirt = ax - acx;
acxtail = ax - (acx + bvirt) + (bvirt - cx);
bvirt = bx - bcx;
bcxtail = bx - (bcx + bvirt) + (bvirt - cx);
bvirt = ay - acy;
acytail = ay - (acy + bvirt) + (bvirt - cy);
bvirt = by - bcy;
bcytail = by - (bcy + bvirt) + (bvirt - cy);
if (acxtail === 0 && acytail === 0 && bcxtail === 0 && bcytail === 0) {
return det;
}
errbound = ccwerrboundC * detsum + resulterrbound * Math.abs(det);
det += (acx * bcytail + bcy * acxtail) - (acy * bcxtail + bcx * acytail);
if (det >= errbound || -det >= errbound) return det;
s1 = acxtail * bcy;
c = splitter * acxtail;
ahi = c - (c - acxtail);
alo = acxtail - ahi;
c = splitter * bcy;
bhi = c - (c - bcy);
blo = bcy - bhi;
s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
t1 = acytail * bcx;
c = splitter * acytail;
ahi = c - (c - acytail);
alo = acytail - ahi;
c = splitter * bcx;
bhi = c - (c - bcx);
blo = bcx - bhi;
t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
_i = s0 - t0;
bvirt = s0 - _i;
u[0] = s0 - (_i + bvirt) + (bvirt - t0);
_j = s1 + _i;
bvirt = _j - s1;
_0 = s1 - (_j - bvirt) + (_i - bvirt);
_i = _0 - t1;
bvirt = _0 - _i;
u[1] = _0 - (_i + bvirt) + (bvirt - t1);
u3 = _j + _i;
bvirt = u3 - _j;
u[2] = _j - (u3 - bvirt) + (_i - bvirt);
u[3] = u3;
const C1len = sum(4, B, 4, u, C1);
s1 = acx * bcytail;
c = splitter * acx;
ahi = c - (c - acx);
alo = acx - ahi;
c = splitter * bcytail;
bhi = c - (c - bcytail);
blo = bcytail - bhi;
s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
t1 = acy * bcxtail;
c = splitter * acy;
ahi = c - (c - acy);
alo = acy - ahi;
c = splitter * bcxtail;
bhi = c - (c - bcxtail);
blo = bcxtail - bhi;
t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
_i = s0 - t0;
bvirt = s0 - _i;
u[0] = s0 - (_i + bvirt) + (bvirt - t0);
_j = s1 + _i;
bvirt = _j - s1;
_0 = s1 - (_j - bvirt) + (_i - bvirt);
_i = _0 - t1;
bvirt = _0 - _i;
u[1] = _0 - (_i + bvirt) + (bvirt - t1);
u3 = _j + _i;
bvirt = u3 - _j;
u[2] = _j - (u3 - bvirt) + (_i - bvirt);
u[3] = u3;
const C2len = sum(C1len, C1, 4, u, C2);
s1 = acxtail * bcytail;
c = splitter * acxtail;
ahi = c - (c - acxtail);
alo = acxtail - ahi;
c = splitter * bcytail;
bhi = c - (c - bcytail);
blo = bcytail - bhi;
s0 = alo * blo - (s1 - ahi * bhi - alo * bhi - ahi * blo);
t1 = acytail * bcxtail;
c = splitter * acytail;
ahi = c - (c - acytail);
alo = acytail - ahi;
c = splitter * bcxtail;
bhi = c - (c - bcxtail);
blo = bcxtail - bhi;
t0 = alo * blo - (t1 - ahi * bhi - alo * bhi - ahi * blo);
_i = s0 - t0;
bvirt = s0 - _i;
u[0] = s0 - (_i + bvirt) + (bvirt - t0);
_j = s1 + _i;
bvirt = _j - s1;
_0 = s1 - (_j - bvirt) + (_i - bvirt);
_i = _0 - t1;
bvirt = _0 - _i;
u[1] = _0 - (_i + bvirt) + (bvirt - t1);
u3 = _j + _i;
bvirt = u3 - _j;
u[2] = _j - (u3 - bvirt) + (_i - bvirt);
u[3] = u3;
const Dlen = sum(C2len, C2, 4, u, D);
return D[Dlen - 1];
}
function orient2d(ax, ay, bx, by, cx, cy) {
const detleft = (ay - cy) * (bx - cx);
const detright = (ax - cx) * (by - cy);
const det = detleft - detright;
if (detleft === 0 || detright === 0 || (detleft > 0) !== (detright > 0)) return det;
const detsum = Math.abs(detleft + detright);
if (Math.abs(det) >= ccwerrboundA * detsum) return det;
return -orient2dadapt(ax, ay, bx, by, cx, cy, detsum);
}
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 (orient2d(i0x, i0y, i1x, i1y, i2x, i2y) < 0) {
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], orient2d(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1]) >= 0) {
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], orient2d(x, y, coords[2 * n], coords[2 * n + 1], coords[2 * q], coords[2 * q + 1]) < 0) {
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], orient2d(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1]) < 0) {
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 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];
}
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;
}
}
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;
}
}
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");
this.delaunay = delaunay;
this._circumcenters = new Float64Array(delaunay.points.length * 2);
this.vectors = new Float64Array(delaunay.points.length * 2);
this.xmax = xmax, this.xmin = xmin;
this.ymax = ymax, this.ymin = ymin;
this._init();
}
update() {
this.delaunay.update();
this._init();
return this;
}
_init() {
const {delaunay: {points, hull, triangles}, vectors} = this;
let bx, by; // lazily computed barycenter of the hull
// Compute circumcenters.
const circumcenters = this.circumcenters = this._circumcenters.subarray(0, triangles.length / 3 * 2);
for (let i = 0, j = 0, n = triangles.length, x, y; 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 dx = x2 - x1;
const dy = y2 - y1;
const ex = x3 - x1;
const ey = y3 - y1;
const ab = (dx * ey - dy * ex) * 2;
if (Math.abs(ab) < 1e-9) {
// For a degenerate triangle, the circumcenter is at the infinity, in a
// direction orthogonal to the halfedge and away from the “center” of
// the diagram <bx, by>, defined as the hull’s barycenter.
if (bx === undefined) {
bx = by = 0;
for (const i of hull) bx += points[i * 2], by += points[i * 2 + 1];
bx /= hull.length, by /= hull.length;
}
const a = 1e9 * Math.sign((bx - x1) * ey - (by - y1) * ex);
x = (x1 + x3) / 2 - a * ey;
y = (y1 + y3) / 2 + a * ex;
} else {
const d = 1 / ab;
const bl = dx * dx + dy * dy;
const cl = ex * ex + ey * ey;
x = x1 + (ey * bl - dy * cl) * d;
y = y1 + (dx * cl - ex * bl) * d;
}
circumcenters[j] = x;
circumcenters[j + 1] = y;
}
// 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];
vectors.fill(0);
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 || !points.length) return;
context.moveTo(points[0], points[1]);
let n = points.length;
while (points[0] === points[n-2] && points[1] === points[n-1] && n > 1) n -= 2;
for (let i = 2; i < n; i += 2) {
if (points[i] !== points[i-2] || points[i+1] !== points[i-1])
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) cell.index = i, 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;
}
*neighbors(i) {
const ci = this._clip(i);
if (ci) for (const j of this.delaunay.neighbors(i)) {
const cj = this._clip(j);
// find the common edge
if (cj) loop: for (let ai = 0, li = ci.length; ai < li; ai += 2) {
for (let aj = 0, lj = cj.length; aj < lj; aj += 2) {
if (ci[ai] === cj[aj]
&& ci[ai + 1] === cj[aj + 1]
&& ci[(ai + 2) % li] === cj[(aj + lj - 2) % lj]
&& ci[(ai + 3) % li] === cj[(aj + lj - 1) % lj]) {
yield j;
break loop;
}
}
}
}
}
_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 this._simplify(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 = 0;
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) {
// for more robustness, always consider the segment in the same order
const flip = c0 < c1;
if (flip) [x0, y0, x1, y1, c0, c1] = [x1, y1, x0, y0, c1, c0];
while (true) {
if (c0 === 0 && c1 === 0) return flip ? [x1, y1, x0, y0] : [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
}
// Note: this implicitly checks for out of bounds: if P[j] or P[j+1] are
// undefined, the conditional statement will be executed.
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);
}
_simplify(P) {
if (P && P.length > 4) {
for (let i = 0; i < P.length; i+= 2) {
const j = (i + 2) % P.length, k = (i + 4) % P.length;
if (P[i] === P[j] && P[j] === P[k] || P[i + 1] === P[j + 1] && P[j + 1] === P[k + 1]) {
P.splice(j, 2), i -= 2;
}
}
if (!P.length) P = null;
}
return P;
}
}
const tau = 2 * Math.PI, pow = Math.pow;
function pointX(p) {
return p[0];
}
function pointY(p) {
return p[1];
}
// A triangulation is collinear if all its triangles have a non-null area
function collinear(d) {
const {triangles, coords} = d;
for (let i = 0; i < triangles.length; i += 3) {
const a = 2 * triangles[i],
b = 2 * triangles[i + 1],
c = 2 * triangles[i + 2],
cross = (coords[c] - coords[a]) * (coords[b + 1] - coords[a + 1])
- (coords[b] - coords[a]) * (coords[c + 1] - coords[a + 1]);
if (cross > 1e-10) return false;
}
return true;
}
function jitter(x, y, r) {
return [x + Math.sin(x + y) * r, y + Math.cos(x - y) * r];
}
class Delaunay {
static from(points, fx = pointX, fy = pointY, that) {
return new Delaunay("length" in points
? flatArray(points, fx, fy, that)
: Float64Array.from(flatIterable(points, fx, fy, that)));
}
constructor(points) {
this._delaunator = new Delaunator(points);
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();
return this;
}
_init() {
const d = this._delaunator, points = this.points;
// check for collinear
if (d.hull && d.hull.length > 2 && collinear(d)) {
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.hypot(bounds[3] - bounds[1], bounds[2] - bounds[0]);
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];
}
this._delaunator = new Delaunator(points);
} else {
delete this.collinear;
}
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];
inedges[hull[0]] = 1;
if (hull.length === 2) {
inedges[hull[1]] = 0;
this.triangles[1] = hull[1];
this.triangles[2] = hull[1];
}
}
}
voronoi(bounds) {
return new Voronoi(this, bounds);
}
*neighbors(i) {
const {inedges, hull, _hullIndex, halfedges, triangles, collinear} = this;
// degenerate case with several collinear points
if (collinear) {
const l = collinear.indexOf(i);
if (l > 0) yield collinear[l - 1];
if (l < collinear.length - 1) yield 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, hull, _hullIndex, halfedges, triangles, points} = this;
if (inedges[i] === -1 || !points.length) return (i + 1) % (points.length >> 1);
let c = i;
let dc = pow(x - points[i * 2], 2) + pow(y - points[i * 2 + 1], 2);
const e0 = inedges[i];
let e = e0;
do {
let t = triangles[e];
const dt = pow(x - points[t * 2], 2) + pow(y - points[t * 2 + 1], 2);
if (dt < dc) dc = dt, c = t;
e = e % 3 === 2 ? e - 2 : e + 1;
if (triangles[e] !== i) break; // bad triangulation
e = halfedges[e];
if (e === -1) {
e = hull[(_hullIndex[i] + 1) % hull.length];
if (e !== t) {
if (pow(x - points[e * 2], 2) + pow(y - points[e * 2 + 1], 2) < dc) return e;
}
break;
}
} while (e !== e0);
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) {
if (r === undefined && (!context || typeof context.moveTo !== "function")) r = context, context = null;
r = r == undefined ? 2 : +r;
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();
}
}
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;
}
}
exports.Delaunay = Delaunay;
exports.Voronoi = Voronoi;
Object.defineProperty(exports, '__esModule', { value: true });
})));