// 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 , 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 }); })));