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three-conic-polygon-geometry

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// Version 2.1.3 three-conic-polygon-geometry - https://github.com/vasturiano/three-conic-polygon-geometry (function (global, factory) { typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory(require('three')) : typeof define === 'function' && define.amd ? define(['three'], factory) : (global = typeof globalThis !== 'undefined' ? globalThis : global || self, global.ConicPolygonGeometry = factory(global.THREE)); })(this, (function (three) { 'use strict'; function _arrayLikeToArray(r, a) { (null == a || a > r.length) && (a = r.length); for (var e = 0, n = Array(a); e < a; e++) n[e] = r[e]; return n; } function _arrayWithHoles(r) { if (Array.isArray(r)) return r; } function _arrayWithoutHoles(r) { if (Array.isArray(r)) return _arrayLikeToArray(r); } function _assertThisInitialized(e) { if (void 0 === e) throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); return e; } function _callSuper(t, o, e) { return o = _getPrototypeOf(o), _possibleConstructorReturn(t, _isNativeReflectConstruct() ? Reflect.construct(o, [], _getPrototypeOf(t).constructor) : o.apply(t, e)); } function _classCallCheck(a, n) { if (!(a instanceof n)) throw new TypeError("Cannot call a class as a function"); } function _createClass(e, r, t) { return Object.defineProperty(e, "prototype", { writable: false }), e; } function _getPrototypeOf(t) { return _getPrototypeOf = Object.setPrototypeOf ? Object.getPrototypeOf.bind() : function (t) { return t.__proto__ || Object.getPrototypeOf(t); }, _getPrototypeOf(t); } function _inherits(t, e) { if ("function" != typeof e && null !== e) throw new TypeError("Super expression must either be null or a function"); t.prototype = Object.create(e && e.prototype, { constructor: { value: t, writable: true, configurable: true } }), Object.defineProperty(t, "prototype", { writable: false }), e && _setPrototypeOf(t, e); } function _isNativeReflectConstruct() { try { var t = !Boolean.prototype.valueOf.call(Reflect.construct(Boolean, [], function () {})); } catch (t) {} return (_isNativeReflectConstruct = function () { return !!t; })(); } function _iterableToArray(r) { if ("undefined" != typeof Symbol && null != r[Symbol.iterator] || null != r["@@iterator"]) return Array.from(r); } function _iterableToArrayLimit(r, l) { var t = null == r ? null : "undefined" != typeof Symbol && r[Symbol.iterator] || r["@@iterator"]; if (null != t) { var e, n, i, u, a = [], f = true, o = false; try { if (i = (t = t.call(r)).next, 0 === l) ; else for (; !(f = (e = i.call(t)).done) && (a.push(e.value), a.length !== l); f = !0); } catch (r) { o = true, n = r; } finally { try { if (!f && null != t.return && (u = t.return(), Object(u) !== u)) return; } finally { if (o) throw n; } } return a; } } function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); } function _nonIterableSpread() { throw new TypeError("Invalid attempt to spread non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); } function _possibleConstructorReturn(t, e) { if (e && ("object" == typeof e || "function" == typeof e)) return e; if (void 0 !== e) throw new TypeError("Derived constructors may only return object or undefined"); return _assertThisInitialized(t); } function _setPrototypeOf(t, e) { return _setPrototypeOf = Object.setPrototypeOf ? Object.setPrototypeOf.bind() : function (t, e) { return t.__proto__ = e, t; }, _setPrototypeOf(t, e); } function _slicedToArray(r, e) { return _arrayWithHoles(r) || _iterableToArrayLimit(r, e) || _unsupportedIterableToArray(r, e) || _nonIterableRest(); } function _toConsumableArray(r) { return _arrayWithoutHoles(r) || _iterableToArray(r) || _unsupportedIterableToArray(r) || _nonIterableSpread(); } function _unsupportedIterableToArray(r, a) { if (r) { if ("string" == typeof r) return _arrayLikeToArray(r, a); var t = {}.toString.call(r).slice(8, -1); return "Object" === t && r.constructor && (t = r.constructor.name), "Map" === t || "Set" === t ? Array.from(r) : "Arguments" === t || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(t) ? _arrayLikeToArray(r, a) : void 0; } } function ascending(a, b) { return a == null || b == null ? NaN : a < b ? -1 : a > b ? 1 : a >= b ? 0 : NaN; } function descending(a, b) { return a == null || b == null ? NaN : b < a ? -1 : b > a ? 1 : b >= a ? 0 : NaN; } function bisector(f) { let compare1, compare2, delta; // If an accessor is specified, promote it to a comparator. In this case we // can test whether the search value is (self-) comparable. We can’t do this // for a comparator (except for specific, known comparators) because we can’t // tell if the comparator is symmetric, and an asymmetric comparator can’t be // used to test whether a single value is comparable. if (f.length !== 2) { compare1 = ascending; compare2 = (d, x) => ascending(f(d), x); delta = (d, x) => f(d) - x; } else { compare1 = f === ascending || f === descending ? f : zero$1; compare2 = f; delta = f; } function left(a, x, lo = 0, hi = a.length) { if (lo < hi) { if (compare1(x, x) !== 0) return hi; do { const mid = (lo + hi) >>> 1; if (compare2(a[mid], x) < 0) lo = mid + 1; else hi = mid; } while (lo < hi); } return lo; } function right(a, x, lo = 0, hi = a.length) { if (lo < hi) { if (compare1(x, x) !== 0) return hi; do { const mid = (lo + hi) >>> 1; if (compare2(a[mid], x) <= 0) lo = mid + 1; else hi = mid; } while (lo < hi); } return lo; } function center(a, x, lo = 0, hi = a.length) { const i = left(a, x, lo, hi - 1); return i > lo && delta(a[i - 1], x) > -delta(a[i], x) ? i - 1 : i; } return {left, center, right}; } function zero$1() { return 0; } function number$1(x) { return x === null ? NaN : +x; } const ascendingBisect = bisector(ascending); const bisectRight = ascendingBisect.right; bisector(number$1).center; function extent(values, valueof) { let min; let max; if (valueof === undefined) { for (const value of values) { if (value != null) { if (min === undefined) { if (value >= value) min = max = value; } else { if (min > value) min = value; if (max < value) max = value; } } } } else { let index = -1; for (let value of values) { if ((value = valueof(value, ++index, values)) != null) { if (min === undefined) { if (value >= value) min = max = value; } else { if (min > value) min = value; if (max < value) max = value; } } } } return [min, max]; } // https://github.com/python/cpython/blob/a74eea238f5baba15797e2e8b570d153bc8690a7/Modules/mathmodule.c#L1423 class Adder { constructor() { this._partials = new Float64Array(32); this._n = 0; } add(x) { const p = this._partials; let i = 0; for (let j = 0; j < this._n && j < 32; j++) { const y = p[j], hi = x + y, lo = Math.abs(x) < Math.abs(y) ? x - (hi - y) : y - (hi - x); if (lo) p[i++] = lo; x = hi; } p[i] = x; this._n = i + 1; return this; } valueOf() { const p = this._partials; let n = this._n, x, y, lo, hi = 0; if (n > 0) { hi = p[--n]; while (n > 0) { x = hi; y = p[--n]; hi = x + y; lo = y - (hi - x); if (lo) break; } if (n > 0 && ((lo < 0 && p[n - 1] < 0) || (lo > 0 && p[n - 1] > 0))) { y = lo * 2; x = hi + y; if (y == x - hi) hi = x; } } return hi; } } const e10 = Math.sqrt(50), e5 = Math.sqrt(10), e2 = Math.sqrt(2); function tickSpec(start, stop, count) { const step = (stop - start) / Math.max(0, count), power = Math.floor(Math.log10(step)), error = step / Math.pow(10, power), factor = error >= e10 ? 10 : error >= e5 ? 5 : error >= e2 ? 2 : 1; let i1, i2, inc; if (power < 0) { inc = Math.pow(10, -power) / factor; i1 = Math.round(start * inc); i2 = Math.round(stop * inc); if (i1 / inc < start) ++i1; if (i2 / inc > stop) --i2; inc = -inc; } else { inc = Math.pow(10, power) * factor; i1 = Math.round(start / inc); i2 = Math.round(stop / inc); if (i1 * inc < start) ++i1; if (i2 * inc > stop) --i2; } if (i2 < i1 && 0.5 <= count && count < 2) return tickSpec(start, stop, count * 2); return [i1, i2, inc]; } function ticks(start, stop, count) { stop = +stop, start = +start, count = +count; if (!(count > 0)) return []; if (start === stop) return [start]; const reverse = stop < start, [i1, i2, inc] = reverse ? tickSpec(stop, start, count) : tickSpec(start, stop, count); if (!(i2 >= i1)) return []; const n = i2 - i1 + 1, ticks = new Array(n); if (reverse) { if (inc < 0) for (let i = 0; i < n; ++i) ticks[i] = (i2 - i) / -inc; else for (let i = 0; i < n; ++i) ticks[i] = (i2 - i) * inc; } else { if (inc < 0) for (let i = 0; i < n; ++i) ticks[i] = (i1 + i) / -inc; else for (let i = 0; i < n; ++i) ticks[i] = (i1 + i) * inc; } return ticks; } function tickIncrement(start, stop, count) { stop = +stop, start = +start, count = +count; return tickSpec(start, stop, count)[2]; } function tickStep(start, stop, count) { stop = +stop, start = +start, count = +count; const reverse = stop < start, inc = reverse ? tickIncrement(stop, start, count) : tickIncrement(start, stop, count); return (reverse ? -1 : 1) * (inc < 0 ? 1 / -inc : inc); } function mean(values, valueof) { let count = 0; let sum = 0; if (valueof === undefined) { for (let value of values) { if (value != null && (value = +value) >= value) { ++count, sum += value; } } } else { let index = -1; for (let value of values) { if ((value = valueof(value, ++index, values)) != null && (value = +value) >= value) { ++count, sum += value; } } } if (count) return sum / count; } function* flatten$1(arrays) { for (const array of arrays) { yield* array; } } function merge(arrays) { return Array.from(flatten$1(arrays)); } function earcut(data, holeIndices, dim = 2) { const hasHoles = holeIndices && holeIndices.length; const outerLen = hasHoles ? holeIndices[0] * dim : data.length; let outerNode = linkedList(data, 0, outerLen, dim, true); const triangles = []; if (!outerNode || outerNode.next === outerNode.prev) return triangles; let minX, minY, invSize; if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim); // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox if (data.length > 80 * dim) { minX = data[0]; minY = data[1]; let maxX = minX; let maxY = minY; for (let i = dim; i < outerLen; i += dim) { const x = data[i]; const y = data[i + 1]; if (x < minX) minX = x; if (y < minY) minY = y; if (x > maxX) maxX = x; if (y > maxY) maxY = y; } // minX, minY and invSize are later used to transform coords into integers for z-order calculation invSize = Math.max(maxX - minX, maxY - minY); invSize = invSize !== 0 ? 32767 / invSize : 0; } earcutLinked(outerNode, triangles, dim, minX, minY, invSize, 0); return triangles; } // create a circular doubly linked list from polygon points in the specified winding order function linkedList(data, start, end, dim, clockwise) { let last; if (clockwise === (signedArea(data, start, end, dim) > 0)) { for (let i = start; i < end; i += dim) last = insertNode(i / dim | 0, data[i], data[i + 1], last); } else { for (let i = end - dim; i >= start; i -= dim) last = insertNode(i / dim | 0, data[i], data[i + 1], last); } if (last && equals(last, last.next)) { removeNode(last); last = last.next; } return last; } // eliminate colinear or duplicate points function filterPoints(start, end) { if (!start) return start; if (!end) end = start; let p = start, again; do { again = false; if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) { removeNode(p); p = end = p.prev; if (p === p.next) break; again = true; } else { p = p.next; } } while (again || p !== end); return end; } // main ear slicing loop which triangulates a polygon (given as a linked list) function earcutLinked(ear, triangles, dim, minX, minY, invSize, pass) { if (!ear) return; // interlink polygon nodes in z-order if (!pass && invSize) indexCurve(ear, minX, minY, invSize); let stop = ear; // iterate through ears, slicing them one by one while (ear.prev !== ear.next) { const prev = ear.prev; const next = ear.next; if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) { triangles.push(prev.i, ear.i, next.i); // cut off the triangle removeNode(ear); // skipping the next vertex leads to less sliver triangles ear = next.next; stop = next.next; continue; } ear = next; // if we looped through the whole remaining polygon and can't find any more ears if (ear === stop) { // try filtering points and slicing again if (!pass) { earcutLinked(filterPoints(ear), triangles, dim, minX, minY, invSize, 1); // if this didn't work, try curing all small self-intersections locally } else if (pass === 1) { ear = cureLocalIntersections(filterPoints(ear), triangles); earcutLinked(ear, triangles, dim, minX, minY, invSize, 2); // as a last resort, try splitting the remaining polygon into two } else if (pass === 2) { splitEarcut(ear, triangles, dim, minX, minY, invSize); } break; } } } // check whether a polygon node forms a valid ear with adjacent nodes function isEar(ear) { const a = ear.prev, b = ear, c = ear.next; if (area(a, b, c) >= 0) return false; // reflex, can't be an ear // now make sure we don't have other points inside the potential ear const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y; // triangle bbox const x0 = Math.min(ax, bx, cx), y0 = Math.min(ay, by, cy), x1 = Math.max(ax, bx, cx), y1 = Math.max(ay, by, cy); let p = c.next; while (p !== a) { if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false; p = p.next; } return true; } function isEarHashed(ear, minX, minY, invSize) { const a = ear.prev, b = ear, c = ear.next; if (area(a, b, c) >= 0) return false; // reflex, can't be an ear const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y; // triangle bbox const x0 = Math.min(ax, bx, cx), y0 = Math.min(ay, by, cy), x1 = Math.max(ax, bx, cx), y1 = Math.max(ay, by, cy); // z-order range for the current triangle bbox; const minZ = zOrder(x0, y0, minX, minY, invSize), maxZ = zOrder(x1, y1, minX, minY, invSize); let p = ear.prevZ, n = ear.nextZ; // look for points inside the triangle in both directions while (p && p.z >= minZ && n && n.z <= maxZ) { if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c && pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false; p = p.prevZ; if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c && pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false; n = n.nextZ; } // look for remaining points in decreasing z-order while (p && p.z >= minZ) { if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c && pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false; p = p.prevZ; } // look for remaining points in increasing z-order while (n && n.z <= maxZ) { if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c && pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false; n = n.nextZ; } return true; } // go through all polygon nodes and cure small local self-intersections function cureLocalIntersections(start, triangles) { let p = start; do { const a = p.prev, b = p.next.next; if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) { triangles.push(a.i, p.i, b.i); // remove two nodes involved removeNode(p); removeNode(p.next); p = start = b; } p = p.next; } while (p !== start); return filterPoints(p); } // try splitting polygon into two and triangulate them independently function splitEarcut(start, triangles, dim, minX, minY, invSize) { // look for a valid diagonal that divides the polygon into two let a = start; do { let b = a.next.next; while (b !== a.prev) { if (a.i !== b.i && isValidDiagonal(a, b)) { // split the polygon in two by the diagonal let c = splitPolygon(a, b); // filter colinear points around the cuts a = filterPoints(a, a.next); c = filterPoints(c, c.next); // run earcut on each half earcutLinked(a, triangles, dim, minX, minY, invSize, 0); earcutLinked(c, triangles, dim, minX, minY, invSize, 0); return; } b = b.next; } a = a.next; } while (a !== start); } // link every hole into the outer loop, producing a single-ring polygon without holes function eliminateHoles(data, holeIndices, outerNode, dim) { const queue = []; for (let i = 0, len = holeIndices.length; i < len; i++) { const start = holeIndices[i] * dim; const end = i < len - 1 ? holeIndices[i + 1] * dim : data.length; const list = linkedList(data, start, end, dim, false); if (list === list.next) list.steiner = true; queue.push(getLeftmost(list)); } queue.sort(compareXYSlope); // process holes from left to right for (let i = 0; i < queue.length; i++) { outerNode = eliminateHole(queue[i], outerNode); } return outerNode; } function compareXYSlope(a, b) { let result = a.x - b.x; // when the left-most point of 2 holes meet at a vertex, sort the holes counterclockwise so that when we find // the bridge to the outer shell is always the point that they meet at. if (result === 0) { result = a.y - b.y; if (result === 0) { const aSlope = (a.next.y - a.y) / (a.next.x - a.x); const bSlope = (b.next.y - b.y) / (b.next.x - b.x); result = aSlope - bSlope; } } return result; } // find a bridge between vertices that connects hole with an outer ring and link it function eliminateHole(hole, outerNode) { const bridge = findHoleBridge(hole, outerNode); if (!bridge) { return outerNode; } const bridgeReverse = splitPolygon(bridge, hole); // filter collinear points around the cuts filterPoints(bridgeReverse, bridgeReverse.next); return filterPoints(bridge, bridge.next); } // David Eberly's algorithm for finding a bridge between hole and outer polygon function findHoleBridge(hole, outerNode) { let p = outerNode; const hx = hole.x; const hy = hole.y; let qx = -Infinity; let m; // find a segment intersected by a ray from the hole's leftmost point to the left; // segment's endpoint with lesser x will be potential connection point // unless they intersect at a vertex, then choose the vertex if (equals(hole, p)) return p; do { if (equals(hole, p.next)) return p.next; else if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) { const x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y); if (x <= hx && x > qx) { qx = x; m = p.x < p.next.x ? p : p.next; if (x === hx) return m; // hole touches outer segment; pick leftmost endpoint } } p = p.next; } while (p !== outerNode); if (!m) return null; // look for points inside the triangle of hole point, segment intersection and endpoint; // if there are no points found, we have a valid connection; // otherwise choose the point of the minimum angle with the ray as connection point const stop = m; const mx = m.x; const my = m.y; let tanMin = Infinity; p = m; do { if (hx >= p.x && p.x >= mx && hx !== p.x && pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) { const tan = Math.abs(hy - p.y) / (hx - p.x); // tangential if (locallyInside(p, hole) && (tan < tanMin || (tan === tanMin && (p.x > m.x || (p.x === m.x && sectorContainsSector(m, p)))))) { m = p; tanMin = tan; } } p = p.next; } while (p !== stop); return m; } // whether sector in vertex m contains sector in vertex p in the same coordinates function sectorContainsSector(m, p) { return area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0; } // interlink polygon nodes in z-order function indexCurve(start, minX, minY, invSize) { let p = start; do { if (p.z === 0) p.z = zOrder(p.x, p.y, minX, minY, invSize); p.prevZ = p.prev; p.nextZ = p.next; p = p.next; } while (p !== start); p.prevZ.nextZ = null; p.prevZ = null; sortLinked(p); } // Simon Tatham's linked list merge sort algorithm // http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html function sortLinked(list) { let numMerges; let inSize = 1; do { let p = list; let e; list = null; let tail = null; numMerges = 0; while (p) { numMerges++; let q = p; let pSize = 0; for (let i = 0; i < inSize; i++) { pSize++; q = q.nextZ; if (!q) break; } let qSize = inSize; while (pSize > 0 || (qSize > 0 && q)) { if (pSize !== 0 && (qSize === 0 || !q || p.z <= q.z)) { e = p; p = p.nextZ; pSize--; } else { e = q; q = q.nextZ; qSize--; } if (tail) tail.nextZ = e; else list = e; e.prevZ = tail; tail = e; } p = q; } tail.nextZ = null; inSize *= 2; } while (numMerges > 1); return list; } // z-order of a point given coords and inverse of the longer side of data bbox function zOrder(x, y, minX, minY, invSize) { // coords are transformed into non-negative 15-bit integer range x = (x - minX) * invSize | 0; y = (y - minY) * invSize | 0; x = (x | (x << 8)) & 0x00FF00FF; x = (x | (x << 4)) & 0x0F0F0F0F; x = (x | (x << 2)) & 0x33333333; x = (x | (x << 1)) & 0x55555555; y = (y | (y << 8)) & 0x00FF00FF; y = (y | (y << 4)) & 0x0F0F0F0F; y = (y | (y << 2)) & 0x33333333; y = (y | (y << 1)) & 0x55555555; return x | (y << 1); } // find the leftmost node of a polygon ring function getLeftmost(start) { let p = start, leftmost = start; do { if (p.x < leftmost.x || (p.x === leftmost.x && p.y < leftmost.y)) leftmost = p; p = p.next; } while (p !== start); return leftmost; } // check if a point lies within a convex triangle function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) { return (cx - px) * (ay - py) >= (ax - px) * (cy - py) && (ax - px) * (by - py) >= (bx - px) * (ay - py) && (bx - px) * (cy - py) >= (cx - px) * (by - py); } // check if a point lies within a convex triangle but false if its equal to the first point of the triangle function pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, px, py) { return !(ax === px && ay === py) && pointInTriangle(ax, ay, bx, by, cx, cy, px, py); } // check if a diagonal between two polygon nodes is valid (lies in polygon interior) function isValidDiagonal(a, b) { return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) && // doesn't intersect other edges (locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b) && // locally visible (area(a.prev, a, b.prev) || area(a, b.prev, b)) || // does not create opposite-facing sectors equals(a, b) && area(a.prev, a, a.next) > 0 && area(b.prev, b, b.next) > 0); // special zero-length case } // signed area of a triangle function area(p, q, r) { return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y); } // check if two points are equal function equals(p1, p2) { return p1.x === p2.x && p1.y === p2.y; } // check if two segments intersect function intersects(p1, q1, p2, q2) { const o1 = sign$2(area(p1, q1, p2)); const o2 = sign$2(area(p1, q1, q2)); const o3 = sign$2(area(p2, q2, p1)); const o4 = sign$2(area(p2, q2, q1)); if (o1 !== o2 && o3 !== o4) return true; // general case if (o1 === 0 && onSegment(p1, p2, q1)) return true; // p1, q1 and p2 are collinear and p2 lies on p1q1 if (o2 === 0 && onSegment(p1, q2, q1)) return true; // p1, q1 and q2 are collinear and q2 lies on p1q1 if (o3 === 0 && onSegment(p2, p1, q2)) return true; // p2, q2 and p1 are collinear and p1 lies on p2q2 if (o4 === 0 && onSegment(p2, q1, q2)) return true; // p2, q2 and q1 are collinear and q1 lies on p2q2 return false; } // for collinear points p, q, r, check if point q lies on segment pr function onSegment(p, q, r) { return q.x <= Math.max(p.x, r.x) && q.x >= Math.min(p.x, r.x) && q.y <= Math.max(p.y, r.y) && q.y >= Math.min(p.y, r.y); } function sign$2(num) { return num > 0 ? 1 : num < 0 ? -1 : 0; } // check if a polygon diagonal intersects any polygon segments function intersectsPolygon(a, b) { let p = a; do { if (p.i !== a.i && p.next.i !== a.i && p.i !== b.i && p.next.i !== b.i && intersects(p, p.next, a, b)) return true; p = p.next; } while (p !== a); return false; } // check if a polygon diagonal is locally inside the polygon function locallyInside(a, b) { return area(a.prev, a, a.next) < 0 ? area(a, b, a.next) >= 0 && area(a, a.prev, b) >= 0 : area(a, b, a.prev) < 0 || area(a, a.next, b) < 0; } // check if the middle point of a polygon diagonal is inside the polygon function middleInside(a, b) { let p = a; let inside = false; const px = (a.x + b.x) / 2; const py = (a.y + b.y) / 2; do { if (((p.y > py) !== (p.next.y > py)) && p.next.y !== p.y && (px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x)) inside = !inside; p = p.next; } while (p !== a); return inside; } // link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two; // if one belongs to the outer ring and another to a hole, it merges it into a single ring function splitPolygon(a, b) { const a2 = createNode(a.i, a.x, a.y), b2 = createNode(b.i, b.x, b.y), an = a.next, bp = b.prev; a.next = b; b.prev = a; a2.next = an; an.prev = a2; b2.next = a2; a2.prev = b2; bp.next = b2; b2.prev = bp; return b2; } // create a node and optionally link it with previous one (in a circular doubly linked list) function insertNode(i, x, y, last) { const p = createNode(i, x, y); if (!last) { p.prev = p; p.next = p; } else { p.next = last.next; p.prev = last; last.next.prev = p; last.next = p; } return p; } function removeNode(p) { p.next.prev = p.prev; p.prev.next = p.next; if (p.prevZ) p.prevZ.nextZ = p.nextZ; if (p.nextZ) p.nextZ.prevZ = p.prevZ; } function createNode(i, x, y) { return { i, // vertex index in coordinates array x, y, // vertex coordinates prev: null, // previous and next vertex nodes in a polygon ring next: null, z: 0, // z-order curve value prevZ: null, // previous and next nodes in z-order nextZ: null, steiner: false // indicates whether this is a steiner point }; } function signedArea(data, start, end, dim) { let sum = 0; for (let i = start, j = end - dim; i < end; i += dim) { sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]); j = i; } return sum; } // turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts function flatten(data) { const vertices = []; const holes = []; const dimensions = data[0][0].length; let holeIndex = 0; let prevLen = 0; for (const ring of data) { for (const p of ring) { for (let d = 0; d < dimensions; d++) vertices.push(p[d]); } if (prevLen) { holeIndex += prevLen; holes.push(holeIndex); } prevLen = ring.length; } return {vertices, holes, dimensions}; } const epsilon$2 = 1.1102230246251565e-16; const splitter = 134217729; const resulterrbound = (3 + 8 * epsilon$2) * epsilon$2; // fast_expansion_sum_zeroelim routine from original 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$2) * epsilon$2; const ccwerrboundB = (2 + 12 * epsilon$2) * epsilon$2; const ccwerrboundC = (9 + 64 * epsilon$2) * epsilon$2 * epsilon$2; 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; 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); /** @template {ArrayLike<number>} T */ class Delaunator { /** * Constructs a delaunay triangulation object given an array of points (`[x, y]` by default). * `getX` and `getY` are optional functions of the form `(point) => value` for custom point formats. * * @template P * @param {P[]} points * @param {(p: P) => number} [getX] * @param {(p: P) => number} [getY] */ // @ts-expect-error TS2322 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); } /** * Constructs a delaunay triangulation object given an array of point coordinates of the form: * `[x0, y0, x1, y1, ...]` (use a typed array for best performance). Duplicate points are skipped. * * @param {T} 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); /** @private */ this._triangles = new Uint32Array(maxTriangles * 3); /** @private */ this._halfedges = new Int32Array(maxTriangles * 3); // temporary arrays for tracking the edges of the advancing convex hull /** @private */ this._hashSize = Math.ceil(Math.sqrt(n)); /** @private */ this._hullPrev = new Uint32Array(n); // edge to prev edge /** @private */ this._hullNext = new Uint32Array(n); // edge to next edge /** @private */ this._hullTri = new Uint32Array(n); // edge to adjacent triangle /** @private */ this._hullHash = new Int32Array(this._hashSize); // angular edge hash // temporary arrays for sorting points /** @private */ this._ids = new Uint32Array(n); /** @private */ this._dists = new Float64Array(n); /** @private */ this.trianglesLen = 0; /** @private */ this._cx = 0; /** @private */ this._cy = 0; /** @private */ this._hullStart = 0; /** A `Uint32Array` array of indices that reference points on the convex hull of the input data, counter-clockwise. */ this.hull = this._triangles; /** A `Uint32Array` array of triangle vertex indices (each group of three numbers forms a triangle). All triangles are directed counterclockwise. */ this.triangles = this._triangles; /** * A `Int32Array` array of triangle half-edge indices that allows you to traverse the triangulation. * `i`-th half-edge in the array corresponds to vertex `triangles[i]` the half-edge is coming from. * `halfedges[i]` is the index of a twin half-edge in an adjacent triangle (or `-1` for outer half-edges on the convex hull). */ this.halfedges = this._halfedges; this.update(); } /** * Updates the triangulation if you modified `delaunay.coords` values in place, avoiding expensive memory allocations. * Useful for iterative relaxation algorithms such as Lloyd's. */ 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 i0 = 0, i1 = 0, i2 = 0; // pick a seed point close to the center for (let i = 0, minDist = Infinity; 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]; // find the point closest to the seed for (let i = 0, minDist = Infinity; 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]; const d = this._dists[id]; if (d > d0) { hull[j++] = id; d0 = d; } } this.hull = hull.subarray(0, j); this.triangles = new Uint32Array(0); this.halfedges = new Int32Array(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 = 0, yp = 0; 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