diff --git a/src/earcut.ts b/src/earcut.ts new file mode 100644 index 0000000..8c75517 --- /dev/null +++ b/src/earcut.ts @@ -0,0 +1,767 @@ +/* +ISC License + +Copyright (c) 2016, Mapbox + +Permission to use, copy, modify, and/or distribute this software for any purpose +with or without fee is hereby granted, provided that the above copyright notice +and this permission notice appear in all copies. + +THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH +REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND +FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, +INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS +OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER +TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF +THIS SOFTWARE. +*/ + +// Ported to TypeScript by Tony Garnock-Jones tonyg@leastfixedpoint.com, Feb 2023 + +export function earcut( + data: ArrayLike, + holeIndices?: ArrayLike, + dim = 2, +): number[] { + const hasHoles = holeIndices && holeIndices.length; + const outerLen = hasHoles ? holeIndices[0] * dim : data.length; + let outerNode = linkedList(data, 0, outerLen, dim, true); + const triangles: number[] = []; + + if (!outerNode || outerNode.next === outerNode.prev) return triangles; + + let minX: number = NaN; + let minY: number = NaN; + let invSize: number = NaN; + + 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) { + let maxX = minX = data[0]; + let maxY = minY = data[1]; + + for (var 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: ArrayLike, + start: number, + end: number, + dim: number, + clockwise: boolean, +): Node | null { + let last: Node | null = null; + + if (clockwise === (signedArea(data, start, end, dim) > 0)) { + for (let i = start; i < end; i += dim) last = insertNode(i, data[i], data[i + 1], last); + } else { + for (let i = end - dim; i >= start; i -= dim) last = insertNode(i, 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: Node, end?: Node): Node; +function filterPoints(start?: Node | null, end?: Node | null): Node | null; +function filterPoints(start?: Node | null, end?: Node | null): Node | null { + if (!start) return start ?? null; + if (!end) end = start; + + var p: Node = start; + let again: boolean; + 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( + ear0: Node | null, + triangles: number[], + dim: number, + minX: number, + minY: number, + invSize: number, + pass: number, +): void { + if (!ear0) return; + let ear = ear0; + + // interlink polygon nodes in z-order + if (!pass && invSize) indexCurve(ear, minX, minY, invSize); + + let stop = ear; + let prev: Node; + let next: Node; + + // iterate through ears, slicing them one by one + while (ear.prev !== ear.next) { + prev = ear.prev; + next = ear.next; + + if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) { + // cut off the triangle + triangles.push(prev.i / dim | 0); + triangles.push(ear.i / dim | 0); + triangles.push(next.i / dim | 0); + + 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, dim); + 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: Node): boolean { + var 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 + var ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y; + + // triangle bbox; min & max are calculated like this for speed + var x0 = ax < bx ? (ax < cx ? ax : cx) : (bx < cx ? bx : cx), + y0 = ay < by ? (ay < cy ? ay : cy) : (by < cy ? by : cy), + x1 = ax > bx ? (ax > cx ? ax : cx) : (bx > cx ? bx : cx), + y1 = ay > by ? (ay > cy ? ay : cy) : (by > cy ? by : cy); + + var p = c.next; + while (p !== a) { + if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && + pointInTriangle(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: Node, minX: number, minY: number, invSize: number): boolean { + var a = ear.prev, + b = ear, + c = ear.next; + + if (area(a, b, c) >= 0) return false; // reflex, can't be an ear + + var ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y; + + // triangle bbox; min & max are calculated like this for speed + var x0 = ax < bx ? (ax < cx ? ax : cx) : (bx < cx ? bx : cx), + y0 = ay < by ? (ay < cy ? ay : cy) : (by < cy ? by : cy), + x1 = ax > bx ? (ax > cx ? ax : cx) : (bx > cx ? bx : cx), + y1 = ay > by ? (ay > cy ? ay : cy) : (by > cy ? by : cy); + + // z-order range for the current triangle bbox; + var minZ = zOrder(x0, y0, minX, minY, invSize), + maxZ = zOrder(x1, y1, minX, minY, invSize); + + var 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 && + pointInTriangle(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 && + pointInTriangle(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 && + pointInTriangle(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 && + pointInTriangle(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: Node, + triangles: number[], + dim: number, +): Node { + let p = start; + do { + const a = p.prev; + const b = p.next.next; + + if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) { + + triangles.push(a.i / dim | 0); + triangles.push(p.i / dim | 0); + triangles.push(b.i / dim | 0); + + // 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: Node, + triangles: number[], + dim: number, + minX: number, + minY: number, + invSize: number, +): void { + // 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: ArrayLike, + holeIndices: ArrayLike, + outerNode: Node, + dim: number, +): Node { + const queue: Node[] = []; + const len = holeIndices.length; + + for (let i = 0; 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(compareX); + + // process holes from left to right + for (let i = 0; i < queue.length; i++) { + outerNode = eliminateHole(queue[i], outerNode); + } + + return outerNode; +} + +function compareX(a: Node, b: Node): number { + return a.x - b.x; +} + +// find a bridge between vertices that connects hole with an outer ring and and link it +function eliminateHole( + hole: Node, + outerNode: Node, +): Node { + 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: Node, + outerNode: Node, +): Node | null { + let p = outerNode; + const hx = hole.x; + const hy = hole.y; + let qx = -Infinity; + let m: Node | null = null; + + // 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 + do { + if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) { + var 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: Node, p: Node): boolean { + return area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0; +} + +// interlink polygon nodes in z-order +function indexCurve(start: Node, minX: number, minY: number, invSize: number): void { + 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: Node): Node; +function sortLinked(list: Node | null): Node | null; +function sortLinked(list: Node | null): Node | null { + let inSize = 1; + let numMerges: number; + do { + let p: Node | null = list; + let tail = null; + + list = null; + numMerges = 0; + + while (p) { + numMerges++; + let q: Node | null = 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)) { + let e; + 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: number, y: number, minX: number, minY: number, invSize: number): number { + // 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: Node): Node { + let p = start; + let 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: number, + ay: number, + bx: number, + by: number, + cx: number, + cy: number, + px: number, + py: number, +): boolean { + 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 diagonal between two polygon nodes is valid (lies in polygon interior) +function isValidDiagonal(a: Node, b: Node): boolean { + 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: Node, q: Node, r: Node): number { + 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: Node, p2: Node): boolean { + return p1.x === p2.x && p1.y === p2.y; +} + +// check if two segments intersect +function intersects(p1: Node, q1: Node, p2: Node, q2: Node): boolean { + const o1 = sign(area(p1, q1, p2)); + const o2 = sign(area(p1, q1, q2)); + const o3 = sign(area(p2, q2, p1)); + const o4 = sign(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: Node, q: Node, r: Node): boolean { + 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(num: number): -1 | 0 | 1 { + return num > 0 ? 1 : num < 0 ? -1 : 0; +} + +// check if a polygon diagonal intersects any polygon segments +function intersectsPolygon(a: Node, b: Node): boolean { + 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: Node, b: Node): boolean { + 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: Node, b: Node): boolean { + 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: Node, b: Node): Node { + const an = a.next; + const bp = b.prev; + + a.next = b; + b.prev = a; + + const a2 = new Node(a.i, a.x, a.y, null!, an); + an.prev = a2; + + const b2 = new Node(b.i, b.x, b.y, bp, a2); + a2.prev = b2; + bp.next = b2; + + return b2; +} + +// create a node and optionally link it with previous one (in a circular doubly linked list) +function insertNode(i: number, x: number, y: number, last: Node | null): Node { + if (!last) { + const p = new Node(i, x, y, null!, null!); + p.prev = p; + p.next = p; + return p; + } else { + const p = new Node(i, x, y, last, last.next); + last.next.prev = p; + last.next = p; + return p; + } +} + +function removeNode(p: Node) { + 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; +} + +class Node { + z = 0; // z-order curve value + + // previous and next nodes in z-order + prevZ: Node | null = null; + nextZ: Node | null = null; + + // indicates whether this is a steiner point + steiner = false; + + constructor( + public i: number, // vertex index in coordinates array + public x: number, + public y: number, + // previous and next vertex nodes in a polygon ring + public prev: Node, + public next: Node, + ) {} +} + +// return a percentage difference between the polygon area and its triangulation area; +// used to verify correctness of triangulation +earcut.deviation = function ( + data: ArrayLike, + holeIndices: ArrayLike | null | undefined, + dim: number, + triangles: number[], +): number { + const hasHoles = holeIndices && holeIndices.length; + const outerLen = hasHoles ? holeIndices[0] * dim : data.length; + + let polygonArea = Math.abs(signedArea(data, 0, outerLen, dim)); + if (hasHoles) { + 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; + polygonArea -= Math.abs(signedArea(data, start, end, dim)); + } + } + + let trianglesArea = 0; + for (let i = 0; i < triangles.length; i += 3) { + const a = triangles[i] * dim; + const b = triangles[i + 1] * dim; + const c = triangles[i + 2] * dim; + trianglesArea += Math.abs( + (data[a] - data[c]) * (data[b + 1] - data[a + 1]) - + (data[a] - data[b]) * (data[c + 1] - data[a + 1])); + } + + return polygonArea === 0 && trianglesArea === 0 ? 0 : + Math.abs((trianglesArea - polygonArea) / polygonArea); +}; + +function signedArea( + data: ArrayLike, + start: number, + end: number, + dim: number, +): number { + 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; +} + +export type Flattened = { + vertices: number[], + holes: number[], + dimensions: number, +}; + +// turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts +earcut.flatten = function ( + data: number[][][], +): Flattened { + const dim = data[0][0].length; + const result: Flattened = {vertices: [], holes: [], dimensions: dim}; + + let holeIndex = 0; + for (let i = 0; i < data.length; i++) { + for (let j = 0; j < data[i].length; j++) { + for (let d = 0; d < dim; d++) result.vertices.push(data[i][j][d]); + } + if (i > 0) { + holeIndex += data[i - 1].length; + result.holes.push(holeIndex); + } + } + return result; +};