earcut port to TypeScript
This commit is contained in:
parent
fa6398b4dc
commit
5606b3c2a4
|
@ -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<number>,
|
||||
holeIndices?: ArrayLike<number>,
|
||||
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<number>,
|
||||
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<number>,
|
||||
holeIndices: ArrayLike<number>,
|
||||
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<number>,
|
||||
holeIndices: ArrayLike<number> | 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<number>,
|
||||
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;
|
||||
};
|
Loading…
Reference in New Issue