add addzone and update zone in map-adapter interface

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2025-09-29 14:55:14 -04:00
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ISC License
Copyright (c) 2024, 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.
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## Earcut
The fastest and smallest JavaScript polygon triangulation library. 3KB gzipped.
[![Node](https://github.com/mapbox/earcut/actions/workflows/node.yml/badge.svg)](https://github.com/mapbox/earcut/actions/workflows/node.yml)
[![Average time to resolve an issue](http://isitmaintained.com/badge/resolution/mapbox/earcut.svg)](http://isitmaintained.com/project/mapbox/earcut "Average time to resolve an issue")
[![Percentage of issues still open](http://isitmaintained.com/badge/open/mapbox/earcut.svg)](http://isitmaintained.com/project/mapbox/earcut "Percentage of issues still open")
[![](https://img.shields.io/badge/simply-awesome-brightgreen.svg)](https://github.com/mourner/projects)
#### The algorithm
The library implements a modified ear slicing algorithm,
optimized by [z-order curve](http://en.wikipedia.org/wiki/Z-order_curve) hashing
and extended to handle holes, twisted polygons, degeneracies and self-intersections
in a way that doesn't _guarantee_ correctness of triangulation,
but attempts to always produce acceptable results for practical data.
It's based on ideas from
[FIST: Fast Industrial-Strength Triangulation of Polygons](http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html) by Martin Held
and [Triangulation by Ear Clipping](http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf) by David Eberly.
#### Why another triangulation library?
The aim of this project is to create a JS triangulation library
that is **fast enough for real-time triangulation in the browser**,
sacrificing triangulation quality for raw speed and simplicity,
while being robust enough to handle most practical datasets without crashing or producing garbage.
Some benchmarks using Node 0.12:
(ops/sec) | pts | earcut | libtess | poly2tri | pnltri | polyk
------------------| ---- | --------- | -------- | -------- | --------- | ------
OSM building | 15 | _795,935_ | _50,640_ | _61,501_ | _122,966_ | _175,570_
dude shape | 94 | _35,658_ | _10,339_ | _8,784_ | _11,172_ | _13,557_
holed dude shape | 104 | _28,319_ | _8,883_ | _7,494_ | _2,130_ | n/a
complex OSM water | 2523 | _543_ | _77.54_ | failure | failure | n/a
huge OSM water | 5667 | _95_ | _29.30_ | failure | failure | n/a
The original use case it was created for is [Mapbox GL](https://www.mapbox.com/mapbox-gl), WebGL-based interactive maps.
If you want to get correct triangulation even on very bad data with lots of self-intersections
and earcut is not precise enough, take a look at [libtess.js](https://github.com/brendankenny/libtess.js).
#### Usage
```js
const triangles = earcut([10,0, 0,50, 60,60, 70,10]); // returns [1,0,3, 3,2,1]
```
Signature: `earcut(vertices[, holes, dimensions = 2])`.
* `vertices` is a flat array of vertex coordinates like `[x0,y0, x1,y1, x2,y2, ...]`.
* `holes` is an array of hole _indices_ if any
(e.g. `[5, 8]` for a 12-vertex input would mean one hole with vertices 5–7 and another with 8–11).
* `dimensions` is the number of coordinates per vertex in the input array (`2` by default). Only two are used for triangulation (`x` and `y`), and the rest are ignored.
Each group of three vertex indices in the resulting array forms a triangle.
```js
// triangulating a polygon with a hole
earcut([0,0, 100,0, 100,100, 0,100, 20,20, 80,20, 80,80, 20,80], [4]);
// [3,0,4, 5,4,0, 3,4,7, 5,0,1, 2,3,7, 6,5,1, 2,7,6, 6,1,2]
// triangulating a polygon with 3d coords
earcut([10,0,1, 0,50,2, 60,60,3, 70,10,4], null, 3);
// [1,0,3, 3,2,1]
```
If you pass a single vertex as a hole, Earcut treats it as a Steiner point.
Note that Earcut is a **2D** triangulation algorithm, and handles 3D data as if it was projected onto the XY plane (with Z component ignored).
If your input is a multi-dimensional array (e.g. [GeoJSON Polygon](http://geojson.org/geojson-spec.html#polygon)),
you can convert it to the format expected by Earcut with `earcut.flatten`:
```js
const data = earcut.flatten(geojson.geometry.coordinates);
const triangles = earcut(data.vertices, data.holes, data.dimensions);
```
After getting a triangulation, you can verify its correctness with `earcut.deviation`:
```js
const deviation = earcut.deviation(vertices, holes, dimensions, triangles);
```
Returns the relative difference between the total area of triangles and the area of the input polygon.
`0` means the triangulation is fully correct.
#### Install
Install with NPM: `npm install earcut`, then import as a module:
```js
import earcut from 'earcut';
```
Or use as a module directly in the browser with [jsDelivr](https://www.jsdelivr.com/esm):
```html
<script type="module">
import earcut from 'https://cdn.jsdelivr.net/npm/earcut/+esm';
</script>
```
Alternatively, there's a UMD browser bundle with an `earcut` global variable (exposing the main function as `earcut.default`):
```html
<script src="https://cdn.jsdelivr.net/npm/earcut/dist/earcut.min.js"></script>
```
![](https://cloud.githubusercontent.com/assets/25395/5778431/e8ec0c10-9da3-11e4-8d4e-a2ced6a7d2b7.png)
#### Ports to other languages
- [mapbox/earcut.hpp](https://github.com/mapbox/earcut.hpp) (C++11)
- [JaffaKetchup/dart_earcut](https://github.com/JaffaKetchup/dart_earcut) (Dart)
- [earcut4j/earcut4j](https://github.com/earcut4j/earcut4j) (Java)
- [the3deers/earcut-java](https://github.com/the3deers/earcut-java) (Java)
- [Larpon/earcut](https://github.com/Larpon/earcut) (V)
- [Cawfree/earcut-j](https://github.com/Cawfree/earcut-j) (Java, outdated)
- [measuredweighed/SwiftEarcut](https://github.com/measuredweighed/SwiftEarcut) (Swift)
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(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.earcut = {}));
})(this, (function (exports) { 'use strict';
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(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, 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(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
};
}
// return a percentage difference between the polygon area and its triangulation area;
// used to verify correctness of triangulation
function deviation(data, holeIndices, dim, triangles) {
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, 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};
}
exports.default = earcut;
exports.deviation = deviation;
exports.flatten = flatten;
Object.defineProperty(exports, '__esModule', { value: true });
}));
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{
"name": "earcut",
"version": "3.0.2",
"description": "The fastest and smallest JavaScript polygon triangulation library for your WebGL apps",
"main": "src/earcut.js",
"type": "module",
"exports": "./src/earcut.js",
"files": [
"src/earcut.js",
"dist/earcut.min.js",
"dist/earcut.dev.js"
],
"scripts": {
"pretest": "eslint src test/test.js bench/*.js viz/viz.js",
"test": "node --test",
"build": "rollup -c",
"prepublishOnly": "npm run build",
"cov": "node --test --experimental-test-coverage"
},
"author": "Vladimir Agafonkin",
"license": "ISC",
"devDependencies": {
"@rollup/plugin-terser": "^0.4.4",
"benchmark": "^2.1.4",
"eslint": "^9.31.0",
"eslint-config-mourner": "^4.1.0",
"rollup": "^4.45.1"
},
"eslintConfig": {
"extends": "mourner",
"parserOptions": {
"sourceType": "module",
"ecmaVersion": 2020
}
},
"repository": {
"type": "git",
"url": "git://github.com/mapbox/earcut.git"
}
}
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export default 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(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, 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(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
};
}
// return a percentage difference between the polygon area and its triangulation area;
// used to verify correctness of triangulation
export function deviation(data, holeIndices, dim, triangles) {
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, 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
export 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};
}