add addzone and update zone in map-adapter interface
This commit is contained in:
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ISC License
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Copyright (c) 2024, Mapbox
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Permission to use, copy, modify, and/or distribute this software for any purpose
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with or without fee is hereby granted, provided that the above copyright notice
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and this permission notice appear in all copies.
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THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
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REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
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FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
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INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
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OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
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TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
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THIS SOFTWARE.
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## Earcut
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The fastest and smallest JavaScript polygon triangulation library. 3KB gzipped.
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[](https://github.com/mapbox/earcut/actions/workflows/node.yml)
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[](http://isitmaintained.com/project/mapbox/earcut "Average time to resolve an issue")
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[](http://isitmaintained.com/project/mapbox/earcut "Percentage of issues still open")
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[](https://github.com/mourner/projects)
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#### The algorithm
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The library implements a modified ear slicing algorithm,
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optimized by [z-order curve](http://en.wikipedia.org/wiki/Z-order_curve) hashing
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and extended to handle holes, twisted polygons, degeneracies and self-intersections
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in a way that doesn't _guarantee_ correctness of triangulation,
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but attempts to always produce acceptable results for practical data.
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It's based on ideas from
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[FIST: Fast Industrial-Strength Triangulation of Polygons](http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html) by Martin Held
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and [Triangulation by Ear Clipping](http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf) by David Eberly.
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#### Why another triangulation library?
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The aim of this project is to create a JS triangulation library
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that is **fast enough for real-time triangulation in the browser**,
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sacrificing triangulation quality for raw speed and simplicity,
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while being robust enough to handle most practical datasets without crashing or producing garbage.
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Some benchmarks using Node 0.12:
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(ops/sec) | pts | earcut | libtess | poly2tri | pnltri | polyk
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------------------| ---- | --------- | -------- | -------- | --------- | ------
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OSM building | 15 | _795,935_ | _50,640_ | _61,501_ | _122,966_ | _175,570_
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dude shape | 94 | _35,658_ | _10,339_ | _8,784_ | _11,172_ | _13,557_
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holed dude shape | 104 | _28,319_ | _8,883_ | _7,494_ | _2,130_ | n/a
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complex OSM water | 2523 | _543_ | _77.54_ | failure | failure | n/a
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huge OSM water | 5667 | _95_ | _29.30_ | failure | failure | n/a
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The original use case it was created for is [Mapbox GL](https://www.mapbox.com/mapbox-gl), WebGL-based interactive maps.
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If you want to get correct triangulation even on very bad data with lots of self-intersections
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and earcut is not precise enough, take a look at [libtess.js](https://github.com/brendankenny/libtess.js).
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#### Usage
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```js
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const triangles = earcut([10,0, 0,50, 60,60, 70,10]); // returns [1,0,3, 3,2,1]
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```
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Signature: `earcut(vertices[, holes, dimensions = 2])`.
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* `vertices` is a flat array of vertex coordinates like `[x0,y0, x1,y1, x2,y2, ...]`.
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* `holes` is an array of hole _indices_ if any
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(e.g. `[5, 8]` for a 12-vertex input would mean one hole with vertices 5–7 and another with 8–11).
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* `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.
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Each group of three vertex indices in the resulting array forms a triangle.
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```js
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// triangulating a polygon with a hole
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earcut([0,0, 100,0, 100,100, 0,100, 20,20, 80,20, 80,80, 20,80], [4]);
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// [3,0,4, 5,4,0, 3,4,7, 5,0,1, 2,3,7, 6,5,1, 2,7,6, 6,1,2]
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// triangulating a polygon with 3d coords
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earcut([10,0,1, 0,50,2, 60,60,3, 70,10,4], null, 3);
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// [1,0,3, 3,2,1]
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```
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If you pass a single vertex as a hole, Earcut treats it as a Steiner point.
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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).
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If your input is a multi-dimensional array (e.g. [GeoJSON Polygon](http://geojson.org/geojson-spec.html#polygon)),
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you can convert it to the format expected by Earcut with `earcut.flatten`:
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```js
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const data = earcut.flatten(geojson.geometry.coordinates);
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const triangles = earcut(data.vertices, data.holes, data.dimensions);
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```
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After getting a triangulation, you can verify its correctness with `earcut.deviation`:
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```js
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const deviation = earcut.deviation(vertices, holes, dimensions, triangles);
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```
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Returns the relative difference between the total area of triangles and the area of the input polygon.
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`0` means the triangulation is fully correct.
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#### Install
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Install with NPM: `npm install earcut`, then import as a module:
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```js
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import earcut from 'earcut';
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```
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Or use as a module directly in the browser with [jsDelivr](https://www.jsdelivr.com/esm):
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```html
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<script type="module">
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import earcut from 'https://cdn.jsdelivr.net/npm/earcut/+esm';
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</script>
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```
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Alternatively, there's a UMD browser bundle with an `earcut` global variable (exposing the main function as `earcut.default`):
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```html
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<script src="https://cdn.jsdelivr.net/npm/earcut/dist/earcut.min.js"></script>
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```
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#### Ports to other languages
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- [mapbox/earcut.hpp](https://github.com/mapbox/earcut.hpp) (C++11)
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- [JaffaKetchup/dart_earcut](https://github.com/JaffaKetchup/dart_earcut) (Dart)
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- [earcut4j/earcut4j](https://github.com/earcut4j/earcut4j) (Java)
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- [the3deers/earcut-java](https://github.com/the3deers/earcut-java) (Java)
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- [Larpon/earcut](https://github.com/Larpon/earcut) (V)
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- [Cawfree/earcut-j](https://github.com/Cawfree/earcut-j) (Java, outdated)
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- [measuredweighed/SwiftEarcut](https://github.com/measuredweighed/SwiftEarcut) (Swift)
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+695
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(function (global, factory) {
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typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) :
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typeof define === 'function' && define.amd ? define(['exports'], factory) :
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(global = typeof globalThis !== 'undefined' ? globalThis : global || self, factory(global.earcut = {}));
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})(this, (function (exports) { 'use strict';
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function earcut(data, holeIndices, dim = 2) {
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const hasHoles = holeIndices && holeIndices.length;
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const outerLen = hasHoles ? holeIndices[0] * dim : data.length;
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let outerNode = linkedList(data, 0, outerLen, dim, true);
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const triangles = [];
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if (!outerNode || outerNode.next === outerNode.prev) return triangles;
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let minX, minY, invSize;
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if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim);
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// if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
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if (data.length > 80 * dim) {
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minX = data[0];
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minY = data[1];
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let maxX = minX;
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let maxY = minY;
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for (let i = dim; i < outerLen; i += dim) {
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const x = data[i];
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const y = data[i + 1];
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if (x < minX) minX = x;
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if (y < minY) minY = y;
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if (x > maxX) maxX = x;
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if (y > maxY) maxY = y;
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}
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// minX, minY and invSize are later used to transform coords into integers for z-order calculation
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invSize = Math.max(maxX - minX, maxY - minY);
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invSize = invSize !== 0 ? 32767 / invSize : 0;
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}
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earcutLinked(outerNode, triangles, dim, minX, minY, invSize, 0);
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return triangles;
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}
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// create a circular doubly linked list from polygon points in the specified winding order
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function linkedList(data, start, end, dim, clockwise) {
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let last;
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if (clockwise === (signedArea(data, start, end, dim) > 0)) {
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for (let i = start; i < end; i += dim) last = insertNode(i / dim | 0, data[i], data[i + 1], last);
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} else {
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for (let i = end - dim; i >= start; i -= dim) last = insertNode(i / dim | 0, data[i], data[i + 1], last);
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}
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if (last && equals(last, last.next)) {
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removeNode(last);
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last = last.next;
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}
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return last;
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}
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// eliminate colinear or duplicate points
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function filterPoints(start, end) {
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if (!start) return start;
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if (!end) end = start;
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let p = start,
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again;
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do {
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again = false;
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if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) {
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removeNode(p);
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p = end = p.prev;
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if (p === p.next) break;
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again = true;
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} else {
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p = p.next;
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}
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} while (again || p !== end);
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return end;
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}
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// main ear slicing loop which triangulates a polygon (given as a linked list)
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function earcutLinked(ear, triangles, dim, minX, minY, invSize, pass) {
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if (!ear) return;
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// interlink polygon nodes in z-order
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if (!pass && invSize) indexCurve(ear, minX, minY, invSize);
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let stop = ear;
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// iterate through ears, slicing them one by one
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while (ear.prev !== ear.next) {
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const prev = ear.prev;
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const next = ear.next;
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if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) {
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triangles.push(prev.i, ear.i, next.i); // cut off the triangle
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removeNode(ear);
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// skipping the next vertex leads to less sliver triangles
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ear = next.next;
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stop = next.next;
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continue;
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}
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ear = next;
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// if we looped through the whole remaining polygon and can't find any more ears
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if (ear === stop) {
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// try filtering points and slicing again
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if (!pass) {
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earcutLinked(filterPoints(ear), triangles, dim, minX, minY, invSize, 1);
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// if this didn't work, try curing all small self-intersections locally
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} else if (pass === 1) {
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ear = cureLocalIntersections(filterPoints(ear), triangles);
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earcutLinked(ear, triangles, dim, minX, minY, invSize, 2);
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// as a last resort, try splitting the remaining polygon into two
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} else if (pass === 2) {
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splitEarcut(ear, triangles, dim, minX, minY, invSize);
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}
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break;
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}
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}
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}
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// check whether a polygon node forms a valid ear with adjacent nodes
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function isEar(ear) {
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const a = ear.prev,
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b = ear,
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c = ear.next;
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if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
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// now make sure we don't have other points inside the potential ear
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const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y;
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// triangle bbox
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const x0 = Math.min(ax, bx, cx),
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y0 = Math.min(ay, by, cy),
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x1 = Math.max(ax, bx, cx),
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y1 = Math.max(ay, by, cy);
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let p = c.next;
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while (p !== a) {
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if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 &&
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pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) &&
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area(p.prev, p, p.next) >= 0) return false;
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p = p.next;
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}
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return true;
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}
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function isEarHashed(ear, minX, minY, invSize) {
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const a = ear.prev,
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b = ear,
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c = ear.next;
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if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
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const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y;
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// triangle bbox
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const x0 = Math.min(ax, bx, cx),
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y0 = Math.min(ay, by, cy),
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x1 = Math.max(ax, bx, cx),
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y1 = Math.max(ay, by, cy);
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// z-order range for the current triangle bbox;
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const minZ = zOrder(x0, y0, minX, minY, invSize),
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maxZ = zOrder(x1, y1, minX, minY, invSize);
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let p = ear.prevZ,
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n = ear.nextZ;
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// look for points inside the triangle in both directions
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while (p && p.z >= minZ && n && n.z <= maxZ) {
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if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c &&
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pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false;
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p = p.prevZ;
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if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c &&
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pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false;
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n = n.nextZ;
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}
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// look for remaining points in decreasing z-order
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while (p && p.z >= minZ) {
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if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c &&
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pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false;
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p = p.prevZ;
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}
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// look for remaining points in increasing z-order
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while (n && n.z <= maxZ) {
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if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c &&
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pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false;
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n = n.nextZ;
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}
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return true;
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}
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// go through all polygon nodes and cure small local self-intersections
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function cureLocalIntersections(start, triangles) {
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let p = start;
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do {
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const a = p.prev,
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b = p.next.next;
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if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) {
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triangles.push(a.i, p.i, b.i);
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// remove two nodes involved
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removeNode(p);
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removeNode(p.next);
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p = start = b;
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}
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p = p.next;
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} while (p !== start);
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return filterPoints(p);
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}
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// try splitting polygon into two and triangulate them independently
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function splitEarcut(start, triangles, dim, minX, minY, invSize) {
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// look for a valid diagonal that divides the polygon into two
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let a = start;
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do {
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let b = a.next.next;
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while (b !== a.prev) {
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if (a.i !== b.i && isValidDiagonal(a, b)) {
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// split the polygon in two by the diagonal
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let c = splitPolygon(a, b);
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// filter colinear points around the cuts
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a = filterPoints(a, a.next);
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c = filterPoints(c, c.next);
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// run earcut on each half
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earcutLinked(a, triangles, dim, minX, minY, invSize, 0);
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earcutLinked(c, triangles, dim, minX, minY, invSize, 0);
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return;
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}
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b = b.next;
|
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}
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a = a.next;
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} while (a !== start);
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}
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// link every hole into the outer loop, producing a single-ring polygon without holes
|
||||
function eliminateHoles(data, holeIndices, outerNode, dim) {
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||||
const queue = [];
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||||
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||||
for (let i = 0, len = holeIndices.length; i < len; i++) {
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||||
const start = holeIndices[i] * dim;
|
||||
const end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
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||||
const list = linkedList(data, start, end, dim, false);
|
||||
if (list === list.next) list.steiner = true;
|
||||
queue.push(getLeftmost(list));
|
||||
}
|
||||
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||||
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 });
|
||||
|
||||
}));
|
||||
+1
File diff suppressed because one or more lines are too long
+40
@@ -0,0 +1,40 @@
|
||||
{
|
||||
"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"
|
||||
}
|
||||
}
|
||||
+682
@@ -0,0 +1,682 @@
|
||||
|
||||
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};
|
||||
}
|
||||
Reference in New Issue
Block a user