├── .github └── workflows │ └── node.yml ├── .gitignore ├── LICENSE ├── README.md ├── bench ├── basic.js └── bench.js ├── eslint.config.js ├── package-lock.json ├── package.json ├── rollup.config.js ├── src └── earcut.js ├── test ├── expected.json ├── fixtures │ ├── bad-diagonals.json │ ├── bad-hole.json │ ├── boxy.json │ ├── building.json │ ├── collinear-diagonal.json │ ├── degenerate.json │ ├── dude.json │ ├── eberly-3.json │ ├── eberly-6.json │ ├── empty-square.json │ ├── filtered-bridge-jhl.json │ ├── hilbert.json │ ├── hole-touching-outer.json │ ├── hourglass.json │ ├── infinite-loop-jhl.json │ ├── issue107.json │ ├── issue111.json │ ├── issue119.json │ ├── issue131.json │ ├── issue142.json │ ├── issue149.json │ ├── issue16.json │ ├── issue17.json │ ├── issue29.json │ ├── issue34.json │ ├── issue35.json │ ├── issue45.json │ ├── issue52.json │ ├── issue83.json │ ├── outside-ring.json │ ├── rain.json │ ├── self-touching.json │ ├── shared-points.json │ ├── simplified-us-border.json │ ├── steiner.json │ ├── touching-holes.json │ ├── touching-holes2.json │ ├── touching-holes3.json │ ├── touching-holes4.json │ ├── touching-holes5.json │ ├── touching-holes6.json │ ├── touching2.json │ ├── touching3.json │ ├── touching4.json │ ├── water-huge.json │ ├── water-huge2.json │ ├── water.json │ ├── water2.json │ ├── water3.json │ ├── water3b.json │ └── water4.json └── test.js └── viz ├── index.html └── viz.js /.github/workflows/node.yml: -------------------------------------------------------------------------------- 1 | name: Node 2 | on: [push, pull_request] 3 | jobs: 4 | test: 5 | runs-on: ubuntu-latest 6 | steps: 7 | - name: Checkout 8 | uses: actions/checkout@v4 9 | 10 | - name: Setup Node 11 | uses: actions/setup-node@v4 12 | with: 13 | node-version: 20 14 | 15 | - name: Install dependencies 16 | run: npm ci 17 | 18 | - name: Build the bundle 19 | run: npm run build 20 | 21 | - name: Run tests 22 | run: npm test 23 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | coverage 2 | node_modules 3 | dist 4 | *.log 5 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | ISC License 2 | 3 | Copyright (c) 2024, Mapbox 4 | 5 | Permission to use, copy, modify, and/or distribute this software for any purpose 6 | with or without fee is hereby granted, provided that the above copyright notice 7 | and this permission notice appear in all copies. 8 | 9 | THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH 10 | REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND 11 | FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, 12 | INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS 13 | OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER 14 | TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF 15 | THIS SOFTWARE. 16 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | ## Earcut 2 | 3 | The fastest and smallest JavaScript polygon triangulation library. 3KB gzipped. 4 | 5 | [![Node](https://github.com/mapbox/earcut/actions/workflows/node.yml/badge.svg)](https://github.com/mapbox/earcut/actions/workflows/node.yml) 6 | [![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") 7 | [![Percentage of issues still open](http://isitmaintained.com/badge/open/mapbox/earcut.svg)](http://isitmaintained.com/project/mapbox/earcut "Percentage of issues still open") 8 | [![](https://img.shields.io/badge/simply-awesome-brightgreen.svg)](https://github.com/mourner/projects) 9 | 10 | #### The algorithm 11 | 12 | The library implements a modified ear slicing algorithm, 13 | optimized by [z-order curve](http://en.wikipedia.org/wiki/Z-order_curve) hashing 14 | and extended to handle holes, twisted polygons, degeneracies and self-intersections 15 | in a way that doesn't _guarantee_ correctness of triangulation, 16 | but attempts to always produce acceptable results for practical data. 17 | 18 | It's based on ideas from 19 | [FIST: Fast Industrial-Strength Triangulation of Polygons](http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html) by Martin Held 20 | and [Triangulation by Ear Clipping](http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf) by David Eberly. 21 | 22 | #### Why another triangulation library? 23 | 24 | The aim of this project is to create a JS triangulation library 25 | that is **fast enough for real-time triangulation in the browser**, 26 | sacrificing triangulation quality for raw speed and simplicity, 27 | while being robust enough to handle most practical datasets without crashing or producing garbage. 28 | Some benchmarks using Node 0.12: 29 | 30 | (ops/sec) | pts | earcut | libtess | poly2tri | pnltri | polyk 31 | ------------------| ---- | --------- | -------- | -------- | --------- | ------ 32 | OSM building | 15 | _795,935_ | _50,640_ | _61,501_ | _122,966_ | _175,570_ 33 | dude shape | 94 | _35,658_ | _10,339_ | _8,784_ | _11,172_ | _13,557_ 34 | holed dude shape | 104 | _28,319_ | _8,883_ | _7,494_ | _2,130_ | n/a 35 | complex OSM water | 2523 | _543_ | _77.54_ | failure | failure | n/a 36 | huge OSM water | 5667 | _95_ | _29.30_ | failure | failure | n/a 37 | 38 | The original use case it was created for is [Mapbox GL](https://www.mapbox.com/mapbox-gl), WebGL-based interactive maps. 39 | 40 | If you want to get correct triangulation even on very bad data with lots of self-intersections 41 | and earcut is not precise enough, take a look at [libtess.js](https://github.com/brendankenny/libtess.js). 42 | 43 | #### Usage 44 | 45 | ```js 46 | const triangles = earcut([10,0, 0,50, 60,60, 70,10]); // returns [1,0,3, 3,2,1] 47 | ``` 48 | 49 | Signature: `earcut(vertices[, holes, dimensions = 2])`. 50 | 51 | * `vertices` is a flat array of vertex coordinates like `[x0,y0, x1,y1, x2,y2, ...]`. 52 | * `holes` is an array of hole _indices_ if any 53 | (e.g. `[5, 8]` for a 12-vertex input would mean one hole with vertices 5–7 and another with 8–11). 54 | * `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. 55 | 56 | Each group of three vertex indices in the resulting array forms a triangle. 57 | 58 | ```js 59 | // triangulating a polygon with a hole 60 | earcut([0,0, 100,0, 100,100, 0,100, 20,20, 80,20, 80,80, 20,80], [4]); 61 | // [3,0,4, 5,4,0, 3,4,7, 5,0,1, 2,3,7, 6,5,1, 2,7,6, 6,1,2] 62 | 63 | // triangulating a polygon with 3d coords 64 | earcut([10,0,1, 0,50,2, 60,60,3, 70,10,4], null, 3); 65 | // [1,0,3, 3,2,1] 66 | ``` 67 | 68 | If you pass a single vertex as a hole, Earcut treats it as a Steiner point. 69 | 70 | 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). 71 | 72 | If your input is a multi-dimensional array (e.g. [GeoJSON Polygon](http://geojson.org/geojson-spec.html#polygon)), 73 | you can convert it to the format expected by Earcut with `earcut.flatten`: 74 | 75 | ```js 76 | const data = earcut.flatten(geojson.geometry.coordinates); 77 | const triangles = earcut(data.vertices, data.holes, data.dimensions); 78 | ``` 79 | 80 | After getting a triangulation, you can verify its correctness with `earcut.deviation`: 81 | 82 | ```js 83 | const deviation = earcut.deviation(vertices, holes, dimensions, triangles); 84 | ``` 85 | 86 | Returns the relative difference between the total area of triangles and the area of the input polygon. 87 | `0` means the triangulation is fully correct. 88 | 89 | #### Install 90 | 91 | Install with NPM: `npm install earcut`, then import as a module: 92 | 93 | ```js 94 | import earcut from 'earcut'; 95 | ``` 96 | 97 | Or use as a module directly in the browser with [jsDelivr](https://www.jsdelivr.com/esm): 98 | 99 | ```html 100 | 103 | ``` 104 | 105 | Alternatively, there's a UMD browser bundle with an `earcut` global variable (exposing the main function as `earcut.default`): 106 | 107 | ```html 108 | 109 | ``` 110 | 111 | ![](https://cloud.githubusercontent.com/assets/25395/5778431/e8ec0c10-9da3-11e4-8d4e-a2ced6a7d2b7.png) 112 | 113 | #### Ports to other languages 114 | 115 | - [mapbox/earcut.hpp](https://github.com/mapbox/earcut.hpp) (C++11) 116 | - [JaffaKetchup/dart_earcut](https://github.com/JaffaKetchup/dart_earcut) (Dart) 117 | - [earcut4j/earcut4j](https://github.com/earcut4j/earcut4j) (Java) 118 | - [the3deers/earcut-java](https://github.com/the3deers/earcut-java) (Java) 119 | - [Larpon/earcut](https://github.com/Larpon/earcut) (V) 120 | - [Cawfree/earcut-j](https://github.com/Cawfree/earcut-j) (Java, outdated) 121 | - [measuredweighed/SwiftEarcut](https://github.com/measuredweighed/SwiftEarcut) (Swift) 122 | -------------------------------------------------------------------------------- /bench/basic.js: -------------------------------------------------------------------------------- 1 | import earcut, {flatten} from '../src/earcut.js'; 2 | import {readFileSync} from 'fs'; 3 | 4 | const data = JSON.parse(readFileSync(new URL('../test/fixtures/building.json', import.meta.url))); 5 | const {vertices, holes} = flatten(data); 6 | 7 | const start = performance.now(); 8 | let ops = 0; 9 | let passed = 0; 10 | 11 | do { 12 | earcut(vertices, holes); 13 | 14 | ops++; 15 | passed = performance.now() - start; 16 | } while (passed < 1000); 17 | 18 | console.log(`${Math.round(ops * 1000 / passed).toLocaleString()} ops/s`); 19 | -------------------------------------------------------------------------------- /bench/bench.js: -------------------------------------------------------------------------------- 1 | import earcut, {flatten} from '../src/earcut.js'; 2 | import Benchmark from 'benchmark'; 3 | import {readFileSync} from 'fs'; 4 | 5 | function withoutHoles({vertices, holes, dimensions}) { 6 | return { 7 | vertices: vertices.slice(0, holes[0] * dimensions), 8 | holes: [] 9 | }; 10 | } 11 | 12 | function getFixture(name) { 13 | return flatten(JSON.parse(readFileSync(new URL(`../test/fixtures/${name}`, import.meta.url)))); 14 | } 15 | 16 | const samples = { 17 | 'typical OSM building': getFixture('building.json'), 18 | 'dude shape': withoutHoles(getFixture('dude.json')), 19 | 'dude shape with holes': getFixture('dude.json'), 20 | 'complex OSM water': getFixture('water.json') 21 | }; 22 | 23 | for (const name in samples) { 24 | const {vertices, holes, dimensions} = samples[name]; 25 | new Benchmark.Suite() 26 | .add(`${name} (${vertices.length / 2} vertices):`, () => { 27 | earcut(vertices, holes, dimensions); 28 | }) 29 | .on('cycle', logCycle) 30 | .run(); 31 | } 32 | 33 | function logCycle(event) { 34 | console.log(String(event.target)); 35 | } 36 | -------------------------------------------------------------------------------- /eslint.config.js: -------------------------------------------------------------------------------- 1 | export {default} from 'eslint-config-mourner'; 2 | -------------------------------------------------------------------------------- /package.json: -------------------------------------------------------------------------------- 1 | { 2 | "name": "earcut", 3 | "version": "3.0.1", 4 | "description": "The fastest and smallest JavaScript polygon triangulation library for your WebGL apps", 5 | "main": "src/earcut.js", 6 | "type": "module", 7 | "exports": "./src/earcut.js", 8 | "files": [ 9 | "src/earcut.js", 10 | "dist/earcut.min.js", 11 | "dist/earcut.dev.js" 12 | ], 13 | "scripts": { 14 | "pretest": "eslint src test/test.js bench/*.js viz/viz.js", 15 | "test": "node --test", 16 | "build": "rollup -c", 17 | "prepublishOnly": "npm run build", 18 | "cov": "node --test --experimental-test-coverage" 19 | }, 20 | "author": "Vladimir Agafonkin", 21 | "license": "ISC", 22 | "devDependencies": { 23 | "@rollup/plugin-terser": "^0.4.4", 24 | "benchmark": "^2.1.4", 25 | "coveralls": "^3.1.1", 26 | "eslint": "^9.17.0", 27 | "eslint-config-mourner": "^4.0.2", 28 | "rollup": "^4.28.1", 29 | "uglify-js": "^3.19.3", 30 | "watchify": "^4.0.0" 31 | }, 32 | "eslintConfig": { 33 | "extends": "mourner", 34 | "parserOptions": { 35 | "sourceType": "module", 36 | "ecmaVersion": 2020 37 | } 38 | }, 39 | "repository": { 40 | "type": "git", 41 | "url": "git://github.com/mapbox/earcut.git" 42 | } 43 | } 44 | -------------------------------------------------------------------------------- /rollup.config.js: -------------------------------------------------------------------------------- 1 | import terser from '@rollup/plugin-terser'; 2 | 3 | const config = (file, plugins) => ({ 4 | input: 'src/earcut.js', 5 | output: { 6 | name: 'earcut', 7 | exports: 'named', 8 | format: 'umd', 9 | indent: false, 10 | file 11 | }, 12 | plugins 13 | }); 14 | 15 | export default [ 16 | config('dist/earcut.dev.js', []), 17 | config('dist/earcut.min.js', [terser()]) 18 | ]; 19 | -------------------------------------------------------------------------------- /src/earcut.js: -------------------------------------------------------------------------------- 1 | 2 | export default function earcut(data, holeIndices, dim = 2) { 3 | 4 | const hasHoles = holeIndices && holeIndices.length; 5 | const outerLen = hasHoles ? holeIndices[0] * dim : data.length; 6 | let outerNode = linkedList(data, 0, outerLen, dim, true); 7 | const triangles = []; 8 | 9 | if (!outerNode || outerNode.next === outerNode.prev) return triangles; 10 | 11 | let minX, minY, invSize; 12 | 13 | if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim); 14 | 15 | // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox 16 | if (data.length > 80 * dim) { 17 | minX = Infinity; 18 | minY = Infinity; 19 | let maxX = -Infinity; 20 | let maxY = -Infinity; 21 | 22 | for (let i = dim; i < outerLen; i += dim) { 23 | const x = data[i]; 24 | const y = data[i + 1]; 25 | if (x < minX) minX = x; 26 | if (y < minY) minY = y; 27 | if (x > maxX) maxX = x; 28 | if (y > maxY) maxY = y; 29 | } 30 | 31 | // minX, minY and invSize are later used to transform coords into integers for z-order calculation 32 | invSize = Math.max(maxX - minX, maxY - minY); 33 | invSize = invSize !== 0 ? 32767 / invSize : 0; 34 | } 35 | 36 | earcutLinked(outerNode, triangles, dim, minX, minY, invSize, 0); 37 | 38 | return triangles; 39 | } 40 | 41 | // create a circular doubly linked list from polygon points in the specified winding order 42 | function linkedList(data, start, end, dim, clockwise) { 43 | let last; 44 | 45 | if (clockwise === (signedArea(data, start, end, dim) > 0)) { 46 | for (let i = start; i < end; i += dim) last = insertNode(i / dim | 0, data[i], data[i + 1], last); 47 | } else { 48 | for (let i = end - dim; i >= start; i -= dim) last = insertNode(i / dim | 0, data[i], data[i + 1], last); 49 | } 50 | 51 | if (last && equals(last, last.next)) { 52 | removeNode(last); 53 | last = last.next; 54 | } 55 | 56 | return last; 57 | } 58 | 59 | // eliminate colinear or duplicate points 60 | function filterPoints(start, end) { 61 | if (!start) return start; 62 | if (!end) end = start; 63 | 64 | let p = start, 65 | again; 66 | do { 67 | again = false; 68 | 69 | if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) { 70 | removeNode(p); 71 | p = end = p.prev; 72 | if (p === p.next) break; 73 | again = true; 74 | 75 | } else { 76 | p = p.next; 77 | } 78 | } while (again || p !== end); 79 | 80 | return end; 81 | } 82 | 83 | // main ear slicing loop which triangulates a polygon (given as a linked list) 84 | function earcutLinked(ear, triangles, dim, minX, minY, invSize, pass) { 85 | if (!ear) return; 86 | 87 | // interlink polygon nodes in z-order 88 | if (!pass && invSize) indexCurve(ear, minX, minY, invSize); 89 | 90 | let stop = ear; 91 | 92 | // iterate through ears, slicing them one by one 93 | while (ear.prev !== ear.next) { 94 | const prev = ear.prev; 95 | const next = ear.next; 96 | 97 | if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) { 98 | triangles.push(prev.i, ear.i, next.i); // cut off the triangle 99 | 100 | removeNode(ear); 101 | 102 | // skipping the next vertex leads to less sliver triangles 103 | ear = next.next; 104 | stop = next.next; 105 | 106 | continue; 107 | } 108 | 109 | ear = next; 110 | 111 | // if we looped through the whole remaining polygon and can't find any more ears 112 | if (ear === stop) { 113 | // try filtering points and slicing again 114 | if (!pass) { 115 | earcutLinked(filterPoints(ear), triangles, dim, minX, minY, invSize, 1); 116 | 117 | // if this didn't work, try curing all small self-intersections locally 118 | } else if (pass === 1) { 119 | ear = cureLocalIntersections(filterPoints(ear), triangles); 120 | earcutLinked(ear, triangles, dim, minX, minY, invSize, 2); 121 | 122 | // as a last resort, try splitting the remaining polygon into two 123 | } else if (pass === 2) { 124 | splitEarcut(ear, triangles, dim, minX, minY, invSize); 125 | } 126 | 127 | break; 128 | } 129 | } 130 | } 131 | 132 | // check whether a polygon node forms a valid ear with adjacent nodes 133 | function isEar(ear) { 134 | const a = ear.prev, 135 | b = ear, 136 | c = ear.next; 137 | 138 | if (area(a, b, c) >= 0) return false; // reflex, can't be an ear 139 | 140 | // now make sure we don't have other points inside the potential ear 141 | const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y; 142 | 143 | // triangle bbox 144 | const x0 = Math.min(ax, bx, cx), 145 | y0 = Math.min(ay, by, cy), 146 | x1 = Math.max(ax, bx, cx), 147 | y1 = Math.max(ay, by, cy); 148 | 149 | let p = c.next; 150 | while (p !== a) { 151 | if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && 152 | pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && 153 | area(p.prev, p, p.next) >= 0) return false; 154 | p = p.next; 155 | } 156 | 157 | return true; 158 | } 159 | 160 | function isEarHashed(ear, minX, minY, invSize) { 161 | const a = ear.prev, 162 | b = ear, 163 | c = ear.next; 164 | 165 | if (area(a, b, c) >= 0) return false; // reflex, can't be an ear 166 | 167 | const ax = a.x, bx = b.x, cx = c.x, ay = a.y, by = b.y, cy = c.y; 168 | 169 | // triangle bbox 170 | const x0 = Math.min(ax, bx, cx), 171 | y0 = Math.min(ay, by, cy), 172 | x1 = Math.max(ax, bx, cx), 173 | y1 = Math.max(ay, by, cy); 174 | 175 | // z-order range for the current triangle bbox; 176 | const minZ = zOrder(x0, y0, minX, minY, invSize), 177 | maxZ = zOrder(x1, y1, minX, minY, invSize); 178 | 179 | let p = ear.prevZ, 180 | n = ear.nextZ; 181 | 182 | // look for points inside the triangle in both directions 183 | while (p && p.z >= minZ && n && n.z <= maxZ) { 184 | if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c && 185 | pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false; 186 | p = p.prevZ; 187 | 188 | if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c && 189 | pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false; 190 | n = n.nextZ; 191 | } 192 | 193 | // look for remaining points in decreasing z-order 194 | while (p && p.z >= minZ) { 195 | if (p.x >= x0 && p.x <= x1 && p.y >= y0 && p.y <= y1 && p !== a && p !== c && 196 | pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, p.x, p.y) && area(p.prev, p, p.next) >= 0) return false; 197 | p = p.prevZ; 198 | } 199 | 200 | // look for remaining points in increasing z-order 201 | while (n && n.z <= maxZ) { 202 | if (n.x >= x0 && n.x <= x1 && n.y >= y0 && n.y <= y1 && n !== a && n !== c && 203 | pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, n.x, n.y) && area(n.prev, n, n.next) >= 0) return false; 204 | n = n.nextZ; 205 | } 206 | 207 | return true; 208 | } 209 | 210 | // go through all polygon nodes and cure small local self-intersections 211 | function cureLocalIntersections(start, triangles) { 212 | let p = start; 213 | do { 214 | const a = p.prev, 215 | b = p.next.next; 216 | 217 | if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) { 218 | 219 | triangles.push(a.i, p.i, b.i); 220 | 221 | // remove two nodes involved 222 | removeNode(p); 223 | removeNode(p.next); 224 | 225 | p = start = b; 226 | } 227 | p = p.next; 228 | } while (p !== start); 229 | 230 | return filterPoints(p); 231 | } 232 | 233 | // try splitting polygon into two and triangulate them independently 234 | function splitEarcut(start, triangles, dim, minX, minY, invSize) { 235 | // look for a valid diagonal that divides the polygon into two 236 | let a = start; 237 | do { 238 | let b = a.next.next; 239 | while (b !== a.prev) { 240 | if (a.i !== b.i && isValidDiagonal(a, b)) { 241 | // split the polygon in two by the diagonal 242 | let c = splitPolygon(a, b); 243 | 244 | // filter colinear points around the cuts 245 | a = filterPoints(a, a.next); 246 | c = filterPoints(c, c.next); 247 | 248 | // run earcut on each half 249 | earcutLinked(a, triangles, dim, minX, minY, invSize, 0); 250 | earcutLinked(c, triangles, dim, minX, minY, invSize, 0); 251 | return; 252 | } 253 | b = b.next; 254 | } 255 | a = a.next; 256 | } while (a !== start); 257 | } 258 | 259 | // link every hole into the outer loop, producing a single-ring polygon without holes 260 | function eliminateHoles(data, holeIndices, outerNode, dim) { 261 | const queue = []; 262 | 263 | for (let i = 0, len = holeIndices.length; i < len; i++) { 264 | const start = holeIndices[i] * dim; 265 | const end = i < len - 1 ? holeIndices[i + 1] * dim : data.length; 266 | const list = linkedList(data, start, end, dim, false); 267 | if (list === list.next) list.steiner = true; 268 | queue.push(getLeftmost(list)); 269 | } 270 | 271 | queue.sort(compareXYSlope); 272 | 273 | // process holes from left to right 274 | for (let i = 0; i < queue.length; i++) { 275 | outerNode = eliminateHole(queue[i], outerNode); 276 | } 277 | 278 | return outerNode; 279 | } 280 | 281 | function compareXYSlope(a, b) { 282 | let result = a.x - b.x; 283 | // when the left-most point of 2 holes meet at a vertex, sort the holes counterclockwise so that when we find 284 | // the bridge to the outer shell is always the point that they meet at. 285 | if (result === 0) { 286 | result = a.y - b.y; 287 | if (result === 0) { 288 | const aSlope = (a.next.y - a.y) / (a.next.x - a.x); 289 | const bSlope = (b.next.y - b.y) / (b.next.x - b.x); 290 | result = aSlope - bSlope; 291 | } 292 | } 293 | return result; 294 | } 295 | 296 | // find a bridge between vertices that connects hole with an outer ring and and link it 297 | function eliminateHole(hole, outerNode) { 298 | const bridge = findHoleBridge(hole, outerNode); 299 | if (!bridge) { 300 | return outerNode; 301 | } 302 | 303 | const bridgeReverse = splitPolygon(bridge, hole); 304 | 305 | // filter collinear points around the cuts 306 | filterPoints(bridgeReverse, bridgeReverse.next); 307 | return filterPoints(bridge, bridge.next); 308 | } 309 | 310 | // David Eberly's algorithm for finding a bridge between hole and outer polygon 311 | function findHoleBridge(hole, outerNode) { 312 | let p = outerNode; 313 | const hx = hole.x; 314 | const hy = hole.y; 315 | let qx = -Infinity; 316 | let m; 317 | 318 | // find a segment intersected by a ray from the hole's leftmost point to the left; 319 | // segment's endpoint with lesser x will be potential connection point 320 | // unless they intersect at a vertex, then choose the vertex 321 | if (equals(hole, p)) return p; 322 | do { 323 | if (equals(hole, p.next)) return p.next; 324 | else if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) { 325 | const x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y); 326 | if (x <= hx && x > qx) { 327 | qx = x; 328 | m = p.x < p.next.x ? p : p.next; 329 | if (x === hx) return m; // hole touches outer segment; pick leftmost endpoint 330 | } 331 | } 332 | p = p.next; 333 | } while (p !== outerNode); 334 | 335 | if (!m) return null; 336 | 337 | // look for points inside the triangle of hole point, segment intersection and endpoint; 338 | // if there are no points found, we have a valid connection; 339 | // otherwise choose the point of the minimum angle with the ray as connection point 340 | 341 | const stop = m; 342 | const mx = m.x; 343 | const my = m.y; 344 | let tanMin = Infinity; 345 | 346 | p = m; 347 | 348 | do { 349 | if (hx >= p.x && p.x >= mx && hx !== p.x && 350 | pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) { 351 | 352 | const tan = Math.abs(hy - p.y) / (hx - p.x); // tangential 353 | 354 | if (locallyInside(p, hole) && 355 | (tan < tanMin || (tan === tanMin && (p.x > m.x || (p.x === m.x && sectorContainsSector(m, p)))))) { 356 | m = p; 357 | tanMin = tan; 358 | } 359 | } 360 | 361 | p = p.next; 362 | } while (p !== stop); 363 | 364 | return m; 365 | } 366 | 367 | // whether sector in vertex m contains sector in vertex p in the same coordinates 368 | function sectorContainsSector(m, p) { 369 | return area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0; 370 | } 371 | 372 | // interlink polygon nodes in z-order 373 | function indexCurve(start, minX, minY, invSize) { 374 | let p = start; 375 | do { 376 | if (p.z === 0) p.z = zOrder(p.x, p.y, minX, minY, invSize); 377 | p.prevZ = p.prev; 378 | p.nextZ = p.next; 379 | p = p.next; 380 | } while (p !== start); 381 | 382 | p.prevZ.nextZ = null; 383 | p.prevZ = null; 384 | 385 | sortLinked(p); 386 | } 387 | 388 | // Simon Tatham's linked list merge sort algorithm 389 | // http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html 390 | function sortLinked(list) { 391 | let numMerges; 392 | let inSize = 1; 393 | 394 | do { 395 | let p = list; 396 | let e; 397 | list = null; 398 | let tail = null; 399 | numMerges = 0; 400 | 401 | while (p) { 402 | numMerges++; 403 | let q = p; 404 | let pSize = 0; 405 | for (let i = 0; i < inSize; i++) { 406 | pSize++; 407 | q = q.nextZ; 408 | if (!q) break; 409 | } 410 | let qSize = inSize; 411 | 412 | while (pSize > 0 || (qSize > 0 && q)) { 413 | 414 | if (pSize !== 0 && (qSize === 0 || !q || p.z <= q.z)) { 415 | e = p; 416 | p = p.nextZ; 417 | pSize--; 418 | } else { 419 | e = q; 420 | q = q.nextZ; 421 | qSize--; 422 | } 423 | 424 | if (tail) tail.nextZ = e; 425 | else list = e; 426 | 427 | e.prevZ = tail; 428 | tail = e; 429 | } 430 | 431 | p = q; 432 | } 433 | 434 | tail.nextZ = null; 435 | inSize *= 2; 436 | 437 | } while (numMerges > 1); 438 | 439 | return list; 440 | } 441 | 442 | // z-order of a point given coords and inverse of the longer side of data bbox 443 | function zOrder(x, y, minX, minY, invSize) { 444 | // coords are transformed into non-negative 15-bit integer range 445 | x = (x - minX) * invSize | 0; 446 | y = (y - minY) * invSize | 0; 447 | 448 | x = (x | (x << 8)) & 0x00FF00FF; 449 | x = (x | (x << 4)) & 0x0F0F0F0F; 450 | x = (x | (x << 2)) & 0x33333333; 451 | x = (x | (x << 1)) & 0x55555555; 452 | 453 | y = (y | (y << 8)) & 0x00FF00FF; 454 | y = (y | (y << 4)) & 0x0F0F0F0F; 455 | y = (y | (y << 2)) & 0x33333333; 456 | y = (y | (y << 1)) & 0x55555555; 457 | 458 | return x | (y << 1); 459 | } 460 | 461 | // find the leftmost node of a polygon ring 462 | function getLeftmost(start) { 463 | let p = start, 464 | leftmost = start; 465 | do { 466 | if (p.x < leftmost.x || (p.x === leftmost.x && p.y < leftmost.y)) leftmost = p; 467 | p = p.next; 468 | } while (p !== start); 469 | 470 | return leftmost; 471 | } 472 | 473 | // check if a point lies within a convex triangle 474 | function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) { 475 | return (cx - px) * (ay - py) >= (ax - px) * (cy - py) && 476 | (ax - px) * (by - py) >= (bx - px) * (ay - py) && 477 | (bx - px) * (cy - py) >= (cx - px) * (by - py); 478 | } 479 | 480 | // check if a point lies within a convex triangle but false if its equal to the first point of the triangle 481 | function pointInTriangleExceptFirst(ax, ay, bx, by, cx, cy, px, py) { 482 | return !(ax === px && ay === py) && pointInTriangle(ax, ay, bx, by, cx, cy, px, py); 483 | } 484 | 485 | // check if a diagonal between two polygon nodes is valid (lies in polygon interior) 486 | function isValidDiagonal(a, b) { 487 | return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) && // doesn't intersect other edges 488 | (locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b) && // locally visible 489 | (area(a.prev, a, b.prev) || area(a, b.prev, b)) || // does not create opposite-facing sectors 490 | equals(a, b) && area(a.prev, a, a.next) > 0 && area(b.prev, b, b.next) > 0); // special zero-length case 491 | } 492 | 493 | // signed area of a triangle 494 | function area(p, q, r) { 495 | return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y); 496 | } 497 | 498 | // check if two points are equal 499 | function equals(p1, p2) { 500 | return p1.x === p2.x && p1.y === p2.y; 501 | } 502 | 503 | // check if two segments intersect 504 | function intersects(p1, q1, p2, q2) { 505 | const o1 = sign(area(p1, q1, p2)); 506 | const o2 = sign(area(p1, q1, q2)); 507 | const o3 = sign(area(p2, q2, p1)); 508 | const o4 = sign(area(p2, q2, q1)); 509 | 510 | if (o1 !== o2 && o3 !== o4) return true; // general case 511 | 512 | if (o1 === 0 && onSegment(p1, p2, q1)) return true; // p1, q1 and p2 are collinear and p2 lies on p1q1 513 | if (o2 === 0 && onSegment(p1, q2, q1)) return true; // p1, q1 and q2 are collinear and q2 lies on p1q1 514 | if (o3 === 0 && onSegment(p2, p1, q2)) return true; // p2, q2 and p1 are collinear and p1 lies on p2q2 515 | if (o4 === 0 && onSegment(p2, q1, q2)) return true; // p2, q2 and q1 are collinear and q1 lies on p2q2 516 | 517 | return false; 518 | } 519 | 520 | // for collinear points p, q, r, check if point q lies on segment pr 521 | function onSegment(p, q, r) { 522 | 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); 523 | } 524 | 525 | function sign(num) { 526 | return num > 0 ? 1 : num < 0 ? -1 : 0; 527 | } 528 | 529 | // check if a polygon diagonal intersects any polygon segments 530 | function intersectsPolygon(a, b) { 531 | let p = a; 532 | do { 533 | if (p.i !== a.i && p.next.i !== a.i && p.i !== b.i && p.next.i !== b.i && 534 | intersects(p, p.next, a, b)) return true; 535 | p = p.next; 536 | } while (p !== a); 537 | 538 | return false; 539 | } 540 | 541 | // check if a polygon diagonal is locally inside the polygon 542 | function locallyInside(a, b) { 543 | return area(a.prev, a, a.next) < 0 ? 544 | area(a, b, a.next) >= 0 && area(a, a.prev, b) >= 0 : 545 | area(a, b, a.prev) < 0 || area(a, a.next, b) < 0; 546 | } 547 | 548 | // check if the middle point of a polygon diagonal is inside the polygon 549 | function middleInside(a, b) { 550 | let p = a; 551 | let inside = false; 552 | const px = (a.x + b.x) / 2; 553 | const py = (a.y + b.y) / 2; 554 | do { 555 | if (((p.y > py) !== (p.next.y > py)) && p.next.y !== p.y && 556 | (px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x)) 557 | inside = !inside; 558 | p = p.next; 559 | } while (p !== a); 560 | 561 | return inside; 562 | } 563 | 564 | // link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two; 565 | // if one belongs to the outer ring and another to a hole, it merges it into a single ring 566 | function splitPolygon(a, b) { 567 | const a2 = createNode(a.i, a.x, a.y), 568 | b2 = createNode(b.i, b.x, b.y), 569 | an = a.next, 570 | bp = b.prev; 571 | 572 | a.next = b; 573 | b.prev = a; 574 | 575 | a2.next = an; 576 | an.prev = a2; 577 | 578 | b2.next = a2; 579 | a2.prev = b2; 580 | 581 | bp.next = b2; 582 | b2.prev = bp; 583 | 584 | return b2; 585 | } 586 | 587 | // create a node and optionally link it with previous one (in a circular doubly linked list) 588 | function insertNode(i, x, y, last) { 589 | const p = createNode(i, x, y); 590 | 591 | if (!last) { 592 | p.prev = p; 593 | p.next = p; 594 | 595 | } else { 596 | p.next = last.next; 597 | p.prev = last; 598 | last.next.prev = p; 599 | last.next = p; 600 | } 601 | return p; 602 | } 603 | 604 | function removeNode(p) { 605 | p.next.prev = p.prev; 606 | p.prev.next = p.next; 607 | 608 | if (p.prevZ) p.prevZ.nextZ = p.nextZ; 609 | if (p.nextZ) p.nextZ.prevZ = p.prevZ; 610 | } 611 | 612 | function createNode(i, x, y) { 613 | return { 614 | i, // vertex index in coordinates array 615 | x, y, // vertex coordinates 616 | prev: null, // previous and next vertex nodes in a polygon ring 617 | next: null, 618 | z: 0, // z-order curve value 619 | prevZ: null, // previous and next nodes in z-order 620 | nextZ: null, 621 | steiner: false // indicates whether this is a steiner point 622 | }; 623 | } 624 | 625 | // return a percentage difference between the polygon area and its triangulation area; 626 | // used to verify correctness of triangulation 627 | export function deviation(data, holeIndices, dim, triangles) { 628 | const hasHoles = holeIndices && holeIndices.length; 629 | const outerLen = hasHoles ? holeIndices[0] * dim : data.length; 630 | 631 | let polygonArea = Math.abs(signedArea(data, 0, outerLen, dim)); 632 | if (hasHoles) { 633 | for (let i = 0, len = holeIndices.length; i < len; i++) { 634 | const start = holeIndices[i] * dim; 635 | const end = i < len - 1 ? holeIndices[i + 1] * dim : data.length; 636 | polygonArea -= Math.abs(signedArea(data, start, end, dim)); 637 | } 638 | } 639 | 640 | let trianglesArea = 0; 641 | for (let i = 0; i < triangles.length; i += 3) { 642 | const a = triangles[i] * dim; 643 | const b = triangles[i + 1] * dim; 644 | const c = triangles[i + 2] * dim; 645 | trianglesArea += Math.abs( 646 | (data[a] - data[c]) * (data[b + 1] - data[a + 1]) - 647 | (data[a] - data[b]) * (data[c + 1] - data[a + 1])); 648 | } 649 | 650 | return polygonArea === 0 && trianglesArea === 0 ? 0 : 651 | Math.abs((trianglesArea - polygonArea) / polygonArea); 652 | } 653 | 654 | function signedArea(data, start, end, dim) { 655 | let sum = 0; 656 | for (let i = start, j = end - dim; i < end; i += dim) { 657 | sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]); 658 | j = i; 659 | } 660 | return sum; 661 | } 662 | 663 | // turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts 664 | export function flatten(data) { 665 | const vertices = []; 666 | const holes = []; 667 | const dimensions = data[0][0].length; 668 | let holeIndex = 0; 669 | let prevLen = 0; 670 | 671 | for (const ring of data) { 672 | for (const p of ring) { 673 | for (let d = 0; d < dimensions; d++) vertices.push(p[d]); 674 | } 675 | if (prevLen) { 676 | holeIndex += prevLen; 677 | holes.push(holeIndex); 678 | } 679 | prevLen = ring.length; 680 | } 681 | return {vertices, holes, dimensions}; 682 | } 683 | -------------------------------------------------------------------------------- /test/expected.json: -------------------------------------------------------------------------------- 1 | { 2 | "triangles": { 3 | "building": 13, 4 | "dude": 106, 5 | "water": 2482, 6 | "water2": 1212, 7 | "water3": 197, 8 | "water3b": 25, 9 | "water4": 705, 10 | "water-huge": 5176, 11 | "water-huge2": 4462, 12 | "degenerate": 0, 13 | "bad-hole": 42, 14 | "empty-square": 0, 15 | "issue16": 12, 16 | "issue17": 11, 17 | "steiner": 9, 18 | "issue29": 40, 19 | "issue34": 139, 20 | "issue35": 844, 21 | "self-touching": 124, 22 | "outside-ring": 64, 23 | "simplified-us-border": 120, 24 | "touching-holes": 57, 25 | "touching-holes2": 10, 26 | "touching-holes3": 82, 27 | "touching-holes4": 55, 28 | "touching-holes5": 133, 29 | "touching-holes6": 3098, 30 | "hole-touching-outer": 77, 31 | "hilbert": 1024, 32 | "issue45": 10, 33 | "eberly-3": 73, 34 | "eberly-6": 1429, 35 | "issue52": 109, 36 | "shared-points": 4, 37 | "bad-diagonals": 7, 38 | "issue83": 0, 39 | "issue107": 0, 40 | "issue111": 18, 41 | "boxy": 58, 42 | "collinear-diagonal": 14, 43 | "issue119": 18, 44 | "hourglass": 2, 45 | "touching2": 8, 46 | "touching3": 15, 47 | "touching4": 19, 48 | "rain": 2681, 49 | "issue131": 12, 50 | "infinite-loop-jhl": 0, 51 | "filtered-bridge-jhl": 25, 52 | "issue149": 2, 53 | "issue142": 4 54 | }, 55 | "errors": { 56 | "dude": 2e-15, 57 | "water": 0.0008, 58 | "water-huge": 0.0011, 59 | "water-huge2": 0.004, 60 | "bad-hole": 0.019, 61 | "issue16": 4e-16, 62 | "issue17": 2e-16, 63 | "issue29": 2e-15, 64 | "self-touching": 2e-13, 65 | "eberly-6": 2e-14, 66 | "issue142": 0.13 67 | }, 68 | "errors-with-rotation": { 69 | "water-huge": 0.0035, 70 | "water-huge2": 0.061, 71 | "bad-hole": 0.04, 72 | "issue16": 8e-16 73 | } 74 | } -------------------------------------------------------------------------------- /test/fixtures/bad-diagonals.json: -------------------------------------------------------------------------------- 1 | [[[440,4152],[440,4208],[296,4192],[368,4192],[400,4200],[400,4176],[368,4192],[296,4192],[264,4200],[288,4160],[296,4192]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/bad-hole.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[810,2828],[818,2828],[832,2818],[844,2806],[855,2808],[866,2816],[867,2824],[876,2827],[883,2834],[875,2834],[867,2840],[878,2838],[889,2844],[880,2847],[870,2847],[860,2864],[852,2879],[847,2867],[810,2828],[810,2828]], 3 | [[818,2834],[823,2833],[831,2828],[839,2829],[839,2837],[851,2845],[847,2835],[846,2827],[847,2827],[837,2827],[840,2815],[835,2823],[818,2834],[818,2834]], 4 | [[857,2846],[864,2850],[866,2839],[857,2846],[857,2846]], 5 | [[848,2863],[848,2866],[854,2852],[846,2854],[847,2862],[838,2851],[838,2859],[848,2863],[848,2863]] 6 | ] 7 | -------------------------------------------------------------------------------- /test/fixtures/boxy.json: -------------------------------------------------------------------------------- 1 | [[[3432,2779],[3432,2794],[3450,2794],[3450,2825],[3413,2825],[3413,2856],[3395,2856],[3395,2871],[3377,2871],[3377,2856],[3359,2856],[3359,2840],[3341,2840],[3341,2871],[3322,2871],[3322,2887],[3249,2887],[3249,2871],[3268,2871],[3268,2840],[3304,2840],[3304,2825],[3322,2825],[3322,2810],[3304,2810],[3304,2794],[3322,2794],[3322,2779],[3341,2779],[3341,2733],[3359,2733],[3359,2687],[3395,2687],[3395,2702],[3432,2702],[3432,2717],[3450,2717],[3450,2733],[3486,2733],[3486,2748],[3468,2748],[3468,2763],[3450,2763],[3450,2779],[3432,2779]],[[3359,2794],[3341,2794],[3341,2810],[3395,2810],[3395,2794],[3377,2794],[3377,2779],[3359,2779],[3359,2794]],[[3432,2779],[3432,2748],[3413,2748],[3413,2779],[3432,2779]],[[3377,2779],[3395,2779],[3395,2748],[3377,2748],[3377,2779]],[[3377,2717],[3395,2717],[3395,2702],[3377,2702],[3377,2717]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/building.json: -------------------------------------------------------------------------------- 1 | [[[661,112],[661,96],[666,96],[666,87],[743,87],[771,87],[771,114],[750,114],[750,113],[742,113],[742,106],[710,106],[710,113],[666,113],[666,112]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/collinear-diagonal.json: -------------------------------------------------------------------------------- 1 | [[[3468,1913],[3486,1884],[3413,1869],[3322,1869],[3413,1854],[3413,1869],[3486,1869],[3486,1884],[3504,1884],[3504,1869],[3432,1869],[3432,1854],[3395,1854],[3432,1839],[3432,1854],[3450,1839],[3341,1839],[3341,1825],[3195,1825],[3341,1810],[3341,1825],[3450,1825],[3523,1854],[3523,1913]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/degenerate.json: -------------------------------------------------------------------------------- 1 | [[[100,100],[100,100],[200,100],[200,200],[200,100],[0,100]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/dude.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[280.35714, 648.79075],[286.78571, 662.8979],[263.28607, 661.17871],[262.31092, 671.41548],[250.53571, 677.00504],[250.53571, 683.43361],[256.42857, 685.21933],[297.14286, 669.50504],[289.28571, 649.50504],[285, 631.6479],[285, 608.79075],[292.85714, 585.21932],[306.42857, 563.79075],[323.57143, 548.79075],[339.28571, 545.21932],[357.85714, 547.36218],[375, 550.21932],[391.42857, 568.07647],[404.28571, 588.79075],[413.57143, 612.36218],[417.14286, 628.07647],[438.57143, 619.1479],[438.03572, 618.96932],[437.5, 609.50504],[426.96429, 609.86218],[424.64286, 615.57647],[419.82143, 615.04075],[420.35714, 605.04075],[428.39286, 598.43361],[437.85714, 599.68361],[443.57143, 613.79075],[450.71429, 610.21933],[431.42857, 575.21932],[405.71429, 550.21932],[372.85714, 534.50504],[349.28571, 531.6479],[346.42857, 521.6479],[346.42857, 511.6479],[350.71429, 496.6479],[367.85714, 476.6479],[377.14286, 460.93361],[385.71429, 445.21932],[388.57143, 404.50504],[360, 352.36218],[337.14286, 325.93361],[330.71429, 334.50504],[347.14286, 354.50504],[337.85714, 370.21932],[333.57143, 359.50504],[319.28571, 353.07647],[312.85714, 366.6479],[350.71429, 387.36218],[368.57143, 408.07647],[375.71429, 431.6479],[372.14286, 454.50504],[366.42857, 462.36218],[352.85714, 462.36218],[336.42857, 456.6479],[332.85714, 438.79075],[338.57143, 423.79075],[338.57143, 411.6479],[327.85714, 405.93361],[320.71429, 407.36218],[315.71429, 423.07647],[314.28571, 440.21932],[325, 447.71932],[324.82143, 460.93361],[317.85714, 470.57647],[304.28571, 483.79075],[287.14286, 491.29075],[263.03571, 498.61218],[251.60714, 503.07647],[251.25, 533.61218],[260.71429, 533.61218],[272.85714, 528.43361],[286.07143, 518.61218],[297.32143, 508.25504],[297.85714, 507.36218],[298.39286, 506.46932],[307.14286, 496.6479],[312.67857, 491.6479],[317.32143, 503.07647],[322.5, 514.1479],[325.53571, 521.11218],[327.14286, 525.75504],[326.96429, 535.04075],[311.78571, 540.04075],[291.07143, 552.71932],[274.82143, 568.43361],[259.10714, 592.8979],[254.28571, 604.50504],[251.07143, 621.11218],[250.53571, 649.1479],[268.1955, 654.36208]], 3 | [[325, 437], [320, 423], [329, 413], [332, 423]], 4 | [[320.72342, 480], [338.90617, 465.96863], [347.99754, 480.61584], [329.8148, 510.41534], [339.91632, 480.11077], [334.86556, 478.09046]] 5 | ] 6 | -------------------------------------------------------------------------------- /test/fixtures/eberly-3.json: -------------------------------------------------------------------------------- 1 | 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-------------------------------------------------------------------------------- /test/fixtures/eberly-6.json: -------------------------------------------------------------------------------- 1 | [ 2 | 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2 | -------------------------------------------------------------------------------- /test/fixtures/hole-touching-outer.json: -------------------------------------------------------------------------------- 1 | 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-------------------------------------------------------------------------------- /test/fixtures/hourglass.json: -------------------------------------------------------------------------------- 1 | [[[7,18],[7,15],[5,15],[7,13],[7,15],[17,17]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/infinite-loop-jhl.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[-1.0, 2.0], [0.0, 0.0], [2.0, -1.0]], 3 | [[2.0, -1.0], [0.0, 1.0e-28], [-1.0, 2.0]] 4 | ] 5 | -------------------------------------------------------------------------------- /test/fixtures/issue107.json: -------------------------------------------------------------------------------- 1 | [ 2 | [ 3 | [7.943741826741378, 46.46223436733343], 4 | [7.943741826741378, 46.43293749233343], 5 | [7.943741826741378, 46.46223436733343] 6 | ], 7 | [ 8 | [7.973038701741378, 46.46223436733343], 9 | [8.002335576741377, 46.46223436733343], 10 | 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-------------------------------------------------------------------------------- /test/fixtures/issue119.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[2,12],[2,20],[25,20],[25,12]], 3 | [[7,18],[7,15],[5,15]], 4 | [[19,18],[19,17],[17,17]], 5 | [[19,17],[21,17],[19,16]], 6 | [[7,15],[9,15],[7,13]] 7 | ] 8 | -------------------------------------------------------------------------------- /test/fixtures/issue131.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[3506,-2048],[7464,402],[-2048,2685],[-2048,-2048],[3506,-2048]], 3 | [[-2048,-37],[1235,747],[338,-1464],[-116,-1188],[-2048,-381],[-2048,-37]], 4 | [[-1491,-1981],[-1300,-1800],[-1155,-1981],[-1491,-1981]] 5 | ] 6 | -------------------------------------------------------------------------------- /test/fixtures/issue142.json: -------------------------------------------------------------------------------- 1 | [ 2 | 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4 | ] 5 | -------------------------------------------------------------------------------- /test/fixtures/issue16.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[143.129527283745121, 61.240160826593640], 3 | [147.399527283763751, 74.780160826630892], 4 | [154.049527283757931, 90.260160827077932], 5 | [174.429527283762581, 81.710160826332872], 6 | [168.03952728374861, 67.040160826407372], 7 | [159.099527283746281, 53.590160826221112]], 8 | [[156.85952728375561, 67.430160827003422], 9 | [157.489527283760251, 67.160160826519132], 10 | [159.969527283741631, 68.350160826928912], 11 | [161.339527283766071, 67.640160826966172], 12 | [159.649527283763751, 63.310160826891662], 13 | [155.759527283749781, 64.880160826258362]] 14 | ] 15 | -------------------------------------------------------------------------------- /test/fixtures/issue17.json: -------------------------------------------------------------------------------- 1 | [ 2 | 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-------------------------------------------------------------------------------- /test/fixtures/shared-points.json: -------------------------------------------------------------------------------- 1 | [[[4136,1016],[4112,1016],[4104,976],[4136,1016],[4144,984],[4104,976],[4144,968],[4144,984],[4168,992],[4152,1064]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/simplified-us-border.json: -------------------------------------------------------------------------------- 1 | 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2 | -------------------------------------------------------------------------------- /test/fixtures/steiner.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[0,0],[100,0],[100,100],[0,100]], 3 | [[50,50]], 4 | [[30,40]], 5 | [[70,60]], 6 | [[20,70]] 7 | ] 8 | -------------------------------------------------------------------------------- /test/fixtures/touching-holes.json: -------------------------------------------------------------------------------- 1 | [[[3694,2061],[3794,2035],[3812,2123],[3784,2123],[3708,2139],[3694,2061]],[[3752,2109],[3740,2102],[3712,2109],[3715,2125],[3723,2128],[3740,2124],[3742,2112],[3752,2109]],[[3797,2101],[3787,2096],[3780,2106],[3788,2114],[3797,2101]],[[3734,2099],[3732,2091],[3719,2094],[3721,2102],[3734,2099]],[[3777,2082],[3774,2071],[3772,2086],[3765,2091],[3748,2088],[3749,2062],[3738,2081],[3745,2095],[3761,2099],[3777,2082]],[[3719,2079],[3712,2079],[3706,2091],[3712,2097],[3721,2080],[3719,2079]],[[3773,2067],[3761,2053],[3753,2061],[3753,2071],[3756,2075],[3773,2067]],[[3708,2079],[3712,2079],[3714,2076],[3719,2079],[3722,2079],[3718,2088],[3723,2089],[3734,2075],[3730,2068],[3717,2065],[3708,2079]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/touching-holes2.json: -------------------------------------------------------------------------------- 1 | [[[0,0],[20,0],[20,25],[0,25],[0,0]],[[3,3],[2,12],[9,15],[3,3]],[[9,21],[2,12],[7,22],[9,21]]] -------------------------------------------------------------------------------- /test/fixtures/touching-holes3.json: -------------------------------------------------------------------------------- 1 | [[[0,0],[20,0],[20,25],[0,25],[0,0]],[[2,12],[4,23],[5,23],[2,12]],[[2,12],[6,23],[7,23],[2,12]],[[2,12],[8,23],[9,23],[2,12]],[[2,12],[10,23],[11,23],[2,12]],[[2,12],[12,23],[13,23],[2,12]],[[2,12],[14,23],[15,23],[2,12]],[[2,12],[16,23],[17,23],[2,12]],[[2,12],[18,23],[18,22],[2,12]],[[2,12],[18,21],[18,20],[2,12]],[[2,12],[18,19],[18,18],[2,12]],[[2,12],[18,17],[18,16],[2,12]],[[2,12],[18,15],[18,14],[2,12]],[[2,12],[18,13],[18,12],[2,12]],[[2,12],[18,11],[18,10],[2,12]],[[2,12],[18,9],[18,8],[2,12]],[[2,12],[18,7],[18,6],[2,12]],[[2,12],[18,5],[18,4],[2,12]],[[2,12],[18,3],[18,2],[2,12]],[[2,12],[18,1],[17,1],[2,12]],[[2,12],[16,1],[15,1],[2,12]],[[2,12],[14,1],[13,1],[2,12]],[[2,12],[12,1],[11,1],[2,12]],[[2,12],[10,1],[9,1],[2,12]],[[2,12],[8,1],[7,1],[2,12]],[[2,12],[6,1],[5,1],[2,12]],[[2,12],[4,1],[3,1],[2,12]]] -------------------------------------------------------------------------------- /test/fixtures/touching-holes4.json: -------------------------------------------------------------------------------- 1 | [[[-20,0],[20,0],[20,25],[-20,25],[-20,0]],[[2,12],[-1,23],[0,23],[2,12]],[[2,12],[-3,23],[-2,23],[2,12]],[[2,12],[-5,23],[-4,23],[2,12]],[[2,12],[-7,23],[-6,23],[2,12]],[[2,12],[-9,23],[-8,23],[2,12]],[[2,12],[-11,23],[-10,23],[2,12]],[[2,12],[-13,23],[-12,23],[2,12]],[[2,12],[-14,22],[-14,23],[2,12]],[[2,12],[-14,20],[-14,21],[2,12]],[[2,12],[-14,18],[-14,19],[2,12]],[[2,12],[-14,16],[-14,17],[2,12]],[[2,12],[-14,14],[-14,15],[2,12]],[[2,12],[-14,12],[-14,13],[2,12]],[[2,12],[-14,10],[-14,11],[2,12]],[[2,12],[-14,8],[-14,9],[2,12]],[[2,12],[-14,6],[-14,7],[2,12]],[[2,12],[-14,4],[-14,5],[2,12]],[[2,12],[-14,2],[-14,3],[2,12]],[[2,12],[-13,1],[-14,1],[2,12]],[[2,12],[-11,1],[-12,1],[2,12]],[[2,12],[-9,1],[-10,1],[2,12]],[[2,12],[-7,1],[-8,1],[2,12]],[[2,12],[-5,1],[-6,1],[2,12]],[[2,12],[-3,1],[-4,1],[2,12]],[[2,12],[-1,1],[-2,1],[2,12]],[[2,12],[1,1],[0,1],[2,12]]] -------------------------------------------------------------------------------- /test/fixtures/touching-holes5.json: -------------------------------------------------------------------------------- 1 | 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-------------------------------------------------------------------------------- /test/fixtures/touching2.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[120,2031],[92,2368],[94,2200],[33,2119],[42,2112],[53,2068]], 3 | [[44,2104],[79,2132],[88,2115],[44,2104]] 4 | ] 5 | -------------------------------------------------------------------------------- /test/fixtures/touching3.json: -------------------------------------------------------------------------------- 1 | [ 2 | [[1241,887],[1257,891],[1248,904],[1232,911],[1212,911],[1207,911],[1209,900],[1219,898],[1225,907],[1241,887]], 3 | [[1212,902],[1212,911],[1219,909],[1212,902]], 4 | [[1248,891],[1239,896],[1246,898],[1248,891]] 5 | ] 6 | -------------------------------------------------------------------------------- /test/fixtures/touching4.json: -------------------------------------------------------------------------------- 1 | [[[11,10],[0,10],[0,0],[11,0]],[[7,6],[7,9],[10,9]],[[7,5],[10,2],[10,5]],[[6,9],[1,4],[1,9]],[[1,1],[1,4],[4,1]]] 2 | -------------------------------------------------------------------------------- /test/fixtures/water.json: -------------------------------------------------------------------------------- 1 | [ 2 | 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| ] 9 | -------------------------------------------------------------------------------- /test/test.js: -------------------------------------------------------------------------------- 1 | 2 | import test from 'node:test'; 3 | import assert from 'node:assert/strict'; 4 | import earcut, {flatten, deviation} from '../src/earcut.js'; 5 | import fs from 'fs'; 6 | 7 | const expected = JSON.parse(fs.readFileSync(new URL('expected.json', import.meta.url))); 8 | 9 | test('indices-2d', () => { 10 | const indices = earcut([10, 0, 0, 50, 60, 60, 70, 10]); 11 | assert.deepEqual(indices, [1, 0, 3, 3, 2, 1]); 12 | }); 13 | 14 | test('indices-3d', () => { 15 | const indices = earcut([10, 0, 0, 0, 50, 0, 60, 60, 0, 70, 10, 0], null, 3); 16 | assert.deepEqual(indices, [1, 0, 3, 3, 2, 1]); 17 | }); 18 | 19 | test('empty', () => { 20 | assert.deepEqual(earcut([]), []); 21 | }); 22 | 23 | for (const id of Object.keys(expected.triangles)) { 24 | 25 | for (const rotation of [0, 90, 180, 270]) { 26 | test(`${id} rotation ${rotation}`, () => { 27 | const coords = JSON.parse(fs.readFileSync(new URL(`fixtures/${id}.json`, import.meta.url))); 28 | const theta = rotation * Math.PI / 180; 29 | const xx = Math.round(Math.cos(theta)); 30 | const xy = Math.round(-Math.sin(theta)); 31 | const yx = Math.round(Math.sin(theta)); 32 | const yy = Math.round(Math.cos(theta)); 33 | if (rotation) { 34 | for (const ring of coords) { 35 | for (const coord of ring) { 36 | const [x, y] = coord; 37 | coord[0] = xx * x + xy * y; 38 | coord[1] = yx * x + yy * y; 39 | } 40 | } 41 | } 42 | const data = flatten(coords), 43 | indices = earcut(data.vertices, data.holes, data.dimensions), 44 | err = deviation(data.vertices, data.holes, data.dimensions, indices), 45 | expectedTriangles = expected.triangles[id], 46 | expectedDeviation = (rotation !== 0 && expected['errors-with-rotation'][id]) || expected.errors[id] || 0; 47 | 48 | const numTriangles = indices.length / 3; 49 | if (rotation === 0) { 50 | assert.ok(numTriangles === expectedTriangles, `${numTriangles} triangles when expected ${expectedTriangles}`); 51 | } 52 | 53 | if (expectedTriangles > 0) { 54 | assert.ok(err <= expectedDeviation, `deviation ${err} <= ${expectedDeviation}`); 55 | } 56 | }); 57 | } 58 | } 59 | 60 | test('infinite-loop', () => { 61 | earcut([1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 4, 1, 5, 1, 3, 2, 4, 2, 4, 1], [5], 2); 62 | }); 63 | -------------------------------------------------------------------------------- /viz/index.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | debug page 5 | 6 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | -------------------------------------------------------------------------------- /viz/viz.js: -------------------------------------------------------------------------------- 1 | /*eslint @stylistic/js/comma-spacing: 0, no-unused-vars: 0 */ 2 | 3 | import earcut, {flatten, deviation} from '../src/earcut.js'; 4 | 5 | (async function () { 6 | const params = new URLSearchParams(window.location.search.substring(1)); 7 | const fixture = params.get('fixture') || 'water'; 8 | const testPoints = await (await fetch(`../test/fixtures/${fixture}.json`)).json(); 9 | const rotation = params.get('rotation') || 0; 10 | const theta = rotation * Math.PI / 180; 11 | const round = rotation % 90 === 0 ? Math.round : x => x; 12 | const xx = round(Math.cos(theta)); 13 | const xy = round(-Math.sin(theta)); 14 | const yx = round(Math.sin(theta)); 15 | const yy = round(Math.cos(theta)); 16 | for (const ring of testPoints) { 17 | for (const coord of ring) { 18 | const [x, y] = coord; 19 | coord[0] = xx * x + xy * y; 20 | coord[1] = yx * x + yy * y; 21 | } 22 | } 23 | 24 | const canvas = document.getElementById('canvas'); 25 | const ctx = canvas.getContext('2d'); 26 | 27 | let minX = Infinity, 28 | maxX = -Infinity, 29 | minY = Infinity, 30 | maxY = -Infinity; 31 | 32 | for (let i = 0; i < testPoints[0].length; i++) { 33 | minX = Math.min(minX, testPoints[0][i][0]); 34 | maxX = Math.max(maxX, testPoints[0][i][0]); 35 | minY = Math.min(minY, testPoints[0][i][1]); 36 | maxY = Math.max(maxY, testPoints[0][i][1]); 37 | } 38 | 39 | const width = maxX - minX; 40 | const height = maxY - minY; 41 | 42 | canvas.width = window.innerWidth; 43 | canvas.height = canvas.width * height / width + 10; 44 | 45 | const ratio = (canvas.width - 10) / width; 46 | 47 | if (devicePixelRatio > 1) { 48 | canvas.style.width = `${canvas.width}px`; 49 | canvas.style.height = `${canvas.height}px`; 50 | canvas.width *= 2; 51 | canvas.height *= 2; 52 | ctx.scale(2, 2); 53 | } 54 | 55 | const data = flatten(testPoints); 56 | 57 | console.time('earcut'); 58 | const result = earcut(data.vertices, data.holes, data.dimensions); 59 | console.timeEnd('earcut'); 60 | 61 | console.log(`deviation: ${deviation(data.vertices, data.holes, data.dimensions, result)}`); 62 | 63 | const triangles = []; 64 | for (const index of result) { 65 | triangles.push([data.vertices[index * data.dimensions], data.vertices[index * data.dimensions + 1]]); 66 | } 67 | 68 | ctx.lineJoin = 'round'; 69 | 70 | for (let i = 0; i < triangles.length; i += 3) { 71 | drawPoly(triangles.slice(i, i + 3), 'rgba(255,0,0,0.2)', 'rgba(255,255,0,0.2)'); 72 | // drawPoly(triangles.slice(i, i + 3), 'rgba(255,0,0,0.0)', 'rgba(255,0,0,0.3)'); 73 | } 74 | 75 | drawPoly(testPoints, 'black', true); 76 | 77 | function drawPoint(p, color) { 78 | const x = (p[0] - minX) * ratio + 5, 79 | y = (p[1] - minY) * ratio + 5; 80 | ctx.fillStyle = color || 'grey'; 81 | ctx.fillRect(x - 3, y - 3, 6, 6); 82 | } 83 | 84 | function drawPoly(rings, color, fill) { 85 | ctx.beginPath(); 86 | 87 | ctx.strokeStyle = color; 88 | if (fill && fill !== true) ctx.fillStyle = fill; 89 | 90 | if (typeof rings[0][0] === 'number') rings = [rings]; 91 | 92 | for (const points of rings) { 93 | for (let i = 0; i < points.length; i++) { 94 | const x = (points[i][0] - minX) * ratio + 5, 95 | y = (points[i][1] - minY) * ratio + 5; 96 | if (i === 0) ctx.moveTo(x, y); 97 | else ctx.lineTo(x, y); 98 | } 99 | if (fill) ctx.closePath(); 100 | } 101 | ctx.stroke(); 102 | 103 | if (fill && fill !== true) ctx.fill('evenodd'); 104 | } 105 | 106 | function clear() { 107 | ctx.clearRect(0, 0, canvas.width, canvas.height); 108 | } 109 | 110 | function drawNode(node, color) { 111 | drawPoint([node.x, node.y], color); 112 | } 113 | 114 | function drawNodeRing(node, color, fill) { 115 | const start = node; 116 | const points = []; 117 | do { 118 | points.push([node.x, node.y]); 119 | node = node.next; 120 | } while (node !== start); 121 | 122 | console.log(JSON.stringify(points)); 123 | drawPoly(points, color, fill); 124 | } 125 | 126 | function drawNodePolygon(node) { 127 | drawNodeRing(node, 'black', 'rgba(255,255,0,0.2)'); 128 | } 129 | 130 | function drawNodeEdge(node, color) { 131 | drawPoly([[node.x, node.y], [node.next.x, node.next.y]], color); 132 | } 133 | })(); 134 | --------------------------------------------------------------------------------