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https://github.com/mapbox/earcut

The fastest and smallest JavaScript polygon triangulation library for your WebGL apps
https://github.com/mapbox/earcut

algorithm computational-geometry javascript polygon tessellation triangulation

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The fastest and smallest JavaScript polygon triangulation library for your WebGL apps

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## Earcut



The fastest and smallest JavaScript polygon triangulation library. 3KB gzipped.



[![Build Status](https://travis-ci.org/mapbox/earcut.svg?branch=master)](https://travis-ci.org/mapbox/earcut)

[![Coverage Status](https://coveralls.io/repos/mapbox/earcut/badge.svg?branch=master)](https://coveralls.io/r/mapbox/earcut?branch=master)

[![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")

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[![](https://img.shields.io/badge/simply-awesome-brightgreen.svg)](https://github.com/mourner/projects)



#### The algorithm



The library implements a modified ear slicing algorithm,

optimized by [z-order curve](http://en.wikipedia.org/wiki/Z-order_curve) hashing

and extended to handle holes, twisted polygons, degeneracies and self-intersections

in a way that doesn't _guarantee_ correctness of triangulation,

but attempts to always produce acceptable results for practical data.



It's based on ideas from

[FIST: Fast Industrial-Strength Triangulation of Polygons](http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html) by Martin Held

and [Triangulation by Ear Clipping](http://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf) by David Eberly.



#### Why another triangulation library?



The aim of this project is to create a JS triangulation library

that is **fast enough for real-time triangulation in the browser**,

sacrificing triangulation quality for raw speed and simplicity,

while being robust enough to handle most practical datasets without crashing or producing garbage.

Some benchmarks using Node 0.12:



(ops/sec)         | pts  | earcut    | libtess  | poly2tri | pnltri    | polyk

------------------| ---- | --------- | -------- | -------- | --------- | ------

OSM building      | 15   | _795,935_ | _50,640_ | _61,501_ | _122,966_ | _175,570_

dude shape        | 94   | _35,658_  | _10,339_ | _8,784_  | _11,172_  | _13,557_

holed dude shape  | 104  | _28,319_  | _8,883_  | _7,494_  | _2,130_   | n/a

complex OSM water | 2523 | _543_     | _77.54_  | failure  | failure   | n/a

huge OSM water    | 5667 | _95_      | _29.30_  | failure  | failure   | n/a



The original use case it was created for is [Mapbox GL](https://www.mapbox.com/mapbox-gl), WebGL-based interactive maps.



If you want to get correct triangulation even on very bad data with lots of self-intersections

and earcut is not precise enough, take a look at [libtess.js](https://github.com/brendankenny/libtess.js).



#### Usage



```js

var triangles = earcut([10,0, 0,50, 60,60, 70,10]); // returns [1,0,3, 3,2,1]

```



Signature: `earcut(vertices[, holes, dimensions = 2])`.



* `vertices` is a flat array of vertex coordinates like `[x0,y0, x1,y1, x2,y2, ...]`.

* `holes` is an array of hole _indices_ if any

  (e.g. `[5, 8]` for a 12-vertex input would mean one hole with vertices 5–7 and another with 8–11).

* `dimensions` is the number of coordinates per vertex in the input array (`2` by default). Only two are used for triangulation (`x` and `y`), and the rest are ignored.



Each group of three vertex indices in the resulting array forms a triangle.



```js

// triangulating a polygon with a hole

earcut([0,0, 100,0, 100,100, 0,100,  20,20, 80,20, 80,80, 20,80], [4]);

// [3,0,4, 5,4,0, 3,4,7, 5,0,1, 2,3,7, 6,5,1, 2,7,6, 6,1,2]



// triangulating a polygon with 3d coords

earcut([10,0,1, 0,50,2, 60,60,3, 70,10,4], null, 3);

// [1,0,3, 3,2,1]

```



If you pass a single vertex as a hole, Earcut treats it as a Steiner point.



Note that Earcut is a **2D** triangulation algorithm, and handles 3D data as if it was projected onto the XY plane (with Z component ignored).



If your input is a multi-dimensional array (e.g. [GeoJSON Polygon](http://geojson.org/geojson-spec.html#polygon)),

you can convert it to the format expected by Earcut with `earcut.flatten`:



```js

var data = earcut.flatten(geojson.geometry.coordinates);

var triangles = earcut(data.vertices, data.holes, data.dimensions);

```



After getting a triangulation, you can verify its correctness with `earcut.deviation`:



```js

var deviation = earcut.deviation(vertices, holes, dimensions, triangles);

```



Returns the relative difference between the total area of triangles and the area of the input polygon.

`0` means the triangulation is fully correct.



#### Install



NPM and Browserify:



```bash

npm install earcut

```



Browser builds on CDN:



- [development build](https://unpkg.com/[email protected]/dist/earcut.dev.js)

- [minified production build](https://unpkg.com/[email protected]/dist/earcut.min.js)



Running tests:



```bash

npm test

```



![](https://cloud.githubusercontent.com/assets/25395/5778431/e8ec0c10-9da3-11e4-8d4e-a2ced6a7d2b7.png)



#### Ports to other languages



- [mapbox/earcut.hpp](https://github.com/mapbox/earcut.hpp) (C++11)

- [earcut4j/earcut4j](https://github.com/earcut4j/earcut4j) (Java)

- [the3deers/earcut-java](https://github.com/the3deers/earcut-java) (Java)

- [Larpon/earcut](https://github.com/Larpon/earcut) (V)

- [Cawfree/earcut-j](https://github.com/Cawfree/earcut-j) (Java, outdated)



#### Changelog



##### 2.2.4 (Jul 5, 2022)



- Improved performance by 10–15%.

- Fixed another rare race condition that could lead to an infinite loop.



##### 2.2.3 (Jul 8, 2021)



- Fixed a rare race condition that could lead to an infinite loop.



##### 2.2.2 (Jan 21, 2020)



- Fixed yet another rare race condition when a hole shared an edge with an outer ring.



##### 2.2.1 (Sep 19, 2019)



- Fixed another rare case with touching holes.



##### 2.2.0 (Sep 18, 2019)



- Fixed a handful of rare race conditions.



##### 2.1.5 (Feb 5, 2019)



- Fixed a race condition with coincident holes that could lead to bad triangulation.



##### 2.1.4 (Dec 4, 2018)



- Fixed a race condition that could lead to a freeze on degenerate input.



##### 2.1.3 (Jan 4, 2018)



- Improved performance for bigger inputs (5-12%).



##### 2.1.2 (Oct 23, 2017)



- Fixed a few race conditions where bad input would cause an error.



##### 2.1.1 (Mar 17, 2016)



- Fixed a rare race condition where the split routine would choose bad diagonals.

- Fixed a rare race condition in the "cure local intersections" routine.

- Fixed a rare race condition where a hole that shares a point with the outer ring would be handled incorrectly.

- Fixed a bug where a closing point wouldn't be filtered as duplicate, sometimes breaking triangulation.



##### 2.1.0 (Mar 11, 2016)



- Added `earcut.deviation` function for verifying correctness of triangulation.

- Added `earcut.flatten` function for converting GeoJSON-like input into a format Earcut expects.



##### 2.0.9 (Mar 10, 2016)



- Fixed a rare race condition where a hole would be handled incorrectly.



##### 2.0.8 (Jan 19, 2016)



- Fixed a rare race condition with a hole touching outer ring.



##### 2.0.7 (Nov 18, 2015)



- Changed the algorithm to avoid filtering colinear/duplicate vertices unless it can't triangulate the polygon otherwise.

  Improves performance on simpler shapes and fixes some 3D use cases.



##### 2.0.6 (Oct 26, 2015)



- Improved robustness and reliability of the triangulation algorithm.

- Improved performance by up to 15%.

- Significantly improved source code clarity.



##### 2.0.5 (Oct 12, 2015)



- Fixed a z-curve hashing bug that could lead to unexpected results in very rare cases involving shapes with lots of points.



##### 2.0.4 (Oct 8, 2015)



- Fixed one more extremely rare race condition, lol!



##### 2.0.3 (Oct 8, 2015)



- Fixed yet another rare race condition (multiple holes connected with colinear bridges).

- Fixed crash on empty input.



##### 2.0.2 (Jul 8, 2015)



- Fixed one more rare race condition with a holed polygon.



##### 2.0.1 (May 11, 2015)



- Added Steiner points support.



##### 2.0.0 (Apr 30, 2015)



- **Breaking**: changed the API to accept a flat input array of vertices with hole indices and return triangle indices.

  It makes the indexed output much faster than it was before (up to 30%) and improves memory footprint.



##### 1.4.2 (Mar 18, 2015)



- Fixed another rare edge case with a tiny hole in a huge polygon.



##### 1.4.1 (Mar 17, 2015)



- Fixed a rare edge case that led to incomplete triangulation.



##### 1.4.0 (Mar 9, 2015)



- Fixed indexed output to produce indices not multiplied by dimension and work with any number of dimensions.



##### 1.3.0 (Feb 24, 2015)



- Added a second argument to `earcut` that switches output format to flat vertex and index arrays if set to `true`.



##### 1.2.3 (Feb 10, 2015)



- Improved performance (especially on recent v8) by avoiding `Array` `push` with multiple arguments.



##### 1.2.2 (Jan 27, 2015)



- Significantly improved performance for polygons with self-intersections

  (e.g. big OSM water polygons are now handled 2-3x faster)



##### 1.2.1 (Jan 26, 2015)



- Significantly improved performance on polygons with high number of vertices

  by using z-order curve hashing for vertex lookup.

- Slightly improved overall performance with better point filtering.



##### 1.1.0 (Jan 21, 2015)



- Improved performance on polygons with holes by switching from Held to Eberly hole elimination algorithm

- More robustness fixes and tests



##### 1.0.1 — 1.0.6 (Jan 20, 2015)



- Various robustness improvements and fixes.



##### 1.0.0 (Jan 18, 2015)



- Initial release.