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## Earcut

The fastest and smallest JavaScript polygon triangulation library. 2.5KB gzipped.

[![Build Status](https://travis-ci.org/mapbox/earcut.svg?branch=master)](https://travis-ci.org/mapbox/earcut)
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#### 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&ndash;7 and another with 8&ndash;11).
* `dimensions` is the number of coordinates per vertex in the input array (`2` by default).

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.

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/earcut@2.2.2/dist/earcut.dev.js)
- [minified production build](https://unpkg.com/earcut@2.2.2/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

##### 2.2.2 (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 &mdash; 1.0.6 (Jan 20, 2015)

- Various robustness improvements and fixes.

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

- Initial release.
Youez - 2016 - github.com/yon3zu
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