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Delaunator [![Build Status](https://travis-ci.org/mapbox/delaunator.svg?branch=master)](https://travis-ci.org/mapbox/delaunator) [![](https://img.shields.io/badge/simply-awesome-brightgreen.svg)](https://github.com/mourner/projects) [![](https://badgen.net/bundlephobia/minzip/delaunator)](https://unpkg.com/delaunator)\n\nAn incredibly fast JavaScript library for\n[Delaunay triangulation](https://en.wikipedia.org/wiki/Delaunay_triangulation) of 2D points.\n\n- [Interactive Demo](https://mapbox.github.io/delaunator/demo.html)\n- [Guide to data structures](https://mapbox.github.io/delaunator/)\n\n<img src=\"delaunator.png\" alt=\"Delaunay triangulation example\" width=\"600\" />\n\n### Projects based on Delaunator\n\n- [d3-delaunay](https://github.com/d3/d3-delaunay) for Voronoi diagrams, search, traversal and rendering (a part of [D3](https://d3js.org)).\n- [d3-geo-voronoi](https://github.com/Fil/d3-geo-voronoi) for Delaunay triangulations and Voronoi diagrams on a sphere (e.g. for geographic locations).\n\n### Ports to other languages\n\n- [delaunator-rs](https://github.com/mourner/delaunator-rs) (Rust)\n- [fogleman/delaunay](https://github.com/fogleman/delaunay) (Go)\n- [delaunator-cpp](https://github.com/abellgithub/delaunator-cpp) (C++)\n- [delaunator-sharp](https://github.com/nol1fe/delaunator-sharp) (C#)\n- [delaunator-ruby](https://github.com/hendrixfan/delaunator-ruby) (Ruby)\n- [Delaunator-Python](https://github.com/HakanSeven12/Delaunator-Python) (Python)\n- [hx-delaunator](https://github.com/dmitryhryppa/hx-delaunator) (Haxe)\n- [ricardomatias/delaunator](https://github.com/ricardomatias/delaunator) (Kotlin)\n\n## Example\n\n```js\nconst points = [[168, 180], [168, 178], [168, 179], [168, 181], [168, 183], ...];\n\nconst delaunay = Delaunator.from(points);\nconsole.log(delaunay.triangles);\n// [623, 636, 619,  636, 444, 619, ...]\n```\n\n## Install\n\nInstall with NPM (`npm install delaunator`) or Yarn (`yarn add delaunator`), then:\n\n```js\n// import as an ES module\nimport Delaunator from 'delaunator';\n\n// or require in Node / Browserify\nconst Delaunator = require('delaunator');\n```\n\nOr use a browser build directly:\n\n```html\n<script src=\"https://unpkg.com/delaunator@4.0.1/delaunator.min.js\"></script> <!-- minified build -->\n<script src=\"https://unpkg.com/delaunator@4.0.1/delaunator.js\"></script> <!-- dev build -->\n```\n\n## API Reference\n\n#### Delaunator.from(points[, getX, getY])\n\nConstructs a delaunay triangulation object given an array of points (`[x, y]` by default).\n`getX` and `getY` are optional functions of the form `(point) => value` for custom point formats.\nDuplicate points are skipped.\n\n#### new Delaunator(coords)\n\nConstructs a delaunay triangulation object given an array of point coordinates of the form:\n`[x0, y0, x1, y1, ...]` (use a typed array for best performance).\n\n#### delaunay.triangles\n\nA `Uint32Array` array of triangle vertex indices (each group of three numbers forms a triangle).\nAll triangles are directed counterclockwise.\n\nTo get the coordinates of all triangles, use:\n\n```js\nfor (let i = 0; i < triangles.length; i += 3) {\n    coordinates.push([\n        points[triangles[i]],\n        points[triangles[i + 1]],\n        points[triangles[i + 2]]\n    ]);\n}\n```\n\n#### delaunay.halfedges\n\nA `Int32Array` array of triangle half-edge indices that allows you to traverse the triangulation.\n`i`-th half-edge in the array corresponds to vertex `triangles[i]` the half-edge is coming from.\n`halfedges[i]` is the index of a twin half-edge in an adjacent triangle\n(or `-1` for outer half-edges on the convex hull).\n\nThe flat array-based data structures might be counterintuitive,\nbut they're one of the key reasons this library is fast.\n\n#### delaunay.hull\n\nA `Uint32Array` array of indices that reference points on the convex hull of the input data, counter-clockwise.\n\n#### delaunay.coords\n\nAn array of input coordinates in the form `[x0, y0, x1, y1, ....]`,\nof the type provided in the constructor (or `Float64Array` if you used `Delaunator.from`).\n\n#### delaunay.update()\n\nUpdates the triangulation if you modified `delaunay.coords` values in place, avoiding expensive memory allocations.\nUseful for iterative relaxation algorithms such as [Lloyd's](https://en.wikipedia.org/wiki/Lloyd%27s_algorithm).\n\n## Performance\n\nBenchmark results against other Delaunay JS libraries\n(`npm run bench` on Macbook Pro Retina 15\" 2017, Node v10.10.0):\n\n&nbsp; | uniform 100k | gauss 100k | grid 100k | degen 100k | uniform 1&nbsp;million | gauss 1&nbsp;million | grid 1&nbsp;million | degen 1&nbsp;million\n:-- | --: | --: | --: | --: | --: | --: | --: | --:\n**delaunator** | 82ms | 61ms | 66ms | 25ms | 1.07s | 950ms | 830ms | 278ms\n[faster&#8209;delaunay](https://github.com/Bathlamos/delaunay-triangulation) | 473ms | 411ms | 272ms | 68ms | 4.27s | 4.62s | 4.3s | 810ms\n[incremental&#8209;delaunay](https://github.com/mikolalysenko/incremental-delaunay) | 547ms | 505ms | 172ms | 528ms | 5.9s | 6.08s | 2.11s | 6.09s\n[d3&#8209;voronoi](https://github.com/d3/d3-voronoi) | 972ms | 909ms | 358ms | 720ms | 15.04s | 13.86s | 5.55s | 11.13s\n[delaunay&#8209;fast](https://github.com/ironwallaby/delaunay) | 3.8s | 4s | 12.57s | timeout | 132s | 138s | 399s | timeout\n[delaunay](https://github.com/darkskyapp/delaunay) | 4.85s | 5.73s | 15.05s | timeout | 156s | 178s | 326s | timeout\n[delaunay&#8209;triangulate](https://github.com/mikolalysenko/delaunay-triangulate) | 2.24s | 2.04s | OOM | 1.51s | OOM | OOM | OOM | OOM\n[cdt2d](https://github.com/mikolalysenko/cdt2d) | 45s | 51s | 118s | 17s | timeout | timeout | timeout | timeout\n\n## Papers\n\nThe algorithm is based on ideas from the following papers:\n\n- [A simple sweep-line Delaunay triangulation algorithm](http://www.academicpub.org/jao/paperInfo.aspx?paperid=15630), 2013, Liu Yonghe, Feng Jinming and Shao Yuehong\n- [S-hull: a fast radial sweep-hull routine for Delaunay triangulation](http://www.s-hull.org/paper/s_hull.pdf), 2010, David Sinclair\n- [A faster circle-sweep Delaunay triangulation algorithm](http://cglab.ca/~biniaz/papers/Sweep%20Circle.pdf), 2011, Ahmad Biniaz and Gholamhossein Dastghaibyfard\n","_attachments":{},"homepage":"https://github.com/mapbox/delaunator#readme","bugs":{"url":"https://github.com/mapbox/delaunator/issues"},"license":"ISC"}