Earcut

The fastest and smallest polygon triangulation library.
A port of Mapbox's Earcut algorithm to F#.

https://github.com/mapbox/earcut

Status

Stable for .NET 4.7 and .NET 6.0 and JS via Fable.

v3.0.2 ported to F# on 2025-11-8

All tests of the original JS version pass.

All relevant code is in Earcut.fs.
It contains the ported code without any major changes to the original logic.
It has no dependencies.

Performance

The F# port has about the same performance as the original JS version when compiled back to JS with Fable.

The algorithm

The library implements a modified ear slicing algorithm,
optimized by 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 by Martin Held
and Triangulation by Ear Clipping by David Eberly.

Why another triangulation library?

The aim of the original mapbox Earcut project is to create a 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.

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.

Usage

let triangles = Earcut.earcut([| 10.;0.; 0.;50.; 60.;60.; 70.;10.|], [||], 2) // returns [1;0;3; 3;2;1]

Parameters:

• vertices - A flat array of vertex coordinates like [x0, y0, x1, y1, x2, y2, ...].
• holeIndices - An array of hole starting indices. These indices refer to the point array, not the flattened vertices array.
  If you have an index into the flattened vertices array, divide it by dimensions to get the correct hole index.
  (e.g. [|4|] means the hole starts at point 4, i.e. at vertices[4 * dimensions]).
  Use null or an empty array if there are no holes.
• dimensions - The number of coordinates per vertex in the vertices array:
  • 2 if the vertices array is made of x and y coordinates only.
  • 3 if it is made of x, y and z coordinates.
    Only the first two are used for triangulation (x and y), and the rest are ignored.

Returns:

A list of integers. They are indices into the point array (not the flattened vertices array).
Every 3 integers represent the corner vertices of a triangle.
To look up coordinates in the flattened vertices array, multiply the index by dimensions:

x = vertices[i * dimensions]
y = vertices[i * dimensions + 1]

Convenience F# API: earcut_xy and earcut_XY

If your points are objects with x/y (or X/Y) properties, you can use the convenience functions earcut_xy and earcut_XY instead of manually flattening coordinates. They accept a ResizeArray of points and an optional list of holes (also as ResizeArrays of points), and return a flat float[] of triangle vertex coordinates [x0, y0, x1, y1, x2, y2, ...]. Every six consecutive values represent a triangle.

These functions use F# statically resolved type parameters, so any object with the matching members will work.

For example given these Polylines from Euclid:

let outerPoly: Polyline2D = ...
let hole1: Polyline2D = ...
let hole2: Polyline2D = ...


// For points with uppercase .X and .Y members:
let triangles = outerPoly.Points |> Earcut.earcut_XY [||]

// With holes:
let holes = [|hole1.Points; hole2.Points|]
let triangles = outerPoly.Points |> Earcut.earcut_XY holes

Examples

Simple polygon (no holes)

// A quadrilateral with 4 vertices, 2D coordinates
let vertices = [| 10.; 0.;  0.; 50.;  60.; 60.;  70.; 10. |]
let triangles = Earcut.earcut(vertices, [||], 2)
// returns [1; 0; 3;  3; 2; 1]
// Triangle 1: points 1, 0, 3
// Triangle 2: points 3, 2, 1

// Retrieve triangle vertex coordinates:
for t in 0 .. 3 .. triangles.Count - 1 do
    let i0 = triangles.[t]
    let i1 = triangles.[t + 1]
    let i2 = triangles.[t + 2]
    printfn "Triangle: (%g, %g) (%g, %g) (%g, %g)"
        vertices.[i0 * 2] vertices.[i0 * 2 + 1]
        vertices.[i1 * 2] vertices.[i1 * 2 + 1]
        vertices.[i2 * 2] vertices.[i2 * 2 + 1]

Polygon with a hole

// Outer square: points 0-3, hole square: points 4-7
let vertices = [|
    0.;0.;  100.;0.;  100.;100.;  0.;100.          // outer ring
    20.;20.;  80.;20.;  80.;80.;  20.;80.           // hole
|]
let triangles = Earcut.earcut(vertices, [|4|], 2)    // hole starts at point index 4
// returns [0;4;7; 5;4;0; 3;0;7; 5;0;1; 2;3;7; 6;5;1; 2;7;6; 6;1;2]

3D coordinates

// 4 vertices with x, y, z (z is ignored for triangulation)
let vertices = [| 10.;0.;1.;  0.;50.;2.;  60.;60.;3.;  70.;10.;4. |]
let triangles = Earcut.earcut(vertices, null, 3)
// returns [1; 0; 3;  3; 2; 1]

// Retrieve coordinates using dimensions = 3:
let i = triangles.[0]  // e.g. 1
let x = vertices.[i * 3]       // 0.
let y = vertices.[i * 3 + 1]   // 50.
let z = vertices.[i * 3 + 2]   // 2.

Multiple holes

// Outer polygon with two holes
// Outer: points 0-5, Hole1: points 6-9, Hole2: points 10-13
let triangles = Earcut.earcut(vertices, [|6; 10|], 2)
// holeIndices = [|6; 10|] means:
//   hole 1 starts at point 6  -> vertices.[6 * 2]
//   hole 2 starts at point 10 -> vertices.[10 * 2]

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),
you can convert it to the format expected by Earcut with Earcut.flatten:

let data = Earcut.flatten(geojson.geometry.coordinates)
let triangles = Earcut.earcut(data.vertices, data.holes, data.dimensions)

Verification of triangulation correctness

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

let 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.

Build for .NET 4.7 and 6.0

dotnet build

Build to JS with Fable

If you don't have Fable installed yet run:

dotnet tool install fable

then build to JS with:

dotnet fable

Run Tests

build to JS with dotnet fable
run tests with node Test/test.js

Images of test cases

bad-diagonals:

bad-hole:

boxy:

building:

collinear-diagonal:

dude:

eberly-3:

eberly-6:

filtered-bridge-jhl:

hilbert:

hole-touching-outer:

hourglass:

issue111:

issue119:

issue131:

issue142:

issue149:

issue16:

issue17:

issue186:

issue29:

issue34:

issue35:

issue45:

issue52:

outside-ring:

rain:

self-touching:

shared-points:

simplified-us-border:

steiner:

touching-holes:

touching-holes2:

touching-holes3:

touching-holes4:

touching-holes5:

touching-holes6:

touching2:

touching3:

touching4:

water-huge2:

water:

water2:

water3:

water3b:

water4: