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Convex decomposition for 2D polygons


Library for decomposing 2D polygons into convex regions.

Launch the demo!



Download decomp.js or decomp.min.js and include the script in your HTML:

<script src="decomp.js" type="text/javascript"></script>
<!-- or: -->
<script src="decomp.min.js" type="text/javascript"></script>

Then you can use the decomp global.

npm install poly-decomp

Then require it like so:

var decomp = require('poly-decomp');

Basic usage

// Create a concave polygon 
var concavePolygon = [
  [ -1,   1],
  [ -1,   0],
  [  1,   0],
  [  1,   1],
  [0.5, 0.5]
// Decompose into convex polygons, using the faster algorithm 
var convexPolygons = decomp.quickDecomp(concavePolygon);
// ==> [  [[1,0],[1,1],[0.5,0.5]],  [[0.5,0.5],[-1,1],[-1,0],[1,0]]  ] 
// Decompose using the slow (but optimal) algorithm 
var convexPolygons = decomp.decomp(concavePolygon);
// ==> [  [[-1,1],[-1,0],[1,0],[0.5,0.5]],  [[1,0],[1,1],[0.5,0.5]]  ] 

Advanced usage

// Get user input as an array of points. 
var polygon = getUserInput();
// Check if the polygon self-intersects 
    // Reverse the polygon to make sure it uses counter-clockwise winding 
    // Decompose into convex pieces 
    var convexPolygons = decomp.quickDecomp(polygon);
    // Draw each point on an HTML5 Canvas context 
    for(var i=0; i<convexPolygons.length; i++){
        var convexPolygon = convexPolygons[i];
        var firstPoint = convexPolygon[0];
        ctx.moveTo(firstPoint[0], firstPoint[1]);
        for(var j=1; j<convexPolygon.length; j++){
            var point = convexPolygon[j];
            var x = point[0];
            var y = point[1];
            c.lineTo(x, y);


quickDecomp(polygon: Array<Point>): Array<Array<Point>>

var convexPolygons = decomp.quickDecomp(polygon);

Slices the polygon into convex sub-polygons, using a fast algorithm. Note that the input points objects will be re-used in the result array.

decomp(polygon: Array<Point>): Array<Array<Point>>

var convexPolygons = decomp.quickDecomp(polygon);

Decomposes the polygon into one or more convex sub-polygons using an optimal algorithm. Note that the input points objects will be re-used in the result array.

isSimple(polygon: Array<Point>): boolean

    // Polygon does not self-intersect - it's safe to decompose. 
    var convexPolygons = decomp.quickDecomp(polygon);

Returns true if any of the line segments in the polygon intersects. Use this to check if the input polygon is OK to decompose.

makeCCW(polygon: Array<Point>): void

console.log('Polygon with clockwise winding:', polygon);
console.log('Polygon with counter-clockwise winding:', polygon);

Reverses the polygon, if its vertices are not ordered counter-clockwise. Note that the input polygon array will be modified in place.

removeCollinearPoints(polygon: Array<Point>, thresholdAngle: number): void

var before = polygon.length;
decomp.removeCollinearPoints(polygon, 0.1);
var numRemoved = before - polygon.length;
console.log(numRemoved + ' collinear points could be removed');

Removes collinear points in the polygon. This means that if three points are placed along the same line, the middle one will be removed. The thresholdAngle is measured in radians and determines whether the points are collinear or not. Note that the input array will be modified in place.

Change log

  • Rewrote the class based API to a minimal array-based one. See docs.
  • Added method Polygon.prototype.removeCollinearPoints.
  • Added optional parameter thresholdAngle to Point.collinear(a,b,c,thresholdAngle).


Make sure you have git, Node.js, NPM and grunt installed.

git clone; # Clone the repo
cd poly-decomp.js;
npm install;                                     # Install dependencies
                                                 # (make changes to source)
grunt;                                           # Builds build/decomp.js

The most recent commits are currently pushed to the master branch. Thanks for contributing!


The library is a manual port of the C++ library Poly Decomp by Mark Bayazit.

It implements two algorithms, one optimal (but slow) and one less optimal (but fast).