JavaScript Graham's Scan Convex Hull Algorithm

I required a simple implementation to calculate a convex hull from a given array of x, y coordinates, the convex hull's in js I found either were a little buggy, or required dependencies on other libraries. This implementation just takes the x,y coordinates, no other libraries are needed.

These four examples show how to utilise with Google Maps:

Example 1 Example 2 Example 3 Example 4

View GitHub pages

Building

This produces graham_scan.min.js:

npm install
grunt build

Testing

The source is tested with qUnit, tests executed with Google's JS Test Driver.

Usage

//Create a new instance.
var convexHull = new ConvexHullGrahamScan();

//add points (needs to be done for each point, a foreach loop on the input array can be used.)
convexHull.addPoint(x, y);

//getHull() returns the array of points that make up the convex hull.
var hullPoints = convexHull.getHull();

Algorithm

GRAHAM_SCAN(Q)
    Find p0 in Q with minimum y-coordinate (and minimum x-coordinate if there are ties).
    Sort the remaining points of Q (that is, Q − {p0}) by polar angle in counterclockwise order with respect to p0.
    TOP [S] = 0                ▷ Lines 3-6 initialize the stack to contain, from bottom to top, first three points.
    PUSH (p0, S)
    PUSH (p1, S)
    PUSH (p2, S)
    for i = 3 to m             ▷ Perform test for each point p3, ..., pm.
        do while the angle between NEXT_TO_TOP[S], TOP[S], and pi makes a non-left turn  ▷ remove if not a vertex
            do POP(S)
            PUSH (S, pi)
    return S

References

• http://www.personal.kent.edu/~rmuhamma/Compgeometry/MyCG/ConvexHull/GrahamScan/grahamScan.htm
• http://en.wikipedia.org/wiki/Graham_scan

License

MIT License