Math::ConvexHull - Calculate convex hulls using Graham's scan (n*log(n))


  use Math::ConvexHull qw/convex_hull/;
  $hull_array_ref = convex_hull(\@points);


Math::ConvexHull is a simple module that calculates convex hulls from a set of points in 2D space. It is a straightforward implementation of the algorithm known as Graham's scan which, with complexity of O(n*log(n)), is the fastest known method of finding the convex hull of an arbitrary set of points. There are some methods of eliminating points that cannot be part of the convex hull. These may or may not be implemented in a future version.

The implementation cannot deal with duplicate points. Therefore, points which are very, very close (think floating point close) to the previous point are dropped since version 1.02 of the module. However, if you pass in randomly ordered data which contains duplicate points, this safety measure might not help you. In that case, you will have to remove duplicates yourself.


None by default, but you may choose to have the convex_hull() subroutine exported to your namespace using standard Exporter semantics.

convex_hull() subroutine

Math::ConvexHull implements exactly one public subroutine which, surprisingly, is called convex_hull(). convex_hull() expects an array reference to an array of points and returns an array reference to an array of points in the convex hull.

In this context, a point is considered to be a reference to an array containing an x and a y coordinate. So an example use of convex_hull() would be:

  use Data::Dumper;
  use Math::ConvexHull qw/convex_hull/;
  print Dumper convex_hull(
    [0,0],     [1,0],
    [0.2,0.9], [0.2,0.5],
    [0,1],     [1,1],
  # Prints out the points [0,0], [1,0], [0,1], [1,1].

Please note that convex_hull() does not return copies of the points but instead returns the same array references that were passed in.


New versions of this module can be found on or CPAN.

After implementing the algorithm from my CS notes, I found the exact same implementation in the German translation of Orwant et al, "Mastering Algorithms with Perl". Their code reads better than mine, so if you looked at the module sources and don't understand what's going on, I suggest you have a look at the book.

In early 2011, much of the module was rewritten to use the formulation of the algorithm that was shown on the Wikipedia article on Graham's scan at the time. This takes care of issues with including collinear points in the hull.

One of these days, somebody should implement Chan's algorithm instead...


Steffen Mueller, <>


Copyright (C) 2003-2011 by Steffen Mueller

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.6 or, at your option, any later version of Perl 5 you may have available.