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

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

DESCRIPTION
    "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.

  EXPORT
    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.

SEE ALSO
    New versions of this module can be found on http://steffen-mueller.net
    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.

    <http://en.wikipedia.org/wiki/Graham_scan>

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

AUTHOR
    Steffen Mueller, <smueller@cpan.org>

COPYRIGHT AND LICENSE
    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.