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.