# FreeBSD Manual Pages

```Math::ConvexHull(3)   User Contributed Perl Documentation  Math::ConvexHull(3)

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.

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

AUTHOR
Steffen Mueller,	<smueller@cpan.org>