README
1NAME
2 Math::ConvexHull - Calculate convex hulls using Graham's scan (n*log(n))
3
4SYNOPSIS
5 use Math::ConvexHull qw/convex_hull/;
6 $hull_array_ref = convex_hull(\@points);
7
8DESCRIPTION
9 "Math::ConvexHull" is a simple module that calculates convex hulls from
10 a set of points in 2D space. It is a straightforward implementation of
11 the algorithm known as Graham's scan which, with complexity of
12 O(n*log(n)), is the fastest known method of finding the convex hull of
13 an arbitrary set of points. There are some methods of eliminating points
14 that cannot be part of the convex hull. These may or may not be
15 implemented in a future version.
16
17 The implementation cannot deal with duplicate points. Therefore, points
18 which are very, very close (think floating point close) to the previous
19 point are dropped since version 1.02 of the module. However, if you pass
20 in randomly ordered data which contains duplicate points, this safety
21 measure might not help you. In that case, you will have to remove
22 duplicates yourself.
23
24 EXPORT
25 None by default, but you may choose to have the "convex_hull()"
26 subroutine exported to your namespace using standard Exporter semantics.
27
28 convex_hull() subroutine
29 "Math::ConvexHull" implements exactly one public subroutine which,
30 surprisingly, is called "convex_hull()". "convex_hull()" expects an
31 array reference to an array of points and returns an array reference to
32 an array of points in the convex hull.
33
34 In this context, a point is considered to be a reference to an array
35 containing an x and a y coordinate. So an example use of "convex_hull()"
36 would be:
37
38 use Data::Dumper;
39 use Math::ConvexHull qw/convex_hull/;
40
41 print Dumper convex_hull(
42 [
43 [0,0], [1,0],
44 [0.2,0.9], [0.2,0.5],
45 [0,1], [1,1],
46 ]
47 );
48
49 # Prints out the points [0,0], [1,0], [0,1], [1,1].
50
51 Please note that "convex_hull()" does not return *copies* of the points
52 but instead returns the same array references that were passed in.
53
54SEE ALSO
55 New versions of this module can be found on http://steffen-mueller.net
56 or CPAN.
57
58 After implementing the algorithm from my CS notes, I found the exact
59 same implementation in the German translation of Orwant et al,
60 "Mastering Algorithms with Perl". Their code reads better than mine, so
61 if you looked at the module sources and don't understand what's going
62 on, I suggest you have a look at the book.
63
64 In early 2011, much of the module was rewritten to use the formulation
65 of the algorithm that was shown on the Wikipedia article on Graham's
66 scan at the time. This takes care of issues with including collinear
67 points in the hull.
68
69 <http://en.wikipedia.org/wiki/Graham_scan>
70
71 One of these days, somebody should implement Chan's algorithm instead...
72
73AUTHOR
74 Steffen Mueller, <smueller@cpan.org>
75
76COPYRIGHT AND LICENSE
77 Copyright (C) 2003-2011 by Steffen Mueller
78
79 This library is free software; you can redistribute it and/or modify it
80 under the same terms as Perl itself, either Perl version 5.6 or, at your
81 option, any later version of Perl 5 you may have available.
82
83