Math::Geometry::Voronoi - compute Voronoi diagrams from sets of points
use Math::Geometry::Voronoi;
# load a set of points
my @points = ([1, 2],
[1, 3],
[2, 2],
[0, 1],
[0, 10],
[0.5, 11]);
my $geo = Math::Geometry::Voronoi->new(points => \@points);
# compute your diagram
$geo->compute;
# extract features
my $lines = $geo->lines;
my $edges = $geo->edges;
my $vertices = $geo->vertices;
# build polygons
my @polygons = $geo->polygons;
This module computes Voronoi diagrams from a set of input points. Info on
Voronoi diagrams can be found here:
http://en.wikipedia.org/wiki/Voronoi_diagram
This module is a wrapper around a C implementation found here:
http://www.derekbradley.ca/voronoi.html
Which is itself a modification of code by Steve Fortune, the inventor of the
algorithm used (Fortune's algorithm):
http://cm.bell-labs.com/who/sjf/
I made changes to the C code to allow reading input and writing output to/from
Perl data-structures. I also modified the memory allocation code to use Perl's
memory allocator. Finally, I changed all floats to doubles to provide better
precision and to match Perl's NVs.
my @points = ([1, 2],
[1, 3],
[2, 2],
[0, 1],
[0, 10],
[0.5, 11]);
my $geo = Math::Geometry::Voronoi->new(points => \@points);
Create a new object, passing in a single required parameter called 'points'.
This must be an array or arrays containing at least two values each, the X,Y
values for your points. Any extra data will be ignored.
Returns the
sorted set of points used by the voronoi algorithm. This is
the ordering refered to by the
lines() output below.
Call this to build the diagram. Returns nothing.
Returns an array ref containing arrays of lines in the output diagram. The data
by index:
0: the a value in the ax + by = c equation for the line
1: the b value
2: the c value
3: the index of one point for which this line is the bisector.
4: the index of the other point for which this line is the bisector.
Note that 3 and 4 are not the end-points of the line - they are points
perpendicular to the line. Either 3 or 4 may be -1 meaning no point.
Returns an array ref containing arrays of vertices in the output diagram. These
are the points which connect edges running along the lines. The data by index:
0: the x value
1: the y value
Returns an array ref containing arrays of edges in the output diagram. An edge
is defined as a segment of a line running between two vertices. The data by
index:
0: the index of the line
1: the index of vertex 1
2: the index of vertex 2
Either 1 or 2 can be -1 meaning "infinite".
@polys = $geo->polygons();
This method attempts to assemble polygons from non-infinite edges in the
diagram. This part of the code is written in Perl and is of my own invention.
I needed this facility in order to color the diagrams created by this module.
It seems to work reasonably well for my uses but I'm sure it's nowhere near
the quality of Steve Fortune's code! Feedback welcome.
This method returns a reference to an array containing first a point index and
then a list of vertex coordinates. The point is the point inside the polygon
and the vertices are in drawing order for the closed polygon surrounding the
point. For example:
@polys = ( $point_index, [$lat1, $lon1], [$lat2, $lon2], ... );
One optional parameter is available - normalize_vertices. This option is
necessary because the algorithm used needs to match up points from one edge to
another and doing that with floating point numbers requires some kind of
normalization (otherwise 1.1 != 1.10001). For example, if your coordinates are
on an integer grid you might do:
@polys = $geo->polygons(normalize_vertices => sub { int($_[0]) });
Or if you're using floating point and your coordinates are useful down to 2
decimal places:
@polys = $geo->polygons(normalize_vertices => sub { sprintf("%.2f", $_[0]) });
The point is to produce coordinates in a format where they will compare as equal
textually, side-stepping the problem of comparing floats numerically.
Possible projects, if you're in the mood to help out:
- Add the ability to combine polygons based on a mapping of
same-type points. Map overlays get cluttered by internal lines
with you're coloring multiple polygons the same. All edges
connect exactly two polygons, so this should be relatively easy.
Sadly, my limited math skills have thwarted me on this one - I
spent several days but ultimately couldn't get it working reliably
on all possible shapes.
- Remove the need for the normalize_vertices option to polygons(),
somehow (fuzzy matching?).
- Setup a site where people can play with the module visually and
see purty colors. Could be an excuse to play with the new canvas
stuff in modern browsers.
- Add tests that actually examine the output for sanity. So far the
tests just look at the format and range of the output data - to
see if it's actually doing a decent diagram I look at graphical
output.
Sam Tregar <sam@tregar.com>
As far as I can tell the underlying C code used here never had a license
attached to it, or if it did I couldn't find any trace of it. If this worries
you please contact Steve and Derek through the links above.
The Perl and XS code in this library is free software; you can redistribute it
and/or modify it under the same terms as Perl itself, either Perl version
5.8.5 or, at your option, any later version of Perl 5 you may have
available.