# Fortune's Voronoi algorithm implemented in C#

By , 21 Apr 2013
Votes of 3 or less require a comment

## Introduction

Given a set of two dimensional vectors (or data points), a Voronoi graph is a separation of those points into compartments where all points inside one compartment are closer to the contained data point than to any other data point. I won't give any demonstration here, but if you want to know more about Voronoi graphs, check out this.

The applications of Voronoi graphs are quite broad. Very useful for a lot of optimization problems (in most cases, the Delaunay Triangulation which can be easily derived from a Vononoi graph is used there), it ranges to computing topological maps from bitmaps.

[This is an article for freaks. After a rather painful experience writing the thing I hope it will benefit everyone who is looking for this algorithm in a civilized language (or simply does not want to use Fortune's original C implementation).]

In 1987, Steve Fortune described an algorithm to compute such a graph by using a sweep line in combination with a binary tree. A PowerPoint explanation of the algorithm (the one I used to implement it) can be found here. Note that I did not use the linked data structure to represent a graph - I think that is an unnecessary difficulty in the age of `ArrayList`s and `HashSet`s.

## The Implementation

Data points are represented by my own `Vector` class. It can do much more than needed here (but there was no reason to strip it before bringing it) but I won't explain it here. The most important fact is that although working with `double`s the Vector class automatically rounds values to 10 digits (or whatever is set in the `Vector.Precision` field). Yes, sadly, this is very important if you want to sort of compare `double`s.

A `VoronoiGraph` is a class that only contains a `HashSet` of vertices (as 2D vectors) and a `HashSet` of `VoronoiEdge`s - each with references to the left and right data point and (of course) the two vertices that bound the edge. If the edge is (partially or completely) unbounded, the vector `Fortune.VVUnknown` is used.

`BinaryPriorityQueue` is used for the sweep line event queue.

## Usage

The algorithm itself (`Fortune.ComputeVoronoiGraph(IEnumerable)`) takes any `IEnumerable` containing only two dimensional vectors. It will return a `VoronoiGraph`. The algorithm's complexity is O(n ld(n)) with a factor of about 10 microseconds on my machine (2GHz).

Software Developer (Senior)
Germany
I did my diploma in Dresden and Sydney where I dealt with algorithms, agents and other cool AI stuff. Now I moved to Frankfurt to work on my PhD dealing with software structures for artificial intelligence systems. If I can, I do things in C# and ASP.NET, but if I have to, my C++, Java and SQL are not that bad.
Long Live .NET.

 Voronoi Cells C-Bl 27-Jul-09 23:08
 3 data points case SOAD_ 21-Jun-09 6:08
 In the special case of 3 data points, all FixedPoints are equal to the unique Vertize, isn't wrong??   i made a test with: (0,0);(10,0);(0,10).   and for each edge the fixedPoint is equal to (5,5).   I hope your answer BenDi... Excellent tool!!   cheers
 Re: 3 data points case rhill-ca 26-Jun-09 6:45
 Another wrong vertex Sunil Terkar 11-May-09 2:04
 Re: Another wrong vertex BenDi 11-May-09 10:03
 Re: Another wrong vertex Sunil Terkar 12-May-09 0:37
 Re: Another wrong vertex Sunil Terkar 12-May-09 5:09
 Re: Another wrong vertex rhill-ca 26-Jun-09 6:34
 Last Visit: 31-Dec-99 18:00     Last Update: 11-Dec-13 22:23 Refresh « Prev1234567891011 Next »

| Advertise | Privacy | Mobile
Web03 | 2.7.131211.1 | Last Updated 22 Apr 2013