15,388,892 members
Articles / Programming Languages / C#
Article
Posted 10 Aug 2005

417.4K views
51 bookmarked

# Fortune's Voronoi algorithm implemented in C#

Rate me:
A C# implementation of the Fortune algorithm to compute 2D Voronoi graphs.

NOTE: Code has moved to Google Code!

## 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).

## Share

 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.

 Re: How to use Fortune.ComputeVoronoiGraph function Wayne Romer22-Mar-09 20:56 Wayne Romer 22-Mar-09 20:56
 use with sharpmap agelospanagiotakis14-Feb-09 23:51 agelospanagiotakis 14-Feb-09 23:51
 Re: use with sharpmap BenDi30-Mar-09 8:58 BenDi 30-Mar-09 8:58
 problem mabrouki2331-Dec-08 5:03 mabrouki23 31-Dec-08 5:03
 Visualization. Maxim_Barsuk17-Nov-08 22:05 Maxim_Barsuk 17-Nov-08 22:05
 Data points to Polygons Zanele Mkhize3-Sep-08 3:25 Zanele Mkhize 3-Sep-08 3:25
 Re: Data points to Polygons BenDi3-Sep-08 4:46 BenDi 3-Sep-08 4:46
 A vector line is reversed ... plunkman31-Jul-08 9:51 plunkman 31-Jul-08 9:51
 Afternoon First, great piece of code - have always been interest in Thessien Polygons. Implementing your code to determine regions of influence use lat/longs as well as using GDI to show the image plot via HTML. Had to add some extra hashing, as well as Convex Hulling to determine boundries to build out necessary polygons - worked perfect. I have only found one issue, one of lines/vector seem to be computing values that cause the line to plot in the wrong direction. This only occurs if the point it the lowest. Any ideas ... If you there is way you can get me your email address I will gladly to send you the code or at least send you the out graphic. Thanks in advance Ken Ken
 Re: A vector line is reversed ... plunkman31-Jul-08 10:54 plunkman 31-Jul-08 10:54
 ... what a mess! [modified] Salvatore Previti9-Jun-08 6:29 Salvatore Previti 9-Jun-08 6:29
 problem Member 454520718-Apr-08 0:09 Member 4545207 18-Apr-08 0:09
 help please Member 454520717-Apr-08 12:32 Member 4545207 17-Apr-08 12:32
 Re: help please Member 454520717-Apr-08 13:01 Member 4545207 17-Apr-08 13:01
 sample yansike31-Mar-08 16:42 yansike 31-Mar-08 16:42
 error: wrong voronoi diagrams Morton14-Mar-08 2:42 Morton 14-Mar-08 2:42
 Re: error: wrong voronoi diagrams BenDi14-Mar-08 3:53 BenDi 14-Mar-08 3:53
 Re: error: wrong voronoi diagrams Morton18-Mar-08 0:36 Morton 18-Mar-08 0:36
 Doubt CPMO8-Feb-07 6:58 CPMO 8-Feb-07 6:58
 Re: Doubt BenDi8-Feb-07 9:39 BenDi 8-Feb-07 9:39
 Need help! lizc13-Aug-06 10:32 lizc 13-Aug-06 10:32
 What EULA this code has? Andrea N.11-Aug-06 10:38 Andrea N. 11-Aug-06 10:38
 Re: What EULA this code has? BenDi11-Aug-06 11:06 BenDi 11-Aug-06 11:06
 Re: What EULA this code has? Andrea N.11-Aug-06 11:31 Andrea N. 11-Aug-06 11:31
 New Version [modified] BenDi18-May-06 8:11 BenDi 18-May-06 8:11
 Re: New Version AndreAtIvu18-May-06 23:16 AndreAtIvu 18-May-06 23:16
 Last Visit: 31-Dec-99 18:00     Last Update: 7-Aug-22 15:42 Refresh ᐊ Prev123456 Next ᐅ