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Posted 10 Aug 2005


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Fortune's Voronoi algorithm implemented in C#

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21 Apr 2013MPL2 min read
A C# implementation of the Fortune algorithm to compute 2D Voronoi graphs.

NOTE: Code has moved to Google Code! 


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 ArrayLists and HashSets.

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 doubles 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 doubles.

A VoronoiGraph is a class that only contains a HashSet of vertices (as 2D vectors) and a HashSet of VoronoiEdges - 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.


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).


This article, along with any associated source code and files, is licensed under The Mozilla Public License 1.1 (MPL 1.1)


About the Author

Software Developer (Senior)
Germany 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.

Comments and Discussions

AnswerRe: How to use Fortune.ComputeVoronoiGraph function Pin
Wayne Romer22-Mar-09 20:56
MemberWayne Romer22-Mar-09 20:56 
Generaluse with sharpmap Pin
agelospanagiotakis14-Feb-09 23:51
Memberagelospanagiotakis14-Feb-09 23:51 
GeneralRe: use with sharpmap Pin
BenDi30-Mar-09 8:58
MemberBenDi30-Mar-09 8:58 
Generalproblem Pin
mabrouki2331-Dec-08 5:03
Membermabrouki2331-Dec-08 5:03 
GeneralVisualization. Pin
Maxim_Barsuk17-Nov-08 22:05
MemberMaxim_Barsuk17-Nov-08 22:05 
GeneralData points to Polygons Pin
Zanele Mkhize3-Sep-08 3:25
MemberZanele Mkhize3-Sep-08 3:25 
GeneralRe: Data points to Polygons Pin
BenDi3-Sep-08 4:46
MemberBenDi3-Sep-08 4:46 
QuestionA vector line is reversed ... Pin
plunkman31-Jul-08 9:51
Memberplunkman31-Jul-08 9:51 

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



AnswerRe: A vector line is reversed ... Pin
plunkman31-Jul-08 10:54
Memberplunkman31-Jul-08 10:54 
General... what a mess! [modified] Pin
Salvatore Previti9-Jun-08 6:29
MemberSalvatore Previti9-Jun-08 6:29 
Generalproblem Pin
Member 454520718-Apr-08 0:09
MemberMember 454520718-Apr-08 0:09 
Generalhelp please Pin
Member 454520717-Apr-08 12:32
MemberMember 454520717-Apr-08 12:32 
GeneralRe: help please Pin
Member 454520717-Apr-08 13:01
MemberMember 454520717-Apr-08 13:01 
Generalsample Pin
yansike31-Mar-08 16:42
Memberyansike31-Mar-08 16:42 
Generalerror: wrong voronoi diagrams Pin
Morton14-Mar-08 2:42
MemberMorton14-Mar-08 2:42 
GeneralRe: error: wrong voronoi diagrams Pin
BenDi14-Mar-08 3:53
MemberBenDi14-Mar-08 3:53 
GeneralRe: error: wrong voronoi diagrams Pin
Morton18-Mar-08 0:36
MemberMorton18-Mar-08 0:36 
QuestionDoubt Pin
CPMO8-Feb-07 6:58
MemberCPMO8-Feb-07 6:58 
AnswerRe: Doubt Pin
BenDi8-Feb-07 9:39
MemberBenDi8-Feb-07 9:39 
QuestionNeed help! Pin
lizc13-Aug-06 10:32
Memberlizc13-Aug-06 10:32 
QuestionWhat EULA this code has? Pin
Andrea N.11-Aug-06 10:38
MemberAndrea N.11-Aug-06 10:38 
AnswerRe: What EULA this code has? Pin
BenDi11-Aug-06 11:06
MemberBenDi11-Aug-06 11:06 
GeneralRe: What EULA this code has? Pin
Andrea N.11-Aug-06 11:31
MemberAndrea N.11-Aug-06 11:31 
GeneralNew Version [modified] Pin
BenDi18-May-06 8:11
MemberBenDi18-May-06 8:11 
GeneralRe: New Version Pin
AndreAtIvu18-May-06 23:16
MemberAndreAtIvu18-May-06 23:16 

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