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Fortune's Voronoi algorithm implemented in C#

, 21 Apr 2013 MPL
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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

GeneralRe: Another wrong vertex PinmemberSunil Terkar12-May-09 6:09 
GeneralRe: Another wrong vertex Pinmemberrhill-ca26-Jun-09 7:34 
GeneralShort of one edge and one vertex PinmemberSunil Terkar6-May-09 0:11 
GeneralRe: Short of one edge and one vertex Pinmemberrhill-ca26-Jun-09 7:31 
Generalmedial axis Pinmemberled16-Apr-09 10:38 
GeneralThanks! PinmemberReconstructivism30-Mar-09 3:48 
GeneralRays PinmemberWayne Romer22-Mar-09 21:55 
GeneralRe: Rays PinmemberReconstructivism30-Mar-09 3:56 
GeneralRe: Rays PinmemberBenDi30-Mar-09 9:57 
GeneralRe: Rays PinmemberPavel Vladov29-Apr-09 1:54 
GeneralRe: Rays PinmemberBenDi29-Apr-09 10:49 
GeneralRe: Rays PinmemberPavel Vladov30-Apr-09 0:39 
GeneralRe: Rays PinmemberBenDi30-Apr-09 9:04 
GeneralRe: Rays PinmemberPavel Vladov30-Apr-09 23:36 
Ok, thanks for the info. I was planning to use Voronoi diagrams for finding the Maximum Inscribed Circle in a simple polygon, but I guess I should read some more information about its properties to determine if it will work for me.
Software products for fitness and health club management, storehouses, shops and barcode generation.

GeneralRe: Rays PinmemberSlagh14-May-09 23:10 
GeneralRe: Rays PinmemberBenDi16-May-09 3:15 
AnswerRe: Rays PinmemberSlagh21-May-09 20:54 
BugRe: Rays PinmemberPehGuevara27-Feb-13 5:15 
GeneralRe: Rays PinmemberBenDi27-Feb-13 22:53 
GeneralRe: Rays PinmemberPehGuevara27-Feb-13 23:32 
GeneralRe: Rays PinmemberBenDi2-Mar-13 9:28 
GeneralRe: Rays PinmemberPehGuevara6-Mar-13 0:59 
GeneralRe: Rays PinmemberBenDi6-Mar-13 1:16 
AnswerRe: Rays PinmemberPehGuevara7-Mar-13 7:44 
GeneralRe: Rays PinmemberRay Hidayat7-Jun-11 19:06 
GeneralRe: Rays Pinmemberckaut30-Jan-10 5:20 
QuestionHow to use Fortune.ComputeVoronoiGraph function PinmemberSunil Terkar3-Mar-09 5:20 
AnswerRe: How to use Fortune.ComputeVoronoiGraph function PinmemberWayne Romer22-Mar-09 21:56 
Generaluse with sharpmap Pinmemberagelospanagiotakis15-Feb-09 0:51 
GeneralRe: use with sharpmap PinmemberBenDi30-Mar-09 9:58 
Generalproblem Pinmembermabrouki2331-Dec-08 6:03 
GeneralVisualization. PinmemberMaxim_Barsuk17-Nov-08 23:05 
GeneralData points to Polygons PinmemberZanele Mkhize3-Sep-08 4:25 
GeneralRe: Data points to Polygons PinmemberBenDi3-Sep-08 5:46 
QuestionA vector line is reversed ... Pinmemberplunkman31-Jul-08 10:51 
AnswerRe: A vector line is reversed ... Pinmemberplunkman31-Jul-08 11:54 
General... what a mess! [modified] PinmemberNeoGeek9-Jun-08 7:29 
Generalproblem PinmemberMember 454520718-Apr-08 1:09 
Generalhelp please PinmemberMember 454520717-Apr-08 13:32 
GeneralRe: help please PinmemberMember 454520717-Apr-08 14:01 
Generalsample Pinmemberyansike31-Mar-08 17:42 
Generalerror: wrong voronoi diagrams PinmemberMorton14-Mar-08 3:42 
GeneralRe: error: wrong voronoi diagrams PinmemberBenDi14-Mar-08 4:53 
GeneralRe: error: wrong voronoi diagrams PinmemberMorton18-Mar-08 1:36 
QuestionDoubt PinmemberCPMO8-Feb-07 7:58 
AnswerRe: Doubt PinmemberBenDi8-Feb-07 10:39 
QuestionNeed help! Pinmemberlizc13-Aug-06 11:32 
QuestionWhat EULA this code has? PinmemberAndrea N.11-Aug-06 11:38 
AnswerRe: What EULA this code has? PinmemberBenDi11-Aug-06 12:06 
GeneralRe: What EULA this code has? PinmemberAndrea N.11-Aug-06 12:31 

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