Click here to Skip to main content
Click here to Skip to main content

Fortune's Voronoi algorithm implemented in C#

, 21 Apr 2013
Rate this:
Please Sign up or sign in to vote.
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 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.

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).

License

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

Share

About the Author

BenDi
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

 
QuestionInteresting PinmemberMember 1083802822-May-14 11:58 
QuestionHow to get a Polygon list asociated to seed Points Pinmembermarceloarguello70012-Jan-14 9:17 
QuestionSmall example code would be very much appreciated [modified] Pinmemberpan05417-Dec-13 4:20 
Questionvoronoy bad link PinmemberGiovanni Cuccureddu21-Sep-13 21:22 
Questiondivide and conquer . Pinmemberrizikandry23-Jul-13 3:02 
QuestionMESSAGE FROM THE OWNER: Help improve this project on Google Code! PinmemberBenDi21-Apr-13 6:59 
QuestionRounding error when creating circles for new nodes PinmemberBwd Yeti19-Apr-13 0:50 
AnswerRe: Rounding error when creating circles for new nodes PinmemberBenDi21-Apr-13 6:56 
QuestionDon't know where to start [modified] PinmemberMember 998975818-Apr-13 16:58 
GeneralMy vote of 4 PinmemberPehGuevara7-Mar-13 21:40 
QuestionGetting regions from graph PinmemberBixel6-Feb-13 14:14 
AnswerRe: Getting regions from graph PinmemberBenDi6-Feb-13 23:50 
GeneralRe: Getting regions from graph PinmemberBixel7-Feb-13 12:06 
QuestionSeparating braches of a medial axis sampled from inner voronoi points of a polygon PinmemberMember 917583217-Jul-12 16:19 
QuestionFinding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary PinmemberMember 917583214-Jul-12 5:02 
GeneralRe: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary PinmemberBenDi15-Jul-12 0:27 
AnswerRe: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary PinmemberKenneth Haugland17-Jul-12 9:31 
GeneralRe: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary PinmemberMember 917583217-Jul-12 16:11 
QuestionIs there a way to construct polygons from all the edges ? And how ? Pinmemberseb.493-Jun-12 21:36 
QuestionPossible issue. When I draw 2 points I haven't 2 area Pinmemberseb.4930-May-12 23:59 
AnswerRe: Possible issue. When I draw 2 points I haven't 2 area PinmemberBenDi31-May-12 3:11 
GeneralRe: Possible issue. When I draw 2 points I haven't 2 area Pinmemberseb.4931-May-12 4:44 
GeneralRe: Possible issue. When I draw 2 points I haven't 2 area PinmemberBenDi31-May-12 7:00 
GeneralRe: Possible issue. When I draw 2 points I haven't 2 area Pinmemberseb.4931-May-12 9:53 
QuestionThis code is shitted PinmemberMember 868370514-May-12 4:42 
AnswerRe: This code is shitted Pinmembermaamaamaa29-Jun-13 5:42 
QuestionAny way to handle boundaries and holes? PinmemberJames Maeding16-Dec-10 11:03 
AnswerRe: Any way to handle boundaries and holes? Pinmemberxinaesthetic30-Sep-11 7:38 
GeneralMy vote of 5 Pinmembermaurice.calvert31-Aug-10 23:08 
GeneralRe: My vote of 5 PinmemberMember 868370514-May-12 4:45 
GeneralRe: My vote of 5 Pinmembermaurice.calvert14-May-12 5:32 
GeneralRe: My vote of 5 PinmemberMember 868370514-May-12 21:38 
GeneralRe: My vote of 5 Pinmembermaurice.calvert15-May-12 4:56 
Generalplease help soon Pinmemberdaskan8-Aug-09 1:55 
QuestionVoronoi Cells PinmemberC-Bl27-Jul-09 23:08 
Answer3 data points case PinmemberSOAD_21-Jun-09 6:08 
GeneralRe: 3 data points case Pinmemberrhill-ca26-Jun-09 6:45 
GeneralThiessen Polygons PinmemberSOAD_19-Jun-09 14:46 
GeneralAnother wrong vertex PinmemberSunil Terkar11-May-09 2:04 
GeneralRe: Another wrong vertex PinmemberBenDi11-May-09 10:03 
GeneralRe: Another wrong vertex PinmemberSunil Terkar12-May-09 0:37 
GeneralRe: Another wrong vertex PinmemberSunil Terkar12-May-09 5:09 
GeneralRe: Another wrong vertex Pinmemberrhill-ca26-Jun-09 6:34 
GeneralShort of one edge and one vertex PinmemberSunil Terkar5-May-09 23:11 
GeneralRe: Short of one edge and one vertex Pinmemberrhill-ca26-Jun-09 6:31 
Generalmedial axis Pinmemberled16-Apr-09 9:38 
GeneralThanks! PinmemberReconstructivism30-Mar-09 2:48 
GeneralRays PinmemberWayne Romer22-Mar-09 20:55 
GeneralRe: Rays PinmemberReconstructivism30-Mar-09 2:56 
GeneralRe: Rays PinmemberBenDi30-Mar-09 8:57 

General General    News News    Suggestion Suggestion    Question Question    Bug Bug    Answer Answer    Joke Joke    Rant Rant    Admin Admin   

Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages.

| Advertise | Privacy | Mobile
Web03 | 2.8.140827.1 | Last Updated 22 Apr 2013
Article Copyright 2005 by BenDi
Everything else Copyright © CodeProject, 1999-2014
Terms of Service
Layout: fixed | fluid