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Fortune's Voronoi algorithm implemented in C#

, 21 Apr 2013 MPL 221K 2.6K 49
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A C# implementation of the Fortune algorithm to compute 2D Voronoi graphs.

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).

License

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
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

 First PrevNext
 My vote of 5 Kristian Lindberg Vinther9-Jan-15 9:42 Kristian Lindberg Vinther 9-Jan-15 9:42
 Interesting Member 1083802822-May-14 11:58 Member 10838028 22-May-14 11:58
 Re: Interesting Kristian Vinther5-Jan-15 4:32 Kristian Vinther 5-Jan-15 4:32
 How to get a Polygon list asociated to seed Points marceloarguello70012-Jan-14 9:17 marceloarguello700 12-Jan-14 9:17
 Small example code would be very much appreciated pan05417-Dec-13 4:20 pan054 17-Dec-13 4:20
 voronoy bad link Giovanni Cuccureddu21-Sep-13 21:22 Giovanni Cuccureddu 21-Sep-13 21:22
 divide and conquer . rizikandry23-Jul-13 3:02 rizikandry 23-Jul-13 3:02
 MESSAGE FROM THE OWNER: Help improve this project on Google Code! BenDi21-Apr-13 6:59 BenDi 21-Apr-13 6:59
 Rounding error when creating circles for new nodes Bwd Yeti19-Apr-13 0:50 Bwd Yeti 19-Apr-13 0:50
 Re: Rounding error when creating circles for new nodes BenDi21-Apr-13 6:56 BenDi 21-Apr-13 6:56
 Don't know where to start Member 998975818-Apr-13 16:58 Member 9989758 18-Apr-13 16:58
 My vote of 4 PehGuevara7-Mar-13 21:40 PehGuevara 7-Mar-13 21:40
 Getting regions from graph Bixel6-Feb-13 14:14 Bixel 6-Feb-13 14:14
 Re: Getting regions from graph BenDi6-Feb-13 23:50 BenDi 6-Feb-13 23:50
 Re: Getting regions from graph Bixel7-Feb-13 12:06 Bixel 7-Feb-13 12:06
 Separating braches of a medial axis sampled from inner voronoi points of a polygon Member 917583217-Jul-12 16:19 Member 9175832 17-Jul-12 16:19
 I am looking for a method that will allow me to separate all edges and vertices that describe a sampled medial axis from from a closed polygon of points. I would like to accomplish this so I can then fit an individual geometric component to each branch of the medial axis, whether it be a line, spline, or arc. I was thinking of creating a method for the separation using a depth first search that marked each vertex with a degree of greater than one as the split point. I would like to find a algorithm or library that might accomplish this if possible. No need to recreate the wheel. Looking for some good ideas...
 Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary Member 917583214-Jul-12 5:02 Member 9175832 14-Jul-12 5:02
 Re: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary BenDi15-Jul-12 0:27 BenDi 15-Jul-12 0:27
 Re: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary Kenneth Haugland17-Jul-12 9:31 Kenneth Haugland 17-Jul-12 9:31
 Re: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary Member 917583217-Jul-12 16:11 Member 9175832 17-Jul-12 16:11
 Is there a way to construct polygons from all the edges ? And how ? seb.493-Jun-12 21:36 seb.49 3-Jun-12 21:36
 Possible issue. When I draw 2 points I haven't 2 area seb.4930-May-12 23:59 seb.49 30-May-12 23:59
 Re: Possible issue. When I draw 2 points I haven't 2 area BenDi31-May-12 3:11 BenDi 31-May-12 3:11
 Re: Possible issue. When I draw 2 points I haven't 2 area seb.4931-May-12 4:44 seb.49 31-May-12 4:44
 Re: Possible issue. When I draw 2 points I haven't 2 area BenDi31-May-12 7:00 BenDi 31-May-12 7:00
 Re: Possible issue. When I draw 2 points I haven't 2 area seb.4931-May-12 9:53 seb.49 31-May-12 9:53
 This code is shitted Member 868370514-May-12 4:42 Member 8683705 14-May-12 4:42
 Re: This code is shitted maamaamaa29-Jun-13 5:42 maamaamaa 29-Jun-13 5:42
 Any way to handle boundaries and holes? James Maeding16-Dec-10 11:03 James Maeding 16-Dec-10 11:03
 Re: Any way to handle boundaries and holes? xinaesthetic30-Sep-11 7:38 xinaesthetic 30-Sep-11 7:38
 My vote of 5 maurice.calvert31-Aug-10 23:08 maurice.calvert 31-Aug-10 23:08
 Re: My vote of 5 Member 868370514-May-12 4:45 Member 8683705 14-May-12 4:45
 Re: My vote of 5 maurice.calvert14-May-12 5:32 maurice.calvert 14-May-12 5:32
 Re: My vote of 5 Member 868370514-May-12 21:38 Member 8683705 14-May-12 21:38
 Re: My vote of 5 maurice.calvert15-May-12 4:56 maurice.calvert 15-May-12 4:56
 please help soon daskan8-Aug-09 1:55 daskan 8-Aug-09 1:55
 Voronoi Cells C-Bl27-Jul-09 23:08 C-Bl 27-Jul-09 23:08
 3 data points case SOAD_21-Jun-09 6:08 SOAD_ 21-Jun-09 6:08
 Re: 3 data points case rhill-ca26-Jun-09 6:45 rhill-ca 26-Jun-09 6:45
 Thiessen Polygons SOAD_19-Jun-09 14:46 SOAD_ 19-Jun-09 14:46
 Another wrong vertex Sunil Terkar11-May-09 2:04 Sunil Terkar 11-May-09 2:04
 Re: Another wrong vertex BenDi11-May-09 10:03 BenDi 11-May-09 10:03
 Re: Another wrong vertex Sunil Terkar12-May-09 0:37 Sunil Terkar 12-May-09 0:37
 Re: Another wrong vertex Sunil Terkar12-May-09 5:09 Sunil Terkar 12-May-09 5:09
 Re: Another wrong vertex rhill-ca26-Jun-09 6:34 rhill-ca 26-Jun-09 6:34
 Short of one edge and one vertex Sunil Terkar5-May-09 23:11 Sunil Terkar 5-May-09 23:11
 Re: Short of one edge and one vertex rhill-ca26-Jun-09 6:31 rhill-ca 26-Jun-09 6:31
 medial axis led16-Apr-09 9:38 led 16-Apr-09 9:38
 Thanks! Reconstructivism30-Mar-09 2:48 Reconstructivism 30-Mar-09 2:48
 Rays Wayne Romer22-Mar-09 20:55 Wayne Romer 22-Mar-09 20:55
 Last Visit: 31-Dec-99 18:00     Last Update: 1-Aug-15 16:42 Refresh 123 Next »

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