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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.

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).

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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.

 First PrevNext
 My vote of 5 Kristian Lindberg Vinther, 9-Jan-15 10:42 Kristian Lindberg Vinther 9-Jan-15 10:42
 Interesting Member 10838028, 22-May-14 12:58 Member 10838028 22-May-14 12:58
 Re: Interesting Kristian Vinther, 5-Jan-15 5:32 Kristian Vinther 5-Jan-15 5:32
 How to get a Polygon list asociated to seed Points marceloarguello700, 12-Jan-14 10:17 marceloarguello700 12-Jan-14 10:17
 Small example code would be very much appreciated [modified] pan054, 17-Dec-13 5:20 pan054 17-Dec-13 5:20
 divide and conquer . rizikandry, 23-Jul-13 4:02 rizikandry 23-Jul-13 4:02
 MESSAGE FROM THE OWNER: Help improve this project on Google Code! BenDi, 21-Apr-13 7:59 BenDi 21-Apr-13 7:59
 Rounding error when creating circles for new nodes Bwd Yeti, 19-Apr-13 1:50 Bwd Yeti 19-Apr-13 1:50
 Re: Rounding error when creating circles for new nodes BenDi, 21-Apr-13 7:56 BenDi 21-Apr-13 7:56
 Don't know where to start [modified] Member 9989758, 18-Apr-13 17:58 Member 9989758 18-Apr-13 17:58
 My vote of 4 PehGuevara, 7-Mar-13 22:40 PehGuevara 7-Mar-13 22:40
 Getting regions from graph Bixel, 6-Feb-13 15:14 Bixel 6-Feb-13 15:14
 Re: Getting regions from graph BenDi, 7-Feb-13 0:50 BenDi 7-Feb-13 0:50
 Re: Getting regions from graph Bixel, 7-Feb-13 13:06 Bixel 7-Feb-13 13:06
 Separating braches of a medial axis sampled from inner voronoi points of a polygon Member 9175832, 17-Jul-12 17:19 Member 9175832 17-Jul-12 17:19
 Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary Member 9175832, 14-Jul-12 6:02 Member 9175832 14-Jul-12 6:02
 Re: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary BenDi, 15-Jul-12 1:27 BenDi 15-Jul-12 1:27
 Re: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary Kenneth Haugland, 17-Jul-12 10:31 Kenneth Haugland 17-Jul-12 10:31
 Re: Finding distance for VoronoiGraph vertizes representing Medial Axis of closed boundary Member 9175832, 17-Jul-12 17:11 Member 9175832 17-Jul-12 17:11
 Is there a way to construct polygons from all the edges ? And how ? seb.49, 3-Jun-12 22:36 seb.49 3-Jun-12 22:36
 Possible issue. When I draw 2 points I haven't 2 area seb.49, 31-May-12 0:59 seb.49 31-May-12 0:59
 Re: Possible issue. When I draw 2 points I haven't 2 area BenDi, 31-May-12 4:11 BenDi 31-May-12 4:11
 Re: Possible issue. When I draw 2 points I haven't 2 area seb.49, 31-May-12 5:44 seb.49 31-May-12 5:44
 Re: Possible issue. When I draw 2 points I haven't 2 area BenDi, 31-May-12 8:00 BenDi 31-May-12 8:00
 Re: Possible issue. When I draw 2 points I haven't 2 area seb.49, 31-May-12 10:53 seb.49 31-May-12 10:53
 This code is shitted Member 8683705, 14-May-12 5:42 Member 8683705 14-May-12 5:42
 Re: This code is shitted maamaamaa, 29-Jun-13 6:42 maamaamaa 29-Jun-13 6:42
 Any way to handle boundaries and holes? James Maeding, 16-Dec-10 12:03 James Maeding 16-Dec-10 12:03
 Re: Any way to handle boundaries and holes? xinaesthetic, 30-Sep-11 8:38 xinaesthetic 30-Sep-11 8:38
 My vote of 5 maurice.calvert, 1-Sep-10 0:08 maurice.calvert 1-Sep-10 0:08
 Re: My vote of 5 Member 8683705, 14-May-12 5:45 Member 8683705 14-May-12 5:45
 Re: My vote of 5 maurice.calvert, 14-May-12 6:32 maurice.calvert 14-May-12 6:32
 Re: My vote of 5 Member 8683705, 14-May-12 22:38 Member 8683705 14-May-12 22:38
 Re: My vote of 5 maurice.calvert, 15-May-12 5:56 maurice.calvert 15-May-12 5:56
 Voronoi Cells C-Bl, 28-Jul-09 0:08 C-Bl 28-Jul-09 0:08
 Re: 3 data points case rhill-ca, 26-Jun-09 7:45 rhill-ca 26-Jun-09 7:45
 Another wrong vertex Sunil Terkar, 11-May-09 3:04 Sunil Terkar 11-May-09 3:04
 Re: Another wrong vertex BenDi, 11-May-09 11:03 BenDi 11-May-09 11:03
 Re: Another wrong vertex Sunil Terkar, 12-May-09 1:37 Sunil Terkar 12-May-09 1:37
 Re: Another wrong vertex Sunil Terkar, 12-May-09 6:09 Sunil Terkar 12-May-09 6:09
 Re: Another wrong vertex rhill-ca, 26-Jun-09 7:34 rhill-ca 26-Jun-09 7:34
 Short of one edge and one vertex Sunil Terkar, 6-May-09 0:11 Sunil Terkar 6-May-09 0:11
 Re: Short of one edge and one vertex rhill-ca, 26-Jun-09 7:31 rhill-ca 26-Jun-09 7:31
 medial axis led, 16-Apr-09 10:38 led 16-Apr-09 10:38
 Hello: I'm working on a project that involves finding the medial axis of vector polygons and was hoping from all that I've read that using the voronoi would allow me to do this. has anyone has experience w/ working w/ this project and finding the medial axis? thanks, Proctor
 Thanks! Reconstructivism, 30-Mar-09 3:48 Reconstructivism 30-Mar-09 3:48
 Rays Wayne Romer, 22-Mar-09 21:55 Wayne Romer 22-Mar-09 21:55
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