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Posted 10 Aug 2005

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# Fortune's Voronoi algorithm implemented in C#

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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 `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.

 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
 Voronoi Cells C-Bl27-Jul-09 23:08 C-Bl 27-Jul-09 23:08
 Re: 3 data points case rhill-ca26-Jun-09 6:45 rhill-ca 26-Jun-09 6:45
 somebody have a free C# code, to generate the Polygon for each data point using a boundary polygon that could be the convex hull(or extended convex hull) of the data points. thks.
 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
 Re: Rays Reconstructivism30-Mar-09 2:56 Reconstructivism 30-Mar-09 2:56
 Re: Rays BenDi30-Mar-09 8:57 BenDi 30-Mar-09 8:57