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

Visualization of the 2D Voronoi Diagram and the Delaunay Triangulation

, 18 Nov 2008 CPOL
Rate this:
Please Sign up or sign in to vote.
An add-on for the Fortune's algorithm.

Introduction

This example uses a good implementation of the Fortune's algorithm performed by BenDi (see here). The goal of this application is the visualization of the Voronoi diagram.

Background

For more information, see these articles on Wikipedia:

Using the code

The solution for the visualization problem is very easy. We add two static methods on the Fortune class:

/// <summary>
/// Visualization of 2D Voronoi map.
/// </summary>
/// <param name="weight">Weight of result image.</param>
/// <param name="height">Height of result image.</param>
/// <param name="Datapoints">Array of data points.</param>
/// <returns>Result bitmap.</returns>
public static Bitmap GetVoronoyMap(int weight, int height, IEnumerable Datapoints)
{
    Bitmap bmp = new Bitmap(weight, height);
    VoronoiGraph graph = Fortune.ComputeVoronoiGraph(Datapoints);
    Graphics g = Graphics.FromImage(bmp);
    foreach (object o in graph.Vertizes)
    {
        Vector v = (Vector)o;
        g.DrawEllipse(Pens.Black, (int)v[0]-2, (int)v[1]-2, 4, 4);
    }
    foreach (object o in Datapoints)
    {
        Vector v = (Vector)o;
        g.DrawEllipse(Pens.Red, (int)v[0]-1, (int)v[1]-1, 2, 2);
    }
    foreach (object o in graph.Edges)
    {
        VoronoiEdge edge = (VoronoiEdge)o;
        try
        {
            g.DrawLine(Pens.Brown, (int)edge.VVertexA[0], 
              (int)edge.VVertexA[1], (int)edge.VVertexB[0], 
              (int)edge.VVertexB[1]);
        }
        catch { }
    }
    return bmp;
}

/// <summary>
/// Visualization of Delaunay Triangulation
/// </summary>
/// <param name="weight">Weight of result image.</param>
/// <param name="height">Height of result image.</param>
/// <param name="Datapoints">Result bitmap.</param>
/// <returns></returns>
public static Bitmap GetDelaunayTriangulation(int weight, 
              int height, IEnumerable Datapoints)
{
    Bitmap bmp = new Bitmap(weight, height);
    VoronoiGraph graph = Fortune.ComputeVoronoiGraph(Datapoints);
    Graphics g = Graphics.FromImage(bmp);
    foreach (object o in Datapoints)
    {
        Vector v = (Vector)o;
        g.DrawEllipse(Pens.Red, (int)v[0] - 1, (int)v[1] - 1, 2, 2);
        foreach (object obj in graph.Edges)
        {
            VoronoiEdge edge = (VoronoiEdge)obj;
            if ((edge.LeftData[0] == v[0])&(edge.LeftData[1] == v[1]))
            {
                g.DrawLine(Pens.Black, (int)edge.LeftData[0], (int)edge.LeftData[1], 
                          (int)edge.RightData[0], (int)edge.RightData[1]);
            }
        }
    }
    return bmp;
}

And now, we have images with diagrams:

delane.JPG

Figure 1.Delaunay triangulation.

voronoi.JPG

Figure 2.Voronoi diagram.

Points of interest

Voronoi diagram is a very useful thing. It has specially interesting applications on terrain generation. I would like to develop a simple terrain generation algorithm based on the Voronoi diagram in future.

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Share

About the Author

Maxim_Barsuk
Software Developer
Russian Federation Russian Federation
Hello! My name is Maxim Subbotin.
 
Now I work in sphere of web-development. I'm interesting researches in SEO field.
If you interesting, you can see this tool:
 
KeywordCompetitor

Comments and Discussions

 
BugDon't use this code! PinmemberPehGuevara7-Mar-13 7:52 
QuestionWhy when I draw 2 points I don't see a line Pinmemberseb.4931-May-12 0:49 
NewsThis algorithm fails when presented with a large number of points with obtuse angles PinmemberTomcat_101010101014-Sep-10 17:05 
GeneralRays PinmemberProphetLOD26-Jun-09 12:01 
GeneralRe: Rays PinmemberMaxim_Barsuk28-Jun-09 20:13 
GeneralRe: Rays PinmemberProphetLOD3-Jul-09 6:35 
GeneralInteresting vision PinmemberFDemers11-May-09 23:13 
GeneralRe: Interesting vision PinmemberMaxim_Barsuk12-May-09 0:34 
GeneralRe: Interesting vision PinmemberFDemers12-May-09 0:52 
GeneralRe: Interesting vision PinmemberMaxim_Barsuk12-May-09 2:19 
Yes, I understand. This is a cool idea. I'm not sure that the Voronoi diagram can be applied in classical form for this purpose. Perhaps, solution of this problem needs for expanded methods of approximation. If you want, I will try do something like this (don't promise that it will be done quickly). Smile | :)
GeneralRe: Interesting vision PinmemberFDemers12-May-09 2:28 
QuestionWPF? Pinmembersotona20-Nov-08 5:45 
AnswerRe: WPF? PinmemberMaxim_Barsuk20-Nov-08 7:20 
GeneralDelaunay PinmemberGünther M. FOIDL19-Nov-08 5:32 
GeneralRe: Delaunay PinmemberMaxim_Barsuk19-Nov-08 20:08 

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 | Terms of Use | Mobile
Web01 | 2.8.1411023.1 | Last Updated 19 Nov 2008
Article Copyright 2008 by Maxim_Barsuk
Everything else Copyright © CodeProject, 1999-2014
Layout: fixed | fluid