Create temperature maps with 2D Voronoi diagrams

• Download source code - 67.3 KB

Introduction

Voronoi Diagram is a useful mathematic abstraction which has many applications. You can read about it here and here. You can also see some examples here: Visualization of the 2D Voronoi Diagram and the Delaunay Triangulation and Fortune's Voronoi algorithm implemented in C#.

Background

Yesterday, I solved a problem: we have many weather centers and each weather center has coordinates (X, Y) and current temperature value (T). The goal of our solution was to create a temperature map.

Using the code

The structure TemperatureLocation stores data about the weather center: coordinates X, Y, and the temperature value.

public struct TemperatureLocation
{
    private double x;

    public double X
    {
        get { return x; }
        set { x = value; }
    }
    private double y;

    public double Y
    {
        get { return y; }
        set { y = value; }
    }
    private double t;

    public double T
    {
        get { return t; }
        set { t = value; }
    }

    public TemperatureLocation(double x, double y, double t)
    {
        this.x = x;
        this.y = y;
        this.t = t;
    }

    public double GetDistance(TemperatureLocation tl)
    {
        return Math.Sqrt((this.x - tl.x) * (this.x - tl.x) + 
                         (this.y - tl.y) * (this.y - tl.y));
    }
}

The class VoronoiTemparature is designed to create temperature maps. We load data about weather center, the parameters of the image (the color of cold and hot temperatures), and get the image of the map. For a more realistic map (without accurate Voronoi cells), use a simple smooth effect. The result of the test creation map can be seen on Figure 1.

Points of interest

Creating temperature maps is really a problem in meteorology. For a good mapping, we must use interpolation algorithms (for a smooth isotherm). It is one of many Voronoi diagram applications (Voronoi died exactly 100 years ago, on 11-19-1908).