Introduction

This application displays Voronoi diagrams and Delauny triangulations. It uses Fortune's voronoi program to compute the Voronoi diagram. The application consumes your sites and produces PDF.

What are Voronoi diagrams?

Just google or take a look at voronoi.com. You will find many documentation about Voronoi diagrams.

Output

The output is your specified paper. If you choose A4 for papersize the Voronoi diagram is rendered on 20,90 cm x 29,70 cm. For best results place the sites within the output page.

Input

The input for the application is an XML file which contains the Voronoi sites. The structure is very simple:

<?xml version = "1.0"?>
<sites>
  <site x="429.886" y="116.559"/>
  <site x="316.039" y="160.386"/>
  <site x="336.193" y="262.213"/>
  <site x="303.346" y="314.039"/>
  <site x="271.5" y="456.866"/>
  <site x="95.6929" y="485.693"/>
  <site x="199.52" y="355.52"/>
  <site x="303.346" y="225.346"/>
  <site x="225.173" y="123.173"/>
  <site x="70" y="64"/>
</sites>

You can also use units like "cm", "pt", "inch" or "mm". The default unit is point.

Sometimes the sites do not fit on the paper. They need scaling and translating to make them fit. You can specify a scaling factor and offset value for x and y coordinates.

<?xml version = "1.0"?>
<sites x-offset="12" y-offset="24" scale="600">
<site x="0.532095" y="0.894141"/>
<site x="0.189043" y="0.613426"/>
[...]

Now the coordinates of every site will be scaled by 600. The x coordinate will be translate by 12 points and the y coordinate by 24 points.

Templates

Output is driven by a template engine. Three templates are built-in.

Delaunay Triangulation

In the same way that a planar graph has its dual graph, a Voronoi diagram has its dual tessellation, called a Delaunay triangulation.