voronoi_plot

voronoi_plot, a Python code which plots the Voronoi neighborhoods of a set of center points.

The picture is created using discrete pixel geometry, rather than sophisticated analysis. In other words, each center point is assigned a color at random. Then each pixel in the image is colored the same as the nearest center point.

The code allows the user to choose the values of M and N, the number of rows and columns used in the pixel array.

The code allows the user to choose the LP norm in which distances are calculated, with P any positive real value. In particular

• 1: distance = sum of absolute values of differences;
• 2: distance = square root of sum of squares of differences (the Euclidean norm);
• P: distance = P-th root of sum of absolute values of P-th powers of differences;
• float('inf'): distance = maximum of absolute values of differences;

The scipy.spatial.Voronoi() and voronoi_plot_2d() commands can together create and plot a Voronoi diagram when the Euclidean norm is used to measure distance, but they do not have the ability to deal with other norms. This code gives a simple way of viewing such cases.

Usage:

voronoi_plot ( xy, m, n, p )

• xy is the (2,NC) array of center points.
• m is the number of rows in the pixel image;
• n is the number of columns in the pixel image;
• p chooses the P-norm (1, 2,float('inf'), or some positive real value).

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

voronoi_plot is available in a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and codes:

delaunay, a Python code which demonstrates the use of the scipy.spatial function Delaunay(), to compute a Voronoi diagram, and matplotlib.pyplot.triplot(), to display it.

voronoi, a Python code which demonstrates the use of the scipy.spatial function Voronoi(), to compute a Voronoi diagram, and voronoi_plot_2d(), to display it.

Reference:

1. Franz Aurenhammer,
   Voronoi diagrams - a study of a fundamental geometric data structure,
   ACM Computing Surveys,
   Volume 23, Number 3, pages 345-405, September 1991.
2. Herbert Edelsbrunner,
   Geometry and Topology for Mesh Generation,
   Cambridge, 2001,
   QA377.E36,
   ISBN 0-521-79309-2.
3. Joseph O'Rourke,
   Computational Geometry,
   Cambridge University Press,
   Second Edition, 1998,
   QA448.D38.

Source Code:

• voronoi_plot.py, the source code.
• voronoi_plot.sh, runs all the tests.
• voronoi_plot.txt, the output file.

• voronoi.png, 25 random points in a 200x200 pixel array using the L2 norm.