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

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 )
where

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL 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:


Last revised on 16 October 2016.