cvt_1d_lloyd


cvt_1d_lloyd, a Python code which allows the user to carry out Lloyd's algorithm for a Centroidal Voronoi Tessellation (CVT) in the interval [0,1].

The determination of the Voronoi regions is carried out using exact techniques.

For n generators, the solution is known in advance:

x(i) = ( 2 * i - 1 ) / ( 2 * n )
Lloyd's iterative algorithm starts from an arbitrary vector x, however, so it is interesting to see how the approximate solution evolves toward the correct answer.

Usage:

cvt_1d_lloyd ( n, it_num, init, prefix )
where

Licensing:

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

Languages:

cvt_1d_lloyd is available in a MATLAB version and a Python version.

Related Data and Programs:

cvt_2d_sampling, a Python code which computes an N-point Centroidal Voronoi Tessellation (CVT) within the unit square [0,1]x[0,1], under a uniform density, using sampling to estimate the Voronoi regions.

florida_cvt_geo, a Python code which creates a centroidal Voronoi Tessellation (CVT) of the state of Florida, based solely on geometric considerations.

florida_cvt_pop, a Python code which creates a centroidal Voronoi Tessellation (CVT) of the state of Florida, based on population density.

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. Qiang Du, Vance Faber, Max Gunzburger,
    Centroidal Voronoi Tessellations: Applications and Algorithms,
    SIAM Review, Volume 41, 1999, pages 637-676.

Source Code:

RANDOM sets the random initial values, using 40 generators and 400 steps.

SQUASHED sets the "squashed" initial values between 0.01 and 0.02, using 40 generators and 400 steps.


Last revised on 16 September 2016.