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Blaschke Santalo diagrams

Computing Blaschke Santalo Diagrams using Centroidal Voronoi Tessellations

Matlab Codes for generating Blaschke Santalo diagrams related to the paper: The numerical approximation of Blaschke-Santalo diagrams using Centroidal Voronoi Tessellations by B. Bogosel, G. Buttazzo and E. Oudet. If you use the code in your work, please give credit by citing the paper and this Github repository.

The library Geogram is needed to run the code. If possible, it should be compiled to use more than the default 6 digits of precision when writing to files. The file mesh_io.cpp needs to be modified accordingly. The Matlab routine fmincon is used, therefore the Matlab Optimization toolbox is required.

Make sure the correct path to the routine compute_RVD is set in VoronoiGeogram.m. Make sure the Matlab path contains the folder and the contents of the subfolders AlgebraicExample, GeometricExample. For example run addpath(genpath(pwd)) in the main folder. ` The main files of the toolbox are as follows:

• VoronoiGeogram.m computes a restricted Voronoi diagram. A set of points and a polygon are given as inputs.
• BlaschkeSantaloWeb.m is used for the algebraic examples
• RunAPWweb.m is used for the geometric ones

Check the corresponding files for typical examples of usage. Typing help file_name will give you the instructions for the three files listed above.

The code is provided without any guarantee. Since the initialization is random, sometimes the Geogram library will not be able to compute the corresponding Voronoi diagram and the algorithm will crash. Simply restart the computation, it will work most of the time.