

A366544


a(n) is a lower bound for the number of distinct stable centroidal Voronoi tessellations (CVTs) of a square with n generators (seeds).


1



1, 1, 1, 1, 2, 3, 3, 3, 2, 2, 3, 5, 8, 6, 5, 3, 4, 7, 10, 21, 21
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OFFSET

0,5


COMMENTS

Stable CVTs are local minimizers of the CVT function (see first paper).
There are other CVTs which are saddle points.
Lloyd's process converges only to stable CVTs.
An efficient twostep semimanual algorithm is used to recognize identical patterns and a fast code for the Lloyd's process.


REFERENCES

Lin Lu, F. Sun, and H. Pan, Global optimization Centroidal Voronoi Tessellation with Monte Carlo Approach, 2012 IEEECS Log Number TVCG2011030067.


LINKS

Yang Liu, Wenping Wang, Bruno Lévy, Feng Sun, DongMing Yan, Lin Lu, and Chenglei Yang, On centroidal Voronoi tessellation—Energy smoothness and fast computation, ACM Transactions on Graphics, Volume 28, Issue 4, Article No. 101, pp. 117, 2009.


EXAMPLE

As initialization, clustering centers for a large number of points in the square are used. For every set of centers, Lloyd's algorithm is iterated and all variants symmetric with respect to rotations and reflections are removed.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



