Computing 2D Periodic Centroidal Voronoi Tessellation

Authors:
Dong-Ming Yan;Kai Wang;Bruno Levy;Laurent Alonso
Affiliations:
-;-;-;-
Venue:
ISVD '11 Proceedings of the 2011 Eighth International Symposium on Voronoi Diagrams in Science and Engineering
Year:
2011

Citing 0
Cited 2

GPU-based computation of discrete periodic centroidal Voronoi tessellation in hyperbolic space

Computer-Aided Design
Efficient computation of clipped Voronoi diagram for mesh generation

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we propose an efficient algorithm to compute the centroidal Voronoi tessellation in 2D periodic space. We first present a simple algorithm for constructing the periodic Voronoi diagram (PVD) from a Euclidean Voronoi diagram. The presented PVD algorithm considers only a small set of periodic copies of the input sites, which is more efficient than previous approaches requiring full copies of the sites (9 in 2D and 27 in 3D). The presented PVD algorithm is applied in a fast Newton-based framework for computing the centroidal Voronoi tessellation (CVT). We observe that full-hexagonal patterns can be obtained via periodic CVT optimization attributed to the convergence of the Newton-based CVT computation.