Improved initialisation for centroidal Voronoi tessellation and optimal Delaunay triangulation

Authors:
Jonathan Quinn;Feng Sun;Frank C. Langbein;Yu-Kun Lai;Wenping Wang;Ralph R. Martin
Affiliations:
Cardiff University, School of Computer Science and Informatics, 5 The Parade, Cardiff, CF24 3AA, UK;The University of Hong Kong, Pokfulam Road, Hong Kong;Cardiff University, School of Computer Science and Informatics, 5 The Parade, Cardiff, CF24 3AA, UK;Cardiff University, School of Computer Science and Informatics, 5 The Parade, Cardiff, CF24 3AA, UK;The University of Hong Kong, Pokfulam Road, Hong Kong;Cardiff University, School of Computer Science and Informatics, 5 The Parade, Cardiff, CF24 3AA, UK
Venue:
Computer-Aided Design
Year:
2012

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Abstract

Centroidal Voronoi tessellations and optimal Delaunay triangulations can be approximated efficiently by non-linear optimisation algorithms. This paper demonstrates that the point distribution used to initialise the optimisation algorithms is important. Compared to conventional random initialisation, certain low-discrepancy point distributions help convergence towards more spatially regular results and require fewer iterations for planar and volumetric tessellations.