Yet another algorithm for generalized Voronoï Diagrams

Authors:
Ioannis Emiris;Angelos Mantzaflaris;Bernard Mourrain
Affiliations:
University of Athens, Greece;GALAAD, INRIA, France and RICAM, Linz, Austria;GALAAD, INRIA Méditerranée, Sophia-Antipolis, France
Venue:
Proceedings of the 27th Annual ACM Symposium on Applied Computing
Year:
2012

Citing 7
Cited 0

Voronoi diagrams and arrangements

Discrete & Computational Geometry
Curves and surfaces for CAGD: a practical guide

Curves and surfaces for CAGD: a practical guide
Anisotropic voronoi diagrams and guaranteed-quality anisotropic mesh generation

Proceedings of the nineteenth annual symposium on Computational geometry
Subdivision methods for solving polynomial equations

Journal of Symbolic Computation
Exact Delaunay graph of smooth convex pseudo-circles: general predicates, and implementation for ellipses

2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Divide-and-conquer for Voronoi diagrams revisited

Computational Geometry: Theory and Applications
A subdivision approach to planar semi-algebraic sets

GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We design and implement an efficient algorithm for the computation of generalized Voronoï Diagrams (VD's) constrained to a given domain. Our framework is general and applicable to any VD-type where the distance field is given by a polynomial. We use the Bernstein form of polynomials to subdivide the domain and isolate bisector domains or domains that contain a Voronoï vertex. Efficiency is due to a filtering process, based on bounding the distance functions over the subdivided domains. The output is a polygonal description of each Voronoï cell up to any user-defined precision.