Planar minimization diagrams via subdivision with applications to anisotropic voronoi diagrams

H. Bennett, E. Papadopoulou, Chee Yap

Research output: Contribution to journalArticle

Abstract

Let X = (f1,., fn) be a set of scalar functions of the form fi: ℝ2 → ℝ which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered e-isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi-algebraic. We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results.

Original languageEnglish (US)
Pages (from-to)229-247
Number of pages19
JournalEurographics Symposium on Geometry Processing
Volume35
Issue number5
DOIs
StatePublished - 2016

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Voronoi Diagram
Subdivision
Diagram
Scalar
Subdivision Algorithm
Voronoi
Predicate
Clustering
Prototype
Computing
Experimental Results
Arbitrary
Approximation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Geometry and Topology

Cite this

Planar minimization diagrams via subdivision with applications to anisotropic voronoi diagrams. / Bennett, H.; Papadopoulou, E.; Yap, Chee.

In: Eurographics Symposium on Geometry Processing, Vol. 35, No. 5, 2016, p. 229-247.

Research output: Contribution to journalArticle

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