HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Anisotropic Diagrams: Labelle Shewchuk approach revisited

Jean-Daniel Boissonnat 1, 2 Camille Wormser 1, * Mariette Yvinec 1
* Corresponding author
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Futurs
Abstract : F. Labelle and J. Shewchuk have proposed a discrete definition of anisotropic Voronoi diagrams. These diagrams are parametrized by a metric field. Under mild hypotheses on the metric field, such Voronoi diagrams can be refined so that their dual is a triangulation, with elements shaped according to the specified anisotropic metric field. We propose an alternative view of the construction of these diagrams and a variant of Labelle and Shewchuk's meshing algorithm. This variant computes the Voronoi vertices using a higher dimensional power diagram and refines the diagram as long as dual triangles overlap. We see this variant as a first step toward a 3-dimensional anisotropic meshing algorithm.
Document type :
Journal articles
Complete list of metadata

Cited literature [10 references]  Display  Hide  Download

https://hal.inria.fr/inria-00336798
Contributor : Mariette Yvinec Connect in order to contact the contributor
Submitted on : Wednesday, November 5, 2008 - 10:29:20 AM
Last modification on : Friday, February 4, 2022 - 3:16:17 AM
Long-term archiving on: : Monday, June 7, 2010 - 8:26:16 PM

File

aniso-tcs.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec. Anisotropic Diagrams: Labelle Shewchuk approach revisited. Theoretical Computer Science, Elsevier, 2008, pp.163-173. ⟨10.1016/j.tcs.2008.08.006⟩. ⟨inria-00336798⟩

Share

Metrics

Record views

135

Files downloads

230