Efficient delaunay mesh generation from sampled scalar functions

Samrat Goswami, Andrew Gillette, Chandrajit Bajaj

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

Many modern research areas face the challenge of meshing level sets of sampled scalar functions. While many algorithms focus on ensuring geometric qualities of the output mesh, recent attention has been paid to building topologically accurate Delaunay conforming meshes of any level set from such volumetric data. In this paper, we present an algorithm which constructs a surface mesh homeomorphic to the true level set of the sampled scalar function. The presented algorithm also produces a tetrahedral volumetric mesh of good quality, both interior and exterior to the level set. The meshing scheme presented substantially improves over the existing algorithms in terms of efficiency. Finally, we show that when the unknown sampled scalar function, for which the level set is to be meshed, is approximated by a specific class of interpolant, the algorithm can be simplified by taking into account the nature of the interpolation scheme so as to circumvent some of the critical computations which tend to produce numerical instability.

Original languageEnglish (US)
Title of host publicationProceedings of the 16th International Meshing Roundtable, IMR 2007
Pages495-512
Number of pages18
DOIs
StatePublished - 2008
Externally publishedYes
Event16th International Meshing Roundtable, IMR 2007 - Seattle, WA, United States
Duration: Oct 14 2007Oct 17 2007

Other

Other16th International Meshing Roundtable, IMR 2007
CountryUnited States
CitySeattle, WA
Period10/14/0710/17/07

Fingerprint

Mesh generation
Delaunay
Mesh Generation
Level Set
Scalar
Mesh
Meshing
Numerical Instability
Interpolants
Homeomorphic
Interpolation
Interior
Interpolate
Tend
Unknown
Output

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Modeling and Simulation

Cite this

Goswami, S., Gillette, A., & Bajaj, C. (2008). Efficient delaunay mesh generation from sampled scalar functions. In Proceedings of the 16th International Meshing Roundtable, IMR 2007 (pp. 495-512) https://doi.org/10.1007/978-3-540-75103-8_28

Efficient delaunay mesh generation from sampled scalar functions. / Goswami, Samrat; Gillette, Andrew; Bajaj, Chandrajit.

Proceedings of the 16th International Meshing Roundtable, IMR 2007. 2008. p. 495-512.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Goswami, S, Gillette, A & Bajaj, C 2008, Efficient delaunay mesh generation from sampled scalar functions. in Proceedings of the 16th International Meshing Roundtable, IMR 2007. pp. 495-512, 16th International Meshing Roundtable, IMR 2007, Seattle, WA, United States, 10/14/07. https://doi.org/10.1007/978-3-540-75103-8_28
Goswami S, Gillette A, Bajaj C. Efficient delaunay mesh generation from sampled scalar functions. In Proceedings of the 16th International Meshing Roundtable, IMR 2007. 2008. p. 495-512 https://doi.org/10.1007/978-3-540-75103-8_28
Goswami, Samrat ; Gillette, Andrew ; Bajaj, Chandrajit. / Efficient delaunay mesh generation from sampled scalar functions. Proceedings of the 16th International Meshing Roundtable, IMR 2007. 2008. pp. 495-512
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