Stable mesh decimation

Chandrajit Bajaj, Andrew Gillette, Qin Zhang

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

2 Scopus citations

Abstract

Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to guide the reduction process is chosen independent of the function the end user aims to calculate, analyze, or adaptively refine. In this paper, we argue that such a decoupling of structure from function modeling is often unwise as small changes in geometry may cause large changes in the associated function. A stable approach to mesh decimation, therefore, ought to be guided primarily by an analysis of functional sensitivity, a property dependent on both the particular application and the equations used for computation (e.g. integrals, derivatives, or integral/partial differential equations). We present a methodology to elucidate the geometric sensitivity of functionals via two major functional discretization techniques: Galerkin finite element and discrete exterior calculus. A number of examples are given to illustrate the methodology and provide numerical examples to further substantiate our choices.

Original languageEnglish (US)
Title of host publicationProceedings - SPM 2009
Subtitle of host publicationSIAM/ACM Joint Conference on Geometric and Physical Modeling
Pages277-282
Number of pages6
DOIs
StatePublished - Nov 9 2009
Externally publishedYes
EventSPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling - San Francisco, CA, United States
Duration: Oct 5 2009Oct 8 2009

Publication series

NameProceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling

Other

OtherSPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling
CountryUnited States
CitySan Francisco, CA
Period10/5/0910/8/09

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computer Vision and Pattern Recognition
  • Mathematics(all)

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  • Cite this

    Bajaj, C., Gillette, A., & Zhang, Q. (2009). Stable mesh decimation. In Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling (pp. 277-282). [1629290] (Proceedings - SPM 2009: SIAM/ACM Joint Conference on Geometric and Physical Modeling). https://doi.org/10.1145/1629255.1629290