Fair morse functions for extracting the topological structure of a surface mesh

Xinlai Ni, Michael Garland, John C. Hart

Research output: Contribution to conferencePaper

Abstract

Morse theory reveals the topological structure of a shape based on the critical points of a real function over the shape. A poor choice of this real function can lead to a complex configuration of an unnecessarily high number of critical points. This paper solves a relaxed form of Laplace's equation to find a "fair" Morse function with a user-controlled number and configuration of critical points. When the number is minimal, the resulting Morse complex cuts the shape into a disk. Specifying additional critical points at surface features yields a base domain that better represents the geometry and shares the same topology as the original mesh, and can also cluster a mesh into approximately developable patches. We make Morse theory on meshes more robust with teflon saddles and flat edge collapses, and devise a new "intermediate value propagation" multigrid solver for finding fair Morse functions that runs in provably linear time.

Original languageEnglish (US)
Pages613-622
Number of pages10
DOIs
StatePublished - Dec 1 2004
EventACM SIGGRAPH 2004, SIGGRAPH 2004 - Los Angeles, CA, United States
Duration: Aug 8 2004Aug 12 2004

Other

OtherACM SIGGRAPH 2004, SIGGRAPH 2004
CountryUnited States
CityLos Angeles, CA
Period8/8/048/12/04

Keywords

  • Atlas generation
  • Computational topology
  • Morse theory
  • Surface parameterization
  • Texture mapping

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Human-Computer Interaction

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  • Cite this

    Ni, X., Garland, M., & Hart, J. C. (2004). Fair morse functions for extracting the topological structure of a surface mesh. 613-622. Paper presented at ACM SIGGRAPH 2004, SIGGRAPH 2004, Los Angeles, CA, United States. https://doi.org/10.1145/1186562.1015769