Guaranteeing the topology of an implicit surface polygonization for interactive modeling

Barton T. Stander, John C Hart

Research output: Contribution to conferencePaper

Abstract

Morse theory shows how the topology of an implicit surface is affected by its function's critical points, whereas catastrophe theory shows how these critical points behave as the function's parameters change. Interval analysis finds the critical points, and they can also be tracked efficiently during parameter changes. Changes in the function value at these critical points cause changes in the topology. Techniques for modifying the polygonization to accommodate such changes in topology are given. These techniques are robust enough to guarantee the topology of an implicit surface polygonization, and are efficient enough to maintain this guarantee during interactive modeling. The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.

Original languageEnglish (US)
DOIs
StatePublished - Jul 31 2005
Externally publishedYes
EventACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005 - Los Angeles, United States
Duration: Jul 31 2005Aug 4 2005

Other

OtherACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005
CountryUnited States
CityLos Angeles
Period7/31/058/4/05

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Topology

Keywords

  • Catastrophe theory
  • Critical points
  • Implicit surfaces
  • Interactive modeling
  • Interval analysis
  • Morse theory
  • Particle systems
  • Polygonization
  • Topology

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Human-Computer Interaction
  • Software

Cite this

Stander, B. T., & Hart, J. C. (2005). Guaranteeing the topology of an implicit surface polygonization for interactive modeling. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States. https://doi.org/10.1145/1198555.1198642

Guaranteeing the topology of an implicit surface polygonization for interactive modeling. / Stander, Barton T.; Hart, John C.

2005. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States.

Research output: Contribution to conferencePaper

Stander, BT & Hart, JC 2005, 'Guaranteeing the topology of an implicit surface polygonization for interactive modeling' Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States, 7/31/05 - 8/4/05, . https://doi.org/10.1145/1198555.1198642
Stander BT, Hart JC. Guaranteeing the topology of an implicit surface polygonization for interactive modeling. 2005. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States. https://doi.org/10.1145/1198555.1198642
Stander, Barton T. ; Hart, John C. / Guaranteeing the topology of an implicit surface polygonization for interactive modeling. Paper presented at ACM SIGGRAPH 2005 International Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 2005, Los Angeles, United States.
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