Guaranteeing the topology of an implicit surface polygonization for interactive modeling

Barton T. Stander, John C. Hart

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

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)
Title of host publicationProceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997
PublisherAssociation for Computing Machinery, Inc
Pages279-286
Number of pages8
ISBN (Electronic)0897918967, 9780897918961
DOIs
StatePublished - Aug 3 1997
Externally publishedYes
Event24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997 - Los Angeles, United States
Duration: Aug 3 1997Aug 8 1997

Publication series

NameProceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997

Other

Other24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997
CountryUnited States
CityLos Angeles
Period8/3/978/8/97

Keywords

  • Morse theory
  • catastrophe theory
  • critical points
  • implicit surfaces
  • interactive modeling
  • interval analysis
  • particle systems
  • polygonization
  • topology

ASJC Scopus subject areas

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

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