### 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 language | English (US) |
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Title of host publication | Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997 |

Publisher | Association for Computing Machinery, Inc |

Pages | 279-286 |

Number of pages | 8 |

ISBN (Electronic) | 0897918967, 9780897918961 |

DOIs | |

State | Published - Aug 3 1997 |

Event | 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997 - Los Angeles, United States Duration: Aug 3 1997 → Aug 8 1997 |

### Publication series

Name | Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997 |
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### Other

Other | 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997 |
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Country | United States |

City | Los Angeles |

Period | 8/3/97 → 8/8/97 |

### Fingerprint

### 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

### Cite this

*Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997*(pp. 279-286). (Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997). Association for Computing Machinery, Inc. https://doi.org/10.1145/258734.258868