### 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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Pages | 279-286 |

Number of pages | 8 |

State | Published - Jan 1 1997 |

Event | Proceedings of the 1997 Conference on Computer Graphics, SIGGRAPH - Los Angeles, CA, USA Duration: Aug 3 1997 → Aug 8 1997 |

### Other

Other | Proceedings of the 1997 Conference on Computer Graphics, SIGGRAPH |
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City | Los Angeles, CA, USA |

Period | 8/3/97 → 8/8/97 |

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*Guaranteeing the topology of an implicit surface polygonization for interactive modeling*. 279-286. Paper presented at Proceedings of the 1997 Conference on Computer Graphics, SIGGRAPH, Los Angeles, CA, USA, .