### Abstract

This paper presents a robust method for tracing intersection curve segments between continuous rational parametric surfaces, typically rational polynomial parametric surface patches. The tracing procedure is based on a validated ordinary differential equation (ODE) system solver which can be applied, without substantial overhead, for transversal as well as tangential intersections. Application of the validated ODE solver in the context of eliminating the phenomenon of straying and looping is discussed. In addition, we develop a method to fulfill the condition of a continuous gap-free boundary with a definite numerically verified upper bound for the intersection curve error in parameter space and is further mapped to an upper bound for the intersection curve error in 3D model space, which assists in defining well-formed boundary representation models of complex 3D solids.

Original language | English |
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Pages (from-to) | 249-254 |

Number of pages | 6 |

Journal | ACM Symposium on Solid Modeling and Applications, SM |

Publication status | Published - 2004 Dec 1 |

Externally published | Yes |

Event | Ninth ACM Symposium on Solid Modeling and Applications, SM'04 - Genoa, Italy Duration: 2005 Jun 9 → 2005 Jun 11 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*ACM Symposium on Solid Modeling and Applications, SM*, 249-254.