## Abstract

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.

Original language | English |
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Pages (from-to) | 473-483 |

Number of pages | 11 |

Journal | CAD Computer Aided Design |

Volume | 37 |

Issue number | 5 SPEC.ISS. |

DOIs | |

Publication status | Published - 2005 Apr 15 |

Externally published | Yes |

### Bibliographical note

Funding Information:The authors would like to thank the anonymous reviewers for their useful comments. All the algorithms and figures presented in this paper were implemented and generated using the IRIT solid modeling system [4] developed at the Technion, Israel. This research was supported in part by the Israeli Ministry of Science Grant No. 01-01-01509, in part by the Korean Ministry of Science and Technology (MOST) under the Korean-Israeli binational research grant, in part by grants No. R01-2002-000-00512-0 and No. R04-2004-000-10099-0 from the Basic Research Program of the Korea Science and Engineering Foundation (KOSEF), and in part by Kyungpook National University Research Fund 2004.

## Keywords

- Freeform surfaces
- Ringed surfaces
- Ruled surfaces
- Surface-surface intersection
- Swept surfaces

## ASJC Scopus subject areas

- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Industrial and Manufacturing Engineering