### Abstract

We present efficient and robust algorithms for intersecting a freeform surface with a ringed surface or a ruled surface. A ringed surface is given as a one-parameter family of circles. By computing the intersection between a freeform surface and each circle 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; and the intersection curve is constructed by connecting them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of two polynomial equations in the parameter space. The intersection between a freeform surface and a ruled surface can be computed in a similar way.

Original language | English |
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Title of host publication | Proceedings - Geometric Modeling and Processing 2004 |

Editors | S.M. Hu, H. Pottmann |

Pages | 38-45 |

Number of pages | 8 |

Publication status | Published - 2004 Sep 29 |

Externally published | Yes |

Event | Proceedings - Geometric Modeling and Processing 2004 - Beijing, China Duration: 2004 Apr 13 → 2004 Apr 15 |

### Other

Other | Proceedings - Geometric Modeling and Processing 2004 |
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Country | China |

City | Beijing |

Period | 04/4/13 → 04/4/15 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings - Geometric Modeling and Processing 2004*(pp. 38-45)

**Intersecting a freeform surface with a ruled or a ringed surface.** / Seong, Jun Kyung; Kim, Ku Jin; Kim, Myung Soo; Elber, Gershon.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - Geometric Modeling and Processing 2004.*pp. 38-45, Proceedings - Geometric Modeling and Processing 2004, Beijing, China, 04/4/13.

}

TY - GEN

T1 - Intersecting a freeform surface with a ruled or a ringed surface

AU - Seong, Jun Kyung

AU - Kim, Ku Jin

AU - Kim, Myung Soo

AU - Elber, Gershon

PY - 2004/9/29

Y1 - 2004/9/29

N2 - We present efficient and robust algorithms for intersecting a freeform surface with a ringed surface or a ruled surface. A ringed surface is given as a one-parameter family of circles. By computing the intersection between a freeform surface and each circle 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; and the intersection curve is constructed by connecting them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of two polynomial equations in the parameter space. The intersection between a freeform surface and a ruled surface can be computed in a similar way.

AB - We present efficient and robust algorithms for intersecting a freeform surface with a ringed surface or a ruled surface. A ringed surface is given as a one-parameter family of circles. By computing the intersection between a freeform surface and each circle 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; and the intersection curve is constructed by connecting them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of two polynomial equations in the parameter space. The intersection between a freeform surface and a ruled surface can be computed in a similar way.

UR - http://www.scopus.com/inward/record.url?scp=4544292588&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4544292588&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0769520782

SP - 38

EP - 45

BT - Proceedings - Geometric Modeling and Processing 2004

A2 - Hu, S.M.

A2 - Pottmann, H.

ER -