## 抄録

This paper describes a method to extract the generic features of free-form parametric surfaces for shape interrogation. The umbilical points, which are the singular points of the orthogonal net of lines of curvature, have generic features and may act like fingerprints for shape recognition. We investigate the generic features of the umbilics and behavior of lines of curvature which pass through an umbilic on a parametric free-form surface. Our method is based on a coordinate transformation to set the parametric surface in Monge form and on a Taylor expansion to compute the angles of the tangent lines to the lines of curvatures at an umbilic. We also develop a novel and practical criterion which assures the existence of local extrema of principal curvature functions at umbilical points. Finally, numerical experiments illustrate how the generic features of the umbilics can be applied for surface recognition.

本文言語 | English |
---|---|

ページ（範囲） | 133-161 |

ページ数 | 29 |

ジャーナル | Computer Aided Geometric Design |

巻 | 13 |

号 | 2 |

DOI | |

出版ステータス | Published - 1996 3月 |

外部発表 | はい |

## ASJC Scopus subject areas

- モデリングとシミュレーション
- 自動車工学
- 航空宇宙工学
- コンピュータ グラフィックスおよびコンピュータ支援設計