## Abstract

It is shown that two generic triangular surface patches with no base points and of parametric degree m and n respectively, intersect in a curve of degree m^{2}n^{2} which is generally of genus 2m^{2}n^{2} - 3 2m^{2}n - 3 2n^{2}m + 1. Similarly, two generic tensor product surface patches of parametric degree m_{1}×m_{2} and n_{1}×n_{2} respectively, intersect in a curve of degree 4m_{1}m_{2}n_{1}n_{2} and generally of genus 8m_{1}m_{2}n_{1}n_{2} - 2m_{1}m_{2}(n_{1} + n_{2}) - 2n_{1}n_{2}(m_{1} + m_{2}) + 1. For example, two general bicubic patches in general position intersect in a curve of degree 324 and of genus 433. The significance of this genus value lies in the fact that only curves of genus 0 can be expressed parametrically using rational polynomials. Genus and degree equations are also derived for intersection curves involving surface patches with simple base points. A class of surfaces is identified for which any plane section is a rational curve.

Original language | English (US) |
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Pages (from-to) | 253-258 |

Number of pages | 6 |

Journal | Computer Aided Geometric Design |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1988 |

Externally published | Yes |

## ASJC Scopus subject areas

- Modeling and Simulation
- Automotive Engineering
- Aerospace Engineering
- Computer Graphics and Computer-Aided Design