### Abstract

In geometrical modeling, one is often provided a description of a surface that is defined in terms of a triangulation, which is supported by a discrete number of nodes in space. These faceted surface representations are defined to be C-0 continuous, and therefore in general have slope and curvature discontinuities at the triangle sides, unless the tessellation is planar. Unfortunately, analytical and computational methods often require a surface description that has well-defined and smoothly-varying gradients and curvatures; in general spline surfaces possess such properties. Described herein is a process for generating a cubic spline surface that approximates, to within a userspecified tolerance, a given tessellated surface that may be non-convex or multiplyconnected. The method combines a local least-squares technique for specifying knot properties as well as an adaptation technique of selecting the necessary knot spacings. This new technique is first described along a curve for illustrative purposes. It is then expanded to the case of the general surface. A reparameterization technique that is required for surfaces with non-smooth parameterizations is described next. Computed results for two configurations are then shown.

Original language | English (US) |
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Title of host publication | Proceedings of the 17th International Meshing Roundtable, IMR 2008 |

Publisher | Kluwer Academic Publishers |

Pages | 249-266 |

Number of pages | 18 |

ISBN (Print) | 9783540879206 |

DOIs | |

State | Published - 2008 |

Event | 17th International Meshing Roundtable, IMR 2008 - Pittsburgh, PA, United States Duration: Oct 12 2008 → Oct 15 2008 |

### Publication series

Name | Proceedings of the 17th International Meshing Roundtable, IMR 2008 |
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### Other

Other | 17th International Meshing Roundtable, IMR 2008 |
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Country | United States |

City | Pittsburgh, PA |

Period | 10/12/08 → 10/15/08 |

### ASJC Scopus subject areas

- Engineering (miscellaneous)

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## Cite this

*Proceedings of the 17th International Meshing Roundtable, IMR 2008*(pp. 249-266). (Proceedings of the 17th International Meshing Roundtable, IMR 2008). Kluwer Academic Publishers. https://doi.org/10.1007/978-3-540-87921-3_15