### 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 user-specified tolerance, a given tessellated surface that may be non-convex or multiply connected. The method combines a local least-squares technique for specifying knot properties as well as an adaptation technique for 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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Pages (from-to) | 31-40 |

Number of pages | 10 |

Journal | Engineering with Computers |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2011 |

### Keywords

- Behavioral morphing
- Cubic spline
- Least-square fit
- Parametric tessellation
- Reparameterization
- Topological editing

### ASJC Scopus subject areas

- Software
- Modeling and Simulation
- Engineering(all)
- Computer Science Applications

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## Cite this

*Engineering with Computers*,

*27*(1), 31-40. https://doi.org/10.1007/s00366-010-0182-x