## Abstract

New methods for interpolating scattered data on a surface are presented. Similar to G. Nielson's minimum norm network technique, this approach is based upon a functional minimization that characterizes the restriction of the final interpolant to curves which form the edges in a triangulation of the domain surface. However, unlike the known minimum norm network methods we do not use only data points as vertices in the triangulation. We also consider minimum norm networks with tension properties. An appropriate method for extending the network data to a final C^{1} interpolant is described. Both color blended contour regions on the surface and projections of the 4D graph of a function on a surface are used in illustrating examples. Finally, special cases, possible extensions and applications in surface design are addressed.

Original language | English (US) |
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Pages (from-to) | 51-67 |

Number of pages | 17 |

Journal | Computer Aided Geometric Design |

Volume | 9 |

Issue number | 1 |

DOIs | |

State | Published - May 1992 |

Externally published | Yes |

## Keywords

- Scattered data fitting
- functional minimization
- interpolation
- minimum norm network
- scientific visualization.
- surfaces
- tension
- triangular interpolant

## ASJC Scopus subject areas

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