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**Approximate conversion of surface representations with polynomial bases.**
*(English)*
Zbl 0577.65005

The need for methods to convert surface representations has been recognized quite early by the VDA-CAD standard group. When transmitting geometric information from one system to another, one has to ensure a high degree of accuracy, i.e. a least possible loss of information. In using piecewise polynomial representations theoretically matrix multiplication can be applied. But if the two systems do not allow for the same maximal degree, then one has to look for approximate conversion, possibly by additional mesh refinement. In the present paper the authors discuss a certain type of least squares approximation combined with Hermite interpolation for the conversion of tensor product surface representation of given degree and mesh size to another. Many aspects of this process, e.g. curvature errors, degree reduction, subdivision of the given mesh etc. are investigated.

Reviewer: G.Meinardus

### MSC:

65D05 | Numerical interpolation |

41A05 | Interpolation in approximation theory |

41A63 | Multidimensional problems |

53A05 | Surfaces in Euclidean and related spaces |

### Keywords:

geometric modelling systems; data exchange standards; computer; aided design; surface representations; piecewise polynomial representations; mesh refinement; least squares; curvature errors; degree reduction
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\textit{L. Dannenberg} and \textit{H. Nowacki}, Comput. Aided Geom. Des. 2, 123--131 (1985; Zbl 0577.65005)

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### References:

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[3] | Anon, Standard d’échange et de transfert (SET), Aérospatiale. Aérospatiale, Direction Technique (1984), Suresnes, France |

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