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**The approximation of non-degenerate offset surfaces.**
*(English)*
Zbl 0621.65003

Let S be a surface such that the unit surface normal n is defined at each point of S. An offset surface \(S_ 0\) to S is defined as an envelope of the continuum of vectors \(d\updownarrow n\) where d is a real number. There are some difficulties that arise when generating offset surfaces. In his previous paper [ibid. 2, 257-279 (1985; Zbl 0583.65095)] the author considered problems appearing when n is not defined at each point of S. The paper under review deals with the problem of reducing the complexity of the functional representation of \(S_ 0\). The exact functional representation of \(S_ 0\) is typically more complex than that of S. A method for approximation of \(S_ 0\) by bicubic patches is developed. An analysis of the accuracy of the method along with examples is presented.

Reviewer: J.Krč-Jediný

### MSC:

65D15 | Algorithms for approximation of functions |

65D07 | Numerical computation using splines |

65S05 | Graphical methods in numerical analysis |

41A15 | Spline approximation |

41A63 | Multidimensional problems |

53A05 | Surfaces in Euclidean and related spaces |

68U20 | Simulation (MSC2010) |

### Keywords:

geometric modeling; differential geometry; surface approximation; computer graphics; offset surface### Citations:

Zbl 0583.65095
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\textit{R. T. Farouki}, Comput. Aided Geom. Des. 3, 15--43 (1986; Zbl 0621.65003)

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