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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)

Citations:

Zbl 0583.65095
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Full Text: DOI

References:

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