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Optimal approximate conversion of spline surfaces. (English) Zbl 0682.65005
The authors solve the important problem of representing a tensor-product surface given by Bernstein polynomials of high degree by (3,3) of (5,5) Béziers spline patches. The necessary formulas are derived. The problem of smoothing patches at common boundaries and merging patches is discussed but not down to the level of readily implementable procedures. It is pointed out that the formulas derived in the paper yield the spline representation not only of the given surface but also of all its parallel surfaces (here called “offset surfaces”).
Reviewer: H.Guggenheimer

MSC:
65D07 Numerical computation using splines
41A15 Spline approximation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
53A05 Surfaces in Euclidean and related spaces
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