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On beta-continuous functions and their application to the construction of geometrically continuous curves and surfaces. (English) Zbl 0692.41018

Mathematical methods in computer aided geometric design, Pap. Int. Conf., Oslo/Norw. 1988, 299-311 (1989).
[For the entire collection see Zbl 0669.00011.]
The authors introduce the notions of \(\beta\)-continuity and M-continuity and show that the sums, differences, products, quotients, and scalar multiples of \(\beta\)-continuous functions are \(\beta\) continuous. These basic results are applied to various standard constructions of parametrically continuous curves and surfaces - such as rational splines, Catnull-Row splines, affine combinations of curves, as well as ruled, lofted, tensor product, and Boolean sum surfaces - to generate geometrically continuous analogues. Moreover, in order to form geometrically continuous surfaces, the curves used in the construction must satisfy the Beta-constraints.
Reviewer: R.N.Siddiqi

MSC:

41A30 Approximation by other special function classes
41A15 Spline approximation

Citations:

Zbl 0669.00011