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B-spline bases and osculating flats: One result of H. -P. Seidel revisited. (English) Zbl 1027.65020

Summary: Along with the classical requirements on B-splines bases (minimal support, positivity, normalization) we show that it is natural to introduce an additional “end point property”. When dealing with multiple knots, this additional property is exactly the appropriate requirement to obtain the poles of nondegenerate splines as intersections of osculating flats at consecutive knots.
[cf. H.-P. Seidel, RAIRO, Modèlization Math. Anal. Numér. 26, 149-176 (1992; Zbl 0752.65008); ACM Trans. Graph. 12, 1-34 (1993; Zbl 0770.68116)].

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
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References:

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