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B-spline bases and osculating flats : one result of H.-P. Seidel revisited

Marie-Laurence Mazure (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

B-spline bases and osculating flats: One result of H.-P. Seidel revisited

Marie-Laurence Mazure (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

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