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

Published online by Cambridge University Press:  15 January 2003

Marie-Laurence Mazure
Marie-Laurence Mazure*
Affiliation:
Laboratoire de Modélisation et Calcul (LMC-IMAG), Université Joseph Fourier, BP 53, 38041 Grenoble Cedex, France. [email protected].
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Abstract

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 requirementto obtain the poles of nondegenerate splinesas intersections of osculating flats at consecutive knots.

Keywords

Geometric designB-spline basisblossomingosculating flats.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 6 , November 2002 , pp. 1177 - 1186
Copyright
© EDP Sciences, SMAI, 2002

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References

Dyn, N. and Micchelli, C.A., Piecewise polynomial spaces and geometric continuity of curves. Numer. Math. 54 (1988) 319-337. CrossRef
Goodman, T.N.T., Properties of β-splines. J. Approx. Theory 44 (1985) 132-153. CrossRef
Mazure, M.-L., Blossoming: a geometrical approach. Constr. Approx. 15 (1999) 33-68. CrossRef
Mazure, M.-L., Quasi-Chebyshev splines with connexion matrices. Application to variable degree polynomial splines. Comput. Aided Geom. Design 18 (2001) 287-298. CrossRef
Pottmann, H., The geometry of Tchebycheffian splines. Comput. Aided Geom. Design 10 (1993) 181-210. CrossRef
Ramshaw, L., Blossoms are polar forms. Comput. Aided Geom. Design 6 (1989) 323-358. CrossRef
Seidel, H.-P., New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree. RAIRO Modél. Math. Anal. Numér. 26 (1992) 149-176. CrossRef
Seidel, H.-P., Polar forms for geometrically continuous spline curves of arbitrary degree. ACM Trans. Graphics 12 (1993) 1-34. CrossRef