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Some remarks concerning B-splines. (English) Zbl 0606.65004
De Boor-Fix dual functionals have proved to be useful tools in the study of B-splines [see, e.g. C. de Boor, A Practical Guide to Splines (1978; Zbl 0406.41003)]. Using these functionals, the author provides a natural derivation of the Oslo algorithm [see E. Cohen, T. Lyche and R. Riesenfeld, Comput. Graphics Image Process. 14, 87-111 (1980)]. The author mentions that a simple and direct proof of the basic recurrence formula for the Oslo algorithm was found earlier by H. Prautzsch [Computer Aided Geom. Des. 1, 95-96 (1984; Zbl 0552.65010)].
Reviewer: H.P.Dikshit

MSC:
65D07 Numerical computation using splines
41A15 Spline approximation
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References:
[1] Boehm, W., Inserting new knots into B-spline curves, Computer aided design, 12, 199-201, (1980)
[2] de Boor, C., The quasi-interpolant as a tool in elementary spline theory, (), 269-276
[3] de Boor, C., On local linear functionals which vanish at all B-splines but one, (), 120-145
[4] de Boor, C., Splines as linear combinations of B-splines: A survey, (), 1-47
[5] de Boor, C., A practical guide to splines, (1978), Springer New York · Zbl 0406.41003
[6] de Boor, C.; Fix, G., Spline approximation by quasi-interpolants, J. approx. theory, 7, 19-45, (1973) · Zbl 0279.41008
[7] Cohen, E.; Lyche, T.; Riesenfeld, R., Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics, Computer graphics and image processing, 14, 87-111, (1980)
[8] Prautzsch, H., A short proof of the Oslo algorithm, Computer aided geometric design, 1, 95-96, (1984) · Zbl 0552.65010
[9] Schumaker, L., Spline functions: basic theory, (1981), Wiley-Interscience Berlin · Zbl 0449.41004
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