Abstract
A recursion formula for rational B-splines with prescribed poles is given that reduces to DeBoor's recursion when all poles are at infinity. Some properties of polynomial B-splines generalize to these rational B-splines: partition of unity, a knot inserting algorithm, numerical stability. It can be proved that the rational B-splines are identical with the Chebyshevian B-splines constructed by T. Lyche. The recursions are not identical and the one for the rational B-splines is more convenient. Furthermore, the rational B-splines are identified as special NURBS. The weights can be chosen depending on the poles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. DeBoor,Splinefunktionen (Birkhäuser, Basel, 1990).
A. Gresbrand, Rationale B-Splines mit vorgegebenen Polstellen, Thesis, Universität Hannover (1995).
J. Hoschek and D. Lasser,Grundlagen der geometrischen Datenverarbeitung (Teubner, Stuttgart, 1992).
S. Karlin and W.J. Studden,Tchebycheff Systems: With Applications in Analysis and Statistics (Interscience, New York, 1966).
T. Lyche, A. recurrence relation for Chebyshevian B-splines, Report CAT # 37, Dept. of Mathematics, Texas A & M Univ. (Sept. 1983).
T. Lyche, A recurrence relation for Chebyshevian B-splines, Constr. Approx. 1 (1985) 155–173.
G. Mühlbach, On interpolation by rational function with prescribed poles with applications to multivariate interpolation, J. Comp. Appl. Math. 32 (1990) 203–216.
L.L. Schumaker,Spline Functions: Basic Theory (Wiley, New York, 1981).
Author information
Authors and Affiliations
Additional information
Communicated by G. Mühlbach
Rights and permissions
About this article
Cite this article
Gresbrand, A. Rational B-splines with prescribed poles. Numer Algor 12, 151–158 (1996). https://doi.org/10.1007/BF02141746
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02141746