IJPAM: Volume 65, No. 3 (2010)

EVALUATION OF BETA-FUNCTION B-SPLINES, II:
LOCAL BERNSTEIN BASES

Lubomir T. Dechevsky
R&D Group for Mathematical Modelling
Numerical Simulation and Computer Visualization
Faculty of Technology
Narvik University College
2, Lodve Lange's Str., P.O. Box 385, N-8505, Narvik, NORWAY
e-mail: [email protected]
url: http://ansatte.hin.no/ltd/


Abstract.This is the second paper in a sequence of three papers on the evaluation of Beta-function B-splines (BFBS), the first paper in the sequence being [#!d1-2010!#]. This sequence of papers studies explicit representations of BFBS yielding computationally efficient explicit formulae for evaluation of BFBS in terms of polynomial bases used in data interpolation, data fitting and geometric modelling, as well as in the design of multilevel constructions such as, e.g., multiwavelets. While in [#!d1-2010!#] an interpolatory representation of BFBS was developed in terms of local monomial bases, the objective of the present paper is to provide a Bezier-type representation in local Bernstein bases; the last of the three papers will be dedicated to a representation of BFBS in global monomial bases, suitable for use, e.g., in relevance to computing Fourier, Laplace and other transforms.

Received: February 12, 2010

AMS Subject Classification: 33B15, 33B20, 41A15, 65D10, 33F05, 41A30, 65D05, 65D07, 65D20, 65D30

Key Words and Phrases: spline, B-spline, expo-rational, generalized, polynomial, special function, Gamma-function, Euler Beta-function, complete, incomplete, Beta-function B-spline, integration, monomial basis, Bernstein basis, Bezier representation, local, global, interpolation, fitting, geometric modelling, computer-aided geometric design, Fourier transform, Laplace transform

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 3