IJPAM: Volume 65, No. 3 (2010)
WITH BETA-FUNCTION B-SPLINES, I:
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
Abstract.This is the first one in a sequence of several papers dedicated to the development of applications of Euler Beta-function B-splines (BFBS) to Computer-aided Geometric Design (CAGD) and, in particular, for geometric modelling of parametric curves, surfaces and volume deformations. This study is an analogue of the study conducted in [#!Laksa:2005!#,#!AlPhD:2006!#] for the case of expo-rational B-splines (ERBS). An important objective of this study is the comparison between the graphical and computational performance of BFBS versus ERBS, as well as the comparison of BFBS versus classical polynomial Schoenberg B-splines.
In the present paper we discuss parametric curve interpolation based on BFBS, as well as the respective Bezier-type curve representation.
Received: March 2, 2010
AMS Subject Classification: 53A04, 65D05, 65D07, 65D17, 26A63, 26B15, 28A75, 33B15, 33B20, 33F05, 41A15, 41A30, 42A38, 44A10, 50A30, 51M25, 52A38, 53A05, 53A15, 53A17, 53A20, 65D10, 65D20, 65D30
Key Words and Phrases: geometric modelling, parametrization, curve, surface, volume deformation, tensor product, computer-aided geometric design, spline, B-spline, polynomial, exponential, rational, expo-rational, generalized, Euler Beta-function, complete, incomplete, Gamma-function, scalar, vector, point, matrix, piecewise, linear, affine, barycentric, convex, continuous, differentiable, smooth, Hermite interpolation, monomial basis, Bernstein basis, Bezier curve, control polygon, de Casteljau algorithm, Cox-de Boor algorithm, iterative, local, global, constant, variable, functional
Source: International Journal of Pure and Applied Mathematics