IJPAM: Volume 65, No. 3 (2010)

GEOMETRIC MODELLING
WITH BETA-FUNCTION B-SPLINES, I:
PARAMETRIC CURVES

Arne Lakså$^1$, Børre Bang$^2$, Lubomir T. Dechevsky$^3$
$^{1,2,3}$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
$^1$e-mail: [email protected]
url: http://ansatte.hin.no/ala/
$^2$e-mail: [email protected]
url: http://ansatte.hin.no/bb/
$^3$e-mail: [email protected]
url: http://ansatte.hin.no/ltd/


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
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 3