Geometric Modelling with Beta-function B-splines, I: Parametric Curves

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 [12, 10] for the case of expo-rational Bsplines (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. 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 Received: March 2, 2010 c © 2010 Academic Publications Correspondence author 340 A. Laks̊a, B. Bang, L.T. Dechevsky