A ternary three-point scheme for curve designing

Abstract

In this paper, a stationary ternary three-point approximating subdivision scheme is presented, which generates C ² limiting curve and its limiting function has a support on [−3, 2]. The analysis of the scheme is shown using the Laurent polynomial method. Two examples are illustrated for comparison with the ternary three-point approximating subdivision scheme developed by Hassan and Dodgson [Ternary and three point univariate subdivision schemes, in Curve and Surface Fitting: Sant-Malo 2002, A. Cohen, J.-L. Merrien, and L.L. Schumaker, eds., Nashboro Press, Brentwood, 2003, pp. 199–208.], which show that the scheme presented in the paper is better.

Keywords:

• ternary
• approximating subdivision scheme
• convergence and smoothness
• mask
• laurent polynomial

2000 AMS Subject Classifications :

• 41A05
• 41A25
• 41A30
• 65D17
• 65D10

Acknowledgements

I would like to pay my gratitude to Mr Nadeem Ahmad for his kind cooperation and valuable suggestions.