TITLE:
The Odd-Point Ternary Approximating Schemes
AUTHORS:
Ghulam Mustafa, Abdul Ghaffar, Faheem Khan
KEYWORDS:
Approximating Subdivision Scheme, Derivative Continuity, Smoothness Convergence, Shape
Parameters and Laurent Polynomial
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.1 No.2,
July
1,
2011
ABSTRACT: We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C0 to C5 of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point
interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.