Shape preserving rational [3/2] Hermite interpolatory subdivision scheme

Abstract

In this paper, a new Hermite interpolatory subdivision scheme for curve interpolation is introduced. The scheme is constructed from the Rational [3/2] Bernstein Bezier polynomial. We call it the [3/2]-scheme. The limit function of the [3/2]-scheme interpolates both the function values and their derivatives. The proposed scheme has three shape parameters w, w1 and w2. It is shown that if w1=w0+w22, then the [3/2]-scheme reproduces linear polynomial and is C1 provided w and w2 lie in a region of convergence. The scheme also satisfies the shape preserving properties, i.e., monotonicity and convexity. We also compare the [3/2]-scheme with other existing schemes like the [2/2]-scheme and the Merrien scheme introduced recently. An error analysis shows that the [3/2]-scheme is better than the [2/2]-scheme and the Merrien scheme. Further, it is observed that in case w= w1= w2, the [3/2]-scheme reduces to the Merrien scheme.