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

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(0), w(1) and w(2). It is shown that if w(1) = w(0)+w(2)/2 , then the [3/2]-scheme reproduces linear polynomial and is C-1 provided w(0 )and w(2) 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(0) = w(1) = w(2), the [3/2]-scheme reduces to the Merrien scheme.