A Hermite interpolatory subdivision scheme constructed from quadratic rational Bernstein-Bezier spline

Abstract In this paper, a new nonlinear Hermite interpolatory subdivision scheme for curve interpolation is introduced. The scheme is constructed from the rational Bernstein-Bezier (RBB) spline. The limit function of the scheme interpolates both the function values and the derivatives. The work provides convergence analysis, polynomial reproduction, and shape preserving properties of the scheme. In particular, it is shown that the limit functions are globally C 1 and the scheme also reproduces quadratic polynomials. Moreover, the scheme preserves monotonicity and convexity. Several examples are provided to justify our claims.