Smooth reverse subdivision of uniform algebraic hyperbolic B-splines and wavelets

Abstract

In this work, we give an introduction of uniform algebraic hyperbolic [Formula: see text]-splines (UAH [Formula: see text]-splines) generated over the space spanned by [Formula: see text], in which [Formula: see text] is an integer larger than or equal to [Formula: see text] and [Formula: see text] is a tension parameter. Then, we construct a general formula of the refinement equation for any given order [Formula: see text] of these [Formula: see text]-splines. Using the matrix version of this equation, we have also constructed the subdivision formula for UAH [Formula: see text]-spline curves. In order to introduce a new reverse subdivision framework, entitled “Smooth Reverse Subdivision” associated with the cubic UAH [Formula: see text]-splines, by continuing this process, we present a new multiresolution technique for general topology curves. We illustrate our results by numerical experiments.