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

In this work, we give an introduction of uniform algebraic hyperbolic B-splines (UAH B-splines) generated over the space spanned by {sinh(alpha x), cosh(alpha x), ..., x(k-3) sinh(alpha x), x(k-3) cosh(alpha x)}, in which k is an integer larger than or equal to 3 and a is a tension parameter. Then, we construct a general formula of the refinement equation for any given order k of these B-splines. Using the matrix version of this equation, we have also constructed the subdivision formula for UAH B-spline curves. In order to introduce a new reverse subdivision framework, entitled "Smooth Reverse Subdivision" associated with the cubic UAH B-splines, by continuing this process, we present a new multiresolution technique for general topology curves. We illustrate our results by numerical experiments.