Research PaperNo Access

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

Mohamed Ajeddar

https://orcid.org/0000-0001-8096-2872

University Hassan First, FST, MISI Laboratory, Settat, Morocco

E-mail Address: ajeddar@gmail.com

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and

Abdellah Lamnii

University Hassan First, FST, MISI Laboratory, Settat, Morocco

E-mail Address: a_lamnii@yahoo.fr

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https://doi.org/10.1142/S0219691321500181Cited by:4 (Source: Crossref)

Abstract

In this work, we give an introduction of uniform algebraic hyperbolic $B$ -splines (UAH $B$ -splines) generated over the space spanned by ${sinh (α x), cosh (α x), \dots, x^{k - 3} sinh (α x), x^{k - 3} cosh (α x)}$ , in which $k$ is an integer larger than or equal to $3$ and $α$ 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.

Keywords:

AMSC: 41A05, 41A15, 65T60

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