A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme

Abdellah Lamnii, Mohamed Yassir Nour and Ahmed Zidna
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Abdellah Lamnii: Laboratoire MISI, Faculty of Science and Technology, Hassan First University of Settat, Settat 26000, Morocco
Mohamed Yassir Nour: Laboratoire MISI, Faculty of Science and Technology, Hassan First University of Settat, Settat 26000, Morocco
Ahmed Zidna: Laboratoire De Génie Informatique, de Production et de Maintenance, Université Lorraine, 10628 Metz, France

Mathematics, 2021, vol. 9, issue 20, 1-16

Abstract: In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons.

Keywords: generalized B-splines; non-stationary subdivision schemes; reverse subdivision scheme; wavelets; tension parameter (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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