Non-stationary subdivision schemes: State of the art and perspectives

C Conti, N Dyn - Approximation Theory XVI: Nashville, TN, USA, May 19 …, 2021 - Springer
This paper reviews the state of the art of non-stationary subdivision schemes, which are
iterative procedures for generating smooth objects from discrete data, by repeated level …

A family of C2 four-point stationary subdivision schemes with fourth-order accuracy and shape-preserving properties

H Yang, K Kim, J Yoon - Journal of Computational and Applied …, 2024 - Elsevier
The four-point interpolatory scheme and the cubic B-spline are examples of the most well-
known stationary subdivision procedures. They are based on the space of cubic polynomials …

Convergence of univariate non-stationary subdivision schemes via asymptotic similarity

C Conti, N Dyn, C Manni, ML Mazure - Computer Aided Geometric Design, 2015 - Elsevier
A new equivalence notion between non-stationary subdivision schemes, termed asymptotic
similarity, which is weaker than asymptotic equivalence, is introduced and studied. It is …

Regularity of non-stationary subdivision: a matrix approach

M Charina, C Conti, N Guglielmi, V Protasov - Numerische mathematik, 2017 - Springer
In this paper, we study scalar multivariate non-stationary subdivision schemes with integer
dilation matrix M and present a unifying, general approach for checking their convergence …

Reproduction of exponential polynomials by multivariate non-stationary subdivision schemes with a general dilation matrix

M Charina, C Conti, L Romani - Numerische Mathematik, 2014 - Springer
We study scalar multivariate non-stationary subdivision schemes with a general integer
dilation matrix. We characterize the capability of such schemes to reproduce exponential …

Multiresolution subdivision snakes

A Badoual, D Schmitter, V Uhlmann… - IEEE Transactions on …, 2016 - ieeexplore.ieee.org
We present a new family of snakes that satisfy the property of multiresolution by exploiting
subdivision schemes. We show in a generic way how to construct such snakes based on an …

Dual Hermite subdivision schemes of de Rham-type

C Conti, JL Merrien, L Romani - BIT Numerical Mathematics, 2014 - Springer
Though a Hermite subdivision scheme is non-stationary by nature, its non-stationarity can
be of two types, making useful the distinction between Inherently Stationary and Inherently …

A new class of 2m-point binary non-stationary subdivision schemes

A Ghaffar, Z Ullah, M Bari, KS Nisar… - Advances in Difference …, 2019 - Springer
A new class of 2 m-point non-stationary subdivision schemes (SSs) is presented, including
some of their important properties, such as continuity, curvature, torsion monotonicity, and …

Factorization of Hermite subdivision operators preserving exponentials and polynomials

C Conti, M Cotronei, T Sauer - Advances in Computational Mathematics, 2016 - Springer
In this paper we focus on Hermite subdivision operators that act on vector valued data
interpreting their components as function values and associated consecutive derivatives. We …

Level-dependent interpolatory Hermite subdivision schemes and wavelets

M Cotronei, C Moosmüller, T Sauer… - Constructive …, 2019 - Springer
We study many properties of level-dependent Hermite subdivision, focusing on schemes
preserving polynomial and exponential data. We specifically consider interpolatory …