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 …
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 …
known stationary subdivision procedures. They are based on the space of cubic polynomials …
Convergence of univariate non-stationary subdivision schemes via asymptotic similarity
A new equivalence notion between non-stationary subdivision schemes, termed asymptotic
similarity, which is weaker than asymptotic equivalence, is introduced and studied. It is …
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 …
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
We study scalar multivariate non-stationary subdivision schemes with a general integer
dilation matrix. We characterize the capability of such schemes to reproduce exponential …
dilation matrix. We characterize the capability of such schemes to reproduce exponential …
Multiresolution subdivision snakes
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 …
subdivision schemes. We show in a generic way how to construct such snakes based on an …
Dual Hermite subdivision schemes of de Rham-type
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 …
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 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 …
some of their important properties, such as continuity, curvature, torsion monotonicity, and …
Factorization of Hermite subdivision operators preserving exponentials and polynomials
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 …
interpreting their components as function values and associated consecutive derivatives. We …
Level-dependent interpolatory Hermite subdivision schemes and wavelets
We study many properties of level-dependent Hermite subdivision, focusing on schemes
preserving polynomial and exponential data. We specifically consider interpolatory …
preserving polynomial and exponential data. We specifically consider interpolatory …