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 …

Background: Methods of subdivision surfaces modeling and related technology research
have become a hot spot in the field of Computer-Aided Design (CAD) and Computer …

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 …

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 …

Abstract Iterated Function Systems (IFSs) have been at the heart of fractal geometry almost
from its origin, and several generalizations for the notion of IFS have been suggested …

Subdivision schemes are used to generate smooth curves or surfaces by iteratively refining
an initial control polygon or mesh. We focus on univariate, linear, binary subdivision …

An extension of the Banach fixed-point theorem for a sequence of maps on a complete
metric space (X, d) has been presented in a previous paper. It has been shown that …

The main objective of this study is to introduce a new class of 2 q-point approximating
nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The …

We present an affine-invariant non-stationary subdivision scheme for the recursive
refinement of any triangular mesh that is regular or has extraordinary vertices of valence 4 …

Several properties of stationary subdivision schemes are nowadays well understood. In
particular, it is known that the polynomial generation and reproduction capability of a …