Simple regularity criteria for subdivision schemes
SIAM Journal on Mathematical Analysis
Interpolatory subdivision schemes and wavelets
Journal of Approximation Theory
Stationary Subdivision
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
A non-stationary uniform tension controlled interpolating 4-point scheme reproducing conics
Computer Aided Geometric Design
Deducing interpolating subdivision schemes from approximating subdivision schemes
ACM SIGGRAPH Asia 2008 papers
Polynomial reproduction by symmetric subdivision schemes
Journal of Approximation Theory
Journal of Computational and Applied Mathematics
Solving Bezout-like polynomial equations for the design of interpolatory subdivision schemes
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Algebraic conditions on non-stationary subdivision symbols for exponential polynomial reproduction
Journal of Computational and Applied Mathematics
Generalized Daubechies Wavelet Families
IEEE Transactions on Signal Processing
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Exponential splines and minimal-support bases for curve representation
Computer Aided Geometric Design
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
Advances in Computational Mathematics
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In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying quite mild assumptions. To achieve this result we extend our previous work (Conti et al., Linear Algebra Appl 431(10):1971---1987, 2009) to full generality by removing additional assumptions on the input symbols. For the so obtained interpolatory schemes we prove that they are capable of reproducing the same space of exponential polynomials as the one generated by the original approximating scheme. Moreover, we specialize the computational methods for the case of symbols obtained by shifted non-stationary affine combinations of exponential B-splines, that are at the basis of most non-stationary subdivision schemes. In this case we find that the associated family of interpolatory symbols can be determined to satisfy a suitable set of generalized interpolating conditions at the set of the zeros (with reversed signs) of the input symbol. Finally, we discuss some computational examples by showing that the proposed approach can yield novel smooth non-stationary interpolatory subdivision schemes possessing very interesting reproduction properties.