Convergence and smoothness of tensor-product of two non-uniform linear subdivision schemes

The aim of this short note is to provide a rigorous proof that the tensor product of two non-uniform linear convergent subdivision schemes converges and has the same regularity as the minimal regularity of the univariate schemes. It extends results that are known for the uniform linear case and are...

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Bibliographic Details
Published in:Computer aided geometric design 2018-11, Vol.66, p.16-18
Main Authors: Conti, Costanza, Dyn, Nira
Format: Article
Language:English
Subjects:
Convergence
Non-uniform linear subdivision scheme
Smoothness
Tensor-product
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Summary:The aim of this short note is to provide a rigorous proof that the tensor product of two non-uniform linear convergent subdivision schemes converges and has the same regularity as the minimal regularity of the univariate schemes. It extends results that are known for the uniform linear case and are based on symbols, a notion which is no longer available in the non-uniform setting.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2018.08.001