Polynomial generation and quasi-interlpolation in stationary non-uniform subdivision

Authors:
A. Levin
Affiliations:
Cadent, 17 HYata'assiya St., Or Yehuda, 60408, Israel
Venue:
Computer Aided Geometric Design
Year:
2003

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Abstract

We study the necessary and sufficient conditions for the generation of polynomials by stationary subdivision schemes, and we show how to derive appropriate quasi-interpolation rules that have the optimal approximation order. We show that these conditions hold in the context of non-uniform subdivision as well, and we demonstrate how they can be used for the construction of stationary non-uniform subdivision schemes that have a prescribed approximation power.