Polynomial Generation and Quasi-Interpolation
in Stationary Non-Uniform Subdivision
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.
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BiBTeX entry
@article(AdiLevin:2003:cagd:stationary-non-uniform,
author = "A. Levin",
title = "Polynomial Generation and Quasi-Interpolation
in Stationary Non-Uniform Subdivision",
journal = "Computer Aided Geometric Design",
pages = "41-60",
year = 2003,
volume = "20(1)")