The Importance of Polynomial Reproduction in Piecewise-Uniform Subdivision
We survey a number of related methods, which have been published by the author
and collaborators, in the field of subdivision schemes for curves and surfaces.
The theory presented in these works relies mainly on the notion of
polynomial reproduction, i.e. the ability of a scheme to reproduce all
polynomials up to a certain degree as limit functions.
We demonstrate that the study of polynomial reproduction is central to
smoothness analysis and to approximation. In particular, we show how to exploit
polynomial reproduction in the context of piecewise-uniform stationary subdivision.
The applications include boundary treatments for subdivision surfaces, interpolation
of curves by surfaces, subdivision stencils around extraordinary vertices
(construction of C^2 schemes), as well as schemes
that involve different kinds of grids (triangular / quadrilateral).
(Zipped Postscript format, 680Kb)
author = "Adi Levin",
title = "The Importance of Polynomial Reproduction in Piecewise-Uniform Subdivision",
year = "2005",
booktitle = "Mathematics of Surfaces XI",
editor = "Ralph Martin and Helmut Bez and Malcolm Sabin",
publisher = "Springer",
pages = "272-307")