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The Importance of Polynomial Reproduction in Piecewise-Uniform Subdivision

  • Adi Levin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)

Abstract

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).

Keywords

Limit Function Subdivision Scheme Polynomial Generation Subdivision Surface Subdivision Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Adi Levin
    • 1
  1. 1.Cadent LtdOr-YehudaIsrael

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