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Proceedings Paper

Matrix approach of the convergence analysis of recursive subdivision algorithms for parametric surfaces
Author(s): Ruibin Qu
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Paper Abstract

In this paper, we construct a general binary subdivision algorithm (BSA) for surfaces over uniform triangulations and then present a matrix approach of convergence analysis. In the analysis, the idea of `cross differences of directional divided differences' (CDD) is introduced, and it is shown that the convergence of the scheme is characterized by its CDD. This approach is a generalization of the `Dyadic parametrization' technique that was first used by Dyn, Gregory, and Levin to analyze uniform BSA for curves. Conditions for the scheme to generate Cn (n >= 0) surfaces are studied. As an example, the explicit form of the C0 and C1 convergence conditions of the `butterfly scheme' (introduced by Dyn, Gregory, and Levin) and a 10-point interpolatory BSA are formulated.

Paper Details

Date Published: 1 February 1992
PDF: 11 pages
Proc. SPIE 1610, Curves and Surfaces in Computer Vision and Graphics II, (1 February 1992); doi: 10.1117/12.135157
Show Author Affiliations
Ruibin Qu, Brunel Univ. (United Kingdom)

Published in SPIE Proceedings Vol. 1610:
Curves and Surfaces in Computer Vision and Graphics II
Martine J. Silbermann; Hemant D. Tagare, Editor(s)

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