Matrix approach of the convergence analysis of recursive subdivision algorithms for parametric surfaces

Ruibin Qu

doi:10.1117/12.135157

1 February 1992 Matrix approach of the convergence analysis of recursive subdivision algorithms for parametric surfaces

Ruibin Qu

Proceedings Volume 1610, Curves and Surfaces in Computer Vision and Graphics II; (1992) https://doi.org/10.1117/12.135157
Event: Robotics '91, 1991, Boston, MA, United States

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.

Citation Download Citation

Ruibin Qu "Matrix approach of the convergence analysis of recursive subdivision algorithms for parametric surfaces", Proc. SPIE 1610, Curves and Surfaces in Computer Vision and Graphics II, (1 February 1992); https://doi.org/10.1117/12.135157

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