Maharavo Randrianarivony:

A survey on global continuity in geometric processing of CAD objects for the Wavelet-Galerkin scheme

We need to decompose the boundary of a solid into four-sided patches such that there is a regular mapping from the unit square to each patch. In this paper, we focus on the analysis of the global continuity of the mappings over the whole surface. Since we use Coons functions to generate the mappin gs, we demonstrate theoretically that if all curves are parametrized in arc length th en we have good matchings at surface joints. That result is valid for any blending functions of the Coons patches. We wi ll describe a reparametrization technique whose goal is to keep the shape of the init ial curves while achieving arc length parametrization. The reparametrization process is done by using cubic Bezier spline approximation whose accuracy is estimated. For a rational Bezier curve with bounded weights, we develop an algorithm for length com putation where the error will be investigated. The generalization of that result for other types of curves will be discussed. Numerical results are provided to support the theoretical studies. Furthermore, the decomposition techniques are applied to re al CAD data which come from IGES files.

Keywords: CAD, Global continuity, Coons, chord length parametrization, IGES, integral equation, Wavelet Galerkin

Mail an Jens Burmeister

[Thu Feb 19 18:56:37 2009]

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