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Summary

A 2.5D meshing technique for triangulation of spatial surfaces has been presented. The suggested approach consists in approximation of a given surface by a set of Bezier bicubic patches, their separate triangulation in parametric space controlled by a mesh control function extracted from the original surface and the mapping of individual elements from the parametric space back onto the original surface. The proposed methodology for triangulation of surfaces proved to be vital and enables generation of graded meshes on a wide class of surfaces. The crucial point of the whole algorithm is the availability of such a planar triangulator which supports generation of pre-stretched and pre-oriented triangles. The experience of the authors revealed that the meshing algorithm based on the advancing front technique is very suitable for this purpose. The advantage of the suggested methodology lies in the possibility to extend this technique to other tensor product polynomial surfaces which might be more suitable for approximation and manipulation. Two major drawbacks have been identified so far. Firstly, there is a tendency to generate at most two triangles sharing the corner of the parametric space even if this is a reentrant corner on the original surface. This results apparently in (sometimes very) badly shaped triangles around this corner. The second one is tightly connected to the extension of this discretization technique to other tensor product polynomial surfaces which can potentially uncover some other kinds of singularities (e.g. inappropriate weight selection for rational Bezier surfaces). Further research is to be carried out to overcome these problems.



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Daniel Rypl
2005-12-03