Aspect ratio-and size-controlled patterned triangulations of parametric surfaces
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2007-02
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A method to produce patterned, controlled size triangulation of Boundary Representations is presented -- Although the produced patterned triangulations are not immediately suited for fast visualization, they were used in Fixed Grid Finite Element Analysis, and do provide a control on the aspect ratio or shape factor of the triangles produced -- The method presented first calculates a triangulation in the parameter space of the faces in which the B-Rep is partitioned and then maps it to 3D space -- Special emphasis is set in ensuring that the triangulations of neighboring faces meet in a seamless manner, therefore ensuring that a borderless C2 2-manifold would have as triangulation a C0 borderless 2-manifold -- The method works properly under the conditions(i) the parametric form of the face is a 1-1 function, (ii) the parametric pre-image of a parametric face is a connected region, and (iii) the user-requested sampling frequency (samples per length unit ) is higher than twice the spatial frequency of the features in the B-Rep ( thus respecting the Nyquist principle ) -- As the conditions (i) and (ii) are possible under face reparameterization or sub-division and the condition (iii) is the minimum that a triangulation should comply with, the method is deemed as generally applicable
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@inproceedings{2007_Ruiz_Aspect,
title={Aspect Ratio-and Size-Controlled Patterned Triangulations of Parametric Surfaces},
author={Ruiz, O. and Pena, S. And Duque, J. },
booktitle={Proceedings of the ninth IASTED International Conference. Computer Graphics and Imaging.},
isbn={ 978-0-88986-644-7},
address={Innsbruck, Austria},
year={2007},
}