A Robust Procedure to Eliminate Degenerate Faces from Triangle Meshes
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Illumination Dependent Refinement of Multiresolution Meshes
CGI '98 Proceedings of the Computer Graphics International 1998
Mapping Independent Triangulation of Parametric Surfaces
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
A mapping-independent primitive for the triangulation of parametric surfaces
Graphical Models - Special issue on SMI 2002
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
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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.