AMarching-Tetrahedra Algorithm for Feature-Preserving Meshing of Piecewise-Smooth Implicit Surfaces
Bagley, Brigham, Shankar Sastry, Ross Whitaker
Proceedings, 25th International Meshing Roundtable, Elsevier, Science Direct, September 26-30 2016
25th International Meshing Roundtable
Washington DC, U.S.A.
September 26-30, 2016
Brigham Bagley, Scientific Computing and Imaging Institute, US, firstname.lastname@example.org
Shankar Sastry, Scientific Computing and Imaging Institute, US, email@example.com
Ross Whitaker, Scientific Computing and Imaging Institute, US, firstname.lastname@example.org
For visualization and finite element mesh generation, feature-preserving meshing of piecewise-smooth implicit surfaces has been a challenge since the technique was introduced in the 1980s. Tessellation-based techniques have been used with varying degrees of success for this purpose, but they have consistently failed to reproduce smooth curves of surface-surface intersection when two surfaces intersect at sharp angles. Such techniques attempt to discretize all surfaces within a given cell in a single pass by computing edge-surface points of intersection for each edge in the cell and use predefined stencils to generate the surface mesh elements. This approach limits the number of surface-edge intersections on every edge to just one (or some small finite number) because the number of stencils grows exponentially with the number of surfaces. In our tessellation-based approach, we discretize only one surface in each pass over the tetrahedral cells and retetrahedralize the affected cells for the next surface during the next pass. As a result, we manage to preserve sharp features in the domain, and our algorithm scales almost linearly with the number of surfaces. As in the isosurface-stuffing algorithm, we locally warp the initial tessellated domain to ensure that a high-quality surface mesh is generated.
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