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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,
Shankar Sastry, Scientific Computing and Imaging Institute, US,
Ross Whitaker, Scientific Computing and Imaging Institute, US,

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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