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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

INTERNATIONAL
MESHING
ROUNTABLE

25th International Meshing Roundtable
Washington DC, U.S.A.
September 26-30, 2016

Brigham Bagley, Scientific Computing and Imaging Institute, US, brig@sci.utah.edu
Shankar Sastry, Scientific Computing and Imaging Institute, US, sastry@sci.utah.edu
Ross Whitaker, Scientific Computing and Imaging Institute, US, whitaker@sci.utah.edu

Abstract
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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