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Sphere Packing and Applications to Granular Structure Modeling

VanderZee, Evan, Anil N. Hirani, and Damrong Guoy

Proceedings, 17th International Meshing Roundtable, Springer-Verlag, pp.19-36, October 12-15 2008


17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008

Department of Mathematics
Department of Computer Science
Center for Simulation of Advanced Rockets University of Illinois at Urbana-Champaign

A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple domains using completely well-centered tetrahedra. The domains we consider here are space, infinite slab, infinite rectangular prism, cube, and regular tetrahedron. We also demonstrate single tetrahedra with various combinations of the properties of dihedral acuteness, 2-well-centeredness, and 3-well-centeredness.

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