IEEE Transactions on Computers
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Parallel multigrid solver for 3D unstructured finite element problems
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Delaunay Triangulation in Three Dimensions
IEEE Computer Graphics and Applications
Tiling space and slabs with acute tetrahedra
Computational Geometry: Theory and Applications
Sliver removal by lattice refinement
Proceedings of the twenty-second annual symposium on Computational geometry
Modelling three-dimensional geoscientific fields with the Voronoi diagram and its dual
International Journal of Geographical Information Science
A simplex-based approach to implement dimension independent spatial analyses
Computers & Geosciences
A robust efficient tracing scheme for triangulating trimmed parametric surfaces
Computer-Aided Design
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Computer generated solid models must be decomposed into finite element meshes for analysis by the Finite Element Method. To enable decompositions of complex solid models, tetrahedra are employed and to avoid badly skewed tetrahedra for finite element analysis, a Delaunay triangulation is created by Watson's Algorithm [6]. Certain two-dimensional properties of Delaunay triangulations do not extend to the three-dimensional implementation of Watson's Algorithm. Furthermore, serious numerical difficulties can occur due to the nonrandomness of triangulation points, Nonrandomness imposed by the geometry can be ameliorated by using tetrahedral decompositions of icosahedra to fill space. A measure of the quality of tetrahedra is proposed and used to identify undesirable tetrahedra created due to point distributions and geometric constraints of solid models. Postprocessing Delaunay triangulations to rectify undesirable tetrahedra is briefly discussed.