Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations
Joe, Barry
Siam J. Sci. Comput., Vol 16, pp.1292-1307, 1995
Three-dimensional Delaunay triangulations are the most cormnon form of three-dimensional triangulations known, but they are not very suitable for tetrahedral finite element meshes because they tend to contain poorly-shaped sliver tetrahedra. In this paper, we present an algorithm for constructing improved-quality triangulations with respect to a tetrahedron shape measure. This algorithm uses combinations of two or more local transformations to improve a given triangulation towards an optimal triangulation. Experimental results on finite element meshes show that this algorithm is much more effective than previous methods at removing slivers from Delaunay triangulations and producing nearly optimal triangulations. A variation of this algorithm for improving a pseudo-locally-optimal non-Delaunay triangulation towards a Delaunay triangulation is also presented.
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