Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations

Three-dimensional Delaunay triangulations are the most common form of three-dimensional triangulations known, but they are not very suitable for tetrahedral nite 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 nite element meshes show that this algorithm is much more eeective than previous methods at removing slivers from Delau-nay 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.