Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations
Barry Joe · SIAM Journal on Scientific Computing · 1995
Three-dimensional Delaunay triangulation are the most common form of three-dimensional triangulation 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 triangulation with respect to a tetrahedron shape measure. This algorithm uses combination of two or more local transformations to improve a given triangulation toward 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 triangulation and producing nearly optimal triangulation. A variation of this algorithm for improving a pseudo locally optimal non-Delaunay triangulationn toward a Delaunay triangulation is also presented.