There are simple and robust refinements (almost) as good as Delaunay

A new edge-based partition for triangle meshes is presented, the Seven Triangle Quasi-Delaunay partition (7T-QD). The proposed partition joins together ideas of the Seven Triangle Longest-Edge partition (7T-LE), and the classical criteria for constructing Delaunay meshes. The new partition performs similarly compared to the Delaunay triangulation (7T-D) with the benefit of being more robust and with a cheaper cost in computation. It will be proved that in most of the cases the 7T-QD is equal to the 7T-D. In addition, numerical tests will show that the difference on the minimum angle obtained by the 7T-QD and by the 7T-D is negligible.