Dealing with degeneracy in triangulation

Here is a method for dealing with a type of degeneracy that often arises in triangulation then the input contains much regularity, such as four or more points that lie on the same circle in 2D computations or five or more on the same sphere in 3D. The paper shows a dramatic application of Francis Sullivan's and my degeneracy method by Alexander Agathos (http://users.forthnet.gr/ath/agalex), who used it for surface reconstruction and simplification.