# Does DelaunayMesh use exact computations? What is the treatment of non-generic cases?

Computing Delaunay complexes can be sensitive to numerical instabilities, especially in higher dimensions. I would like to know how much I can rely on Mathematica's answers when using DelaunayMesh. There are two questions:

1. Are exact computations used when constructing the mesh? Or is the computation numerical?

2. How does it deal with non-generic cases, when we have, e.g., four points lying on a circle? I know that it triangulates the squares (or n-gons in general). But is it done just arbitrarily or is there some careful treatment implemented, like the Simulation of Simplicity method?

• Good question. Have a look into the documentations of the libraries "tetgen" and "triangle"; as far as I know, those are used as backends for dimension 3 and 2, respectively. Jun 16 at 18:57

I believe that DelaunayMesh will use the Triangle software through TriangleLink, when working in two dimensions.