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