Most iterative algorithms require an initial empty triangle to get the ball rolling. It seems like a commonly used trick is just to make the super triangle very large in comparison with the point set.
But according to "Numerical recipes: the art of scientific computing":
"...if the distance is merely finite (to the boundary points) the constructed triangulation may be not-quite Delaunay. For example its outer boundary could in unusual cases be left slightly concave, with small negative angles on the order of the diameter of the "real" point set divided by the distance to the "fictitious" (boundary) points.
So what options are there for augmenting Cartesian coordinates with points at infinity, without having to convert all the input to a different coordinate system such as homogeneous coordinates? How do these points fit in with the usual geometric predicates CCW and Incircle?
Incircle (a,b,c) Infinity -> False. provided that a,b,c are finite.
But what about when one of a,b,c is a point at infinity? Does the circle become a half-plane and the test then become a CCW check? What if 2 or more points on the circumcircle are infinite? does the circle expand into a full plane causing the test to always yield true? What about CCW? how do you classify a point in relation to a line that has one or more points at infinity?