Faraway point: A senitel point for Delaunay computation
Implementation of incremental Delaunay diagram algorithms often handle boundary cases in somewhat ad-hoc manners. The most common is to add a single point at infinity in one-dimension higher. This does not interact well with perturbation schemes to remove degeneracies-perturbing can introduce flat simplices. We propose a "faraway point" instead, which can be thought of as infintesimal perturbation of the point at infinity. The faraway point resolves this perturbation issue, restoring a nice structural property of the computed polytope that would be lost if there were degeneracies in the input. Furthermore, there is a simple implementation policy consistent with the faraway point.
perturbation schemes voronoi diagram implementation oriented projective geometry