I'm working on a Delaunay triangulation algorithm (specifically, I care about triangulating points on any 2D subspace of (plane in) R3).
I understand how 2D triangulation can be achieved by computing the convex hull of a corresponding 3D paraboloid.
I am therefore attempting something similar with a 4D paraboloid to get 3D triangulation. I'm assuming a similar approach works (find the convex hull of a 4D paraboloid and the projection back to 3D gives the triangulation of my plane).
My question: does it? Can the convex hull of a corresponding 4D paraboloid be used to construct a Delaunay triangulation of 3D points lying in a 2D plane?
Yes, I already know that I can make the problem easier by transforming the 2D plane to R2, and then using the 3D paraboloid/2D plane.