Triangulating the Real Projective Plane

Abstract: We consider the problem of computing a triangulation of the real projective plane P², given a finite point set P as input. We prove that a triangulation of P² always exists if at least six points in P are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P² if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane.