Triangulating the Real Projective Plane

We consider the problem of computing a triangulation of the real projective plane P2 , given a finite point set P = {p1, p2, . . . , pn} 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. Keywords. Computational geometry, triangulation, simplicial complex, projective geometry.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Mridul Aanjaneya, Monique Teillaud
• Keywords: CORR 2007, Education, Projective Plane P2, Real Projective Plane, Triangulation