Triangulating the Real Projective Plane

TL;DR

This paper addresses the problem of triangulating the real projective plane from a finite point set, proving existence conditions and providing the first known algorithm for such triangulations.

Contribution

It establishes the existence of triangulations under general position conditions and introduces the first algorithm for triangulating the real projective plane.

Findings

Triangulation exists if at least six points are in general position.

First computational method for triangulating the real projective plane.

Provides theoretical proof and an algorithm for the problem.

Abstract

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S 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.