Elliptic Plane

The Real Projective Plane with elliptic Metric where the distance between two points $P$ and $Q$ is defined as the Radian Angle between the projection of the points on the surface of a Sphere (which is tangent to the plane at a point $S$) from the Antipode $N$ of the tangent point.

References

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, p. 94, 1969.