We show that the e.m. field of a point charge is the acceleration part of a geodesic equation, in the Beltrami-Klein Ball model of hyperbolic geometry,in 3dim velocity space.The result is obtained by assuming that the interval of interaction is timelike instead of null.This gives rise to a formal 4 velocity of interaction and a rest frame for an inertial observer moving with the formal velocity.The geodesic between two points in the tangent space is given by projective velocity 4 vectors or bivectors.The moment of Lienard-Wiechert potential is the geodesic between the velocity of the source charge and the formal velocity of interaction,in bivector form.The Lorentz force is proportional to the geodesic between the velocity of the source charge and that of the interaction,in the rest frame of the test charge.The energy- stress tensor, the field Lagrangian density, the e.m energy density, the e.m. momentum density also have geometricmeanings.The inverse of the field is related to virtual, uniformly accelerated motions,described by a Rindler-like coordinate system.All e.m. entities are finite everywhere and Lorentz covariant.