Projective Relations on the Sphere

For geographic applications, it is of great interest to study the geometric properties of the sphere. Spatial models that directly deal with geographic coordinates are able to contemplate such aspects that would be otherwise disregarded by flat 2D models. For example, on the Earth’s surface, a point which is to the East of another point could be reached travelling to West as well. Being situated at the North Pole, taking any direction would mean travelling to South. In this paper, we study projective relations on the sphere, a category of spatial relations more general than cardinal directions and that, together with topological relations and qualitative distances, represent the essence of qualitative spatial relations.