Splines on the sphere

There are many problems that involve data fitting of sets on the surface of a sphere, many of them for example in the geosciences. They are usually treated using some kind of mapping onto the plane, in order to later apply some method for the plane which is well-known and proven. This means precision loss in some zones and problems at the poles. We propose a new method that treats the set of data as three-dimensional, and we show some of its advantages