  Formerly the geometry was based on shapes, but since the last centuries this
founding mathematical science deals with transformations, projections and
mappings. Projective geometry identifies a line with a single point, like the
perspective on the horizon line and, due to this fact, it requires a
restructuring of the real mathematical and numerical analysis. In particular,
the problem of interpolating data must be refocused. In this paper we define a
linear structure along with a metric on a projective space, and prove that the
space thus constructed is complete. Then we consider an iterated function
system giving rise to a fractal interpolation function of a set of data.
