The classical hyperbolic plane has a well known
bounded model, the unit disk with the Poincar/'e metric.
One can view this construction also the other way around: on the
hyperbolic plane one can naturally define a new metric, such that the
hyperbolic plane with this new metric is isometric to the euclidean
disc. The hyperbolic isometries are M/"obius maps in this new metric.
  We describe a generalization of this construction to more general
spaces, namely CAT(-1) and Gromov hyperbolic spaces. On these spaces
we define new bounded metrics which are the analoga of the euclidean
disc metric on the hyperbolic plane. This gives in particular a better
understanding of the boundary at infinity, since this boundary is
now at finite distance in the new metric.