  This paper studies the Bondi-Metzner-Sachs group in homogeneous projective
coordinates, because it is then possible to write all transformations of such a
group in a manifestly linear way. The 2-sphere metric, Bondi-Metzner-Sachs
metric, asymptotic Killing vectors, generators of supertranslations, as well as
boosts and rotations of Minkowski spacetime, are all re-expressed in
homogeneous projective coordinates. Last, the integral curves of vector fields
which generate supertranslations are evaluated in detail. This work prepares
the ground for more advanced applications of the differential geometry of
asymptotically flat spacetimes in projective coordinates.
