  We discuss the CP properties of the potential in the general
Two-Higgs-Doublet Model (THDM). This is done in a concise way using real gauge
invariant functions built from the scalar products of the doublet fields. The
space of these invariant functions, parametrising the gauge orbits of the Higgs
fields, is isomorphic to the forward light cone and its interior. CP
transformations are shown to correspond to reflections in the space of the
gauge invariant functions. We consider CP transformations where no mixing of
the Higgs doublets is taken into account as well as the general case where the
Higgs basis is not fixed. We present basis independent conditions for explicit
CP violation which may be checked easily for any THDM potential. Conditions for
spontaneous CP violation, that is CP violation through the vacuum expectation
values of the Higgs fields, are also derived in a basis independent way.
