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

CP Violation in the General Two-Higgs-Doublet Model: a Geometric View