Generalized barycentric coordinate systems allow us to express the
position of a
point in space with respect to a given polygon or higher dimensional
polytope.
We eliminate most of the restrictions of previous approaches and
introduce a
definition for 3D mean value coordinates that is valid for arbitrary 3D
polyhedra
with a straightforward generalization to higher dimensions.
Furthermore, we extend the notion of barycentric coordinates in such a
way as
to allow Hermite interpolation. Finally, we show that barycentric
coordinates can
be used to obtain a novel formula for curvature computation on surfaces.