Continuing investigations of other authors referring to convex polygons and convex polytopes, the author generalizes the standard barycentric coordinate functions for simplices to those for arbitrary convex polytopes. In particular, a planar construction for polygons due to E. Wachspress is extended, where rational coordinate functions for convex polytopes \(P\) are constructed that are nonnegative, have linear precision and minimal degree (this degree depending on the number of facets of the polytope \(P\) and its dimension). The key for this extension is a unique homogeneous polynomial associated with \(P\) and called its adjoint. First adjoints are introduced for polyhedral cones, and then rational combinations of adjoints of various dual cones associated with \(P\) yield the barycentric coordinate functions for \(P\). Finally, the author proves some hints regarding possible future research (simplifications of his approach without resorting to the homogeneous formulation of polyhedral cones, to find further application fields such as continuous trivariate maps over a partition to space into convex polyhedra, etc.), and he announced a subsequent paper containing a proof that the barycentric coordinates discussed here are unique.