  In this note we point out the relation between Brion's formula for the
lattice point generating function of a convex polytope in terms of the vertex
cones [Brion1988] on the one hand, and the polar decomposition \`a la
Lawrence/Varchenko [Lawrence1991, Varchenko1987] on the other.
  We then go on to prove a version of polar decomposition for non-simple
polytopes.
