  We extend many theorems from the context of solid angle sums over rational
polytopes to the context of solid angle sums over real polytopes. Moreover, we
consider any real dilation parameter, as opposed to the traditional integer
dilation parameters. One of the main results is an extension of Macdonald's
solid angle quasipolynomial for rational polytopes to a real analytic function
of the dilation parameter, for any real convex polytope.
