  Closed form solutions for the computation of the solid angle from polygonal
cross-sections are well known, however similar formulae for computation of
projected solid angle are not generally available. Formulae for computing the
projected solid angle from arbitrarily shaped polygons are derived using the
Gauss-Bonnet theorem. This is accomplished by transforming the projected solid
angle integral to an integral over a spherical patch, which is then reduced by
Gauss-Bonnet to a simple summation over its edges, allowing the projected solid
angle to be computed exactly. Application of the formulae allows exact
calculation of projected solid angle over discrete intervals which may be used
for computing radiative flux to surfaces or view factors to free space.
