Let be a smooth parametric surface and let P be a point such that each line that starts
at P intersects S at most once. The solid angle Ω(S) subtended by S at P is the set of
lines starting at P and passing through . Let S(a) be the intersection of Ω(S) with the
surface of the sphere with center P and radius a. Then the measure of the solid angle (in
steradians) is defined to be
Apply the Divergence Theorem to the part of Ω(S) between S(a) and to show that
where is the radius vector from P to any point on S, r = , and the unit normal
vector is directed away from P.
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