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

width=

Apply the Divergence Theorem to the part of Ω(S) between S(a) and to show that

width=

where is the radius vector from P to any point on S, r = width=, and the unit normal

vector is directed away from P.

  • 5 years ago
parametric surface
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