“Stratified sampling of spherical triangles” by Arvo

We present an algorithm for generating uniformly distributed random samples from arbitrary spherical triangles. The algorithm is based on a transformation of the unit square and easily accommodates stratified sampling, an effective means of reducing variance. With the new algorithm it is straightforward to perform stratified sampling of the solid angle subtended by an arbitrary polygon; this is a fundamental operation in image synthesis which has not been addressed in the Monte Carlo literature. We derive the required transformation using elementary spherical trigonometry and provide the complete sampling algorithm.

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