An Area-Preserving Parametrization for Spherical Rectangles

We present an area-preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1]² and range in a region included in the unit-radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1]² onto the spherical rectangle. This allows for easily incorporating stratified, quasi-Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.