An Area‐Preserving Parametrization for Spherical Rectangles

Abstract

Abstract 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.