Goniometric Diagram Mapping for Hemisphere

Abstract

Describing the light intensity over the hemisphere using a goniometric diagram is a common practice in the lighting industry and is prescribed for instance by IESNA (Illuminating Engineering Society of North America) standards. Goniometric diagram specifies the spatial distribution of the emitted power via a hemispherical surface subdivided by meridians and parallels. Similar tabulated representations are extensively used for complex bidirectional refiectance distribution functions (BRDF) that are difficult to approximate with analytical models. We present an approximative bicontinuous mapping from the unit square to a goniometric diagram on the hemisphere. This mapping has low distortion and the error of the approximation is low. The proposed mapping algorithm is obtained as a composition of four mappings. We outline its use for importance sampling of light sources described by goniometric diagrams and for the representation of BRDF.