Goniometric Diagram Mapping for Hemisphere

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
reflectance 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 also 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. This is a joint work with Kirill Dmitriev
and Hans-Peter Seidel.