Multipole expansion of the light vector

摘要

Computing the light field due to an area light source remains anninteresting problem in computer graphics. The paper presents a seriesnapproximation of the light field due to an unoccluded area source, bynexpanding the light field in spherical harmonics. The source can bennonuniform and need not be a planar polygon. The resulting formulas givenexpressions whose cost and accuracy can be chosen between the exact andnexpensive Lambertian solution for a diffuse polygon, and the fast butninexact method of replacing the area source by a point source of equalnpower. The formulas break the computation of the light vector into twonphases: the first phase represents the light source's shape andnbrightness with numerical coefficients, and the second uses thesencoefficients to compute the light field at arbitrary locations. Thenauthor examines the accuracy of the formulas for spherical andnrectangular Lambertian sources, and applies them to obtain lightngradients. The author also shows how to use the formulas to estimatenlight from uniform polygonal sources, sources with polynomially varyingnradiosity, and luminous textures