Analytic illumination in polyhedral environments

Computing direct illumination from area light sources when shadowing is involved remains a perennial and yet difficult problem in rendering. Illumination is formalized as the radiometric quantity of irradiance, and is a function of surface position. This work investigates the irradiance surface function, and develops a closed form expression for shadowed irradiance of a polygonal blocker illuminated by a polygonal light source. This is accomplished using the mechanism of polyhedral splines. Classical polyhedral splines are generalized to a weighted variety that allows for curved facets, and from these objects an expression is developed for general shadowed irradiance from a single occluding polygon.; The polyhedral spline approach does not directly extend to a general multiple blocker configuration; a closed form expression is developed only in the single blocker case. It does, however, suggest a novel way of approaching the problem that ultimately leads to a simple and fast algorithm for computing shadow irradiance that requires little overhead and exhibits desirable stability. The algorithm is extended to handle specular transport, approximate transparency, and perform exact reconstruction from a constant-element radiosity solution.