Computing exact shadow irradiance using splines

摘要

We present a solution to the geenral problem of characterising shadows in scenes involving a uniform polygonal area emitter and a polygonal occluder in arbitrary position by manifesting shadow irradiance as a sopline function.Studying generalized prism-like constructions generated by the emitter and the occluder in a four-dimensional (shadow) space reveals a simpler intrinsic structure of the shadow as ocmpared to the more complicated 2D projection onto a receriver.A closed form expression for the spline shadow irradiance function is derived by twice applying Stokes' theorem to reduce an evaluation over a 4D domain to an explicit formula inetry.