Computing Exact Shadow Irradiance Using Splines

We present a solution to the general problem of characterizing shadows in scenes involving a uniform polygonal area emitter and a polygonal occluder in arbitrary position by manifesting shadow irradiance as a spline function. Studying generalized prism-like constructions generated by the emitter and the occluder in a fourdimensional (shadow) space reveals a simpler intrinsic structure of the shadow as compared to the more complicated 2D projection onto a receiver. 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 involving only 2D faces on the receiver, derived from the scene geometry. This leads to a straightforward computational algorithm and an interactive implementation. Moreover, this approach can be extended to scenes involving multiple emitters and occluders, as well as curved emitters, occluders, and receivers. Spline functions are constructed from th...

• Type: Conference
• Year: 1999
• Where: SIGGRAPH
• Authors: Michael M. Stark, Elaine Cohen, Tom Lyche, Richard F. Riesenfeld
• Keywords: Computer Graphics, Shadow Irradiance, SIGGRAPH 1999, Spline Functions, Spline Shadow Irradiance