Rendering Polygonal Scenes with Di raction Account

Global processing of diiraction phenomena by a half-plane was proposed by Aveneau and M eriaux, using the Geometrical Theory of Diiraction. In this theory, diiraction rays are emitted by diiraction points belonging to the half-plane edge (or dihedron edge). The solution given for nding these points being numerical, it is diicult to implement and leads to low precision solutions with a slow algorithm. In this paper we rst propose a new geometric solution for nding the dihedron diiraction points, which leads to an eecient analytic algorithm. Next we present an implementation of a Ray-Tracing software for polygonal scenes with an automatic diiraction treatment. Since this implies diiraction by dihedra, we present the dihedron data structure and the corresponding algorithm which solves two problems : the existence of diiraction paths, and the impossibility for dihedra to share their edge. These elements lead to an implementation of a Ray-Tracing software with rst diiraction account for any polygonal scenes.