Computing direct shadows cast among disjoint convex polyhedra

Abstract

Since shadows are very important in human perception of three-dimensional scenes from two-dimensional images, the realistic rendering of shadows has been a main problem in computer graphics for many years. While the global illumination simulation methods render excellent images, we sometimes need to determine the geometry of shadow boundaries before performing the global illumination simulation. However, the geometry of soft shadows cast by polygonal light sources is hard to obtain, and the classical method using the visual event surface are too large to be used in practice. In this paper, we present an exact method to compute the boundaries between umbra, penumbra and full-light regions cast among a set of dijoing convex polyhedra, some of which are light sources. We generalize the implementation to compute the shadow boundaries on an arbitrary plane, and extend the plane to a polyhedron to make it possible to obtain the shadow boundaries among the objects themself in the scene. Moreover, we try to obtain not only the boundary but also the shadow image in a scene, by triangulating the shadow boundaries and using the interpolation method.