The fast identification of shadow regions due to area light sources is necessary for realistic rendering and for discontinuity meshing for global illumination. A new shadow-determination algorithm is presented that uses a data structure, called a backprojection, to represent the visible portion of a light source from any point in the scene. A complete discontinuity meshing algorithm is described for polyhedral scenes and area light sources, which includes an important class of light/geometry interactions that have not been implemented before. A fast incremental algorithm for computing backprojections is also described. The use of spatial subdivision, and heuristics based on computed statistics of typical scenes, results in efficient mesh and backprojection computation. Results of the implementation show that the use of the backprojection and discontinuity meshing permits accelerated high-quality rendering of shadows using both ray-casting and polygon-rendering with interpolants.