||Accurate global visibility information has become essential in global illumination rendering. Combinatorial structures such as the visibility complex, the aspect graphs, and the visibility skeleton, are the seeds of a new topic of research motivated by practical problems in computer graphics and global illumination rendering. This is now attracting interest from the computational geometry community, combinatorics, CAD and robotics. The initial motivation has been to accurately represent shadow boundaries generated by occluding surfaces in the path of light from emitting surfaces (sources) to receiving surfaces (receivers). In this thesis we add to the rich body of research generated in this field by considering occluders with curved boundaries. This has profound implications in three main areas: (1) the generation, maintenance and search functions associated with the global visibility complex, (2) mesh generation, and (3) global illumination rendering. We present a new visibility complex based on the proposed visibility skeleton. The new visibility complex has been designed to handle not only polygonal elements but also surfaces with curved boundaries. We have found that even in simple 3D scenes the new visibility complex generates less polygons in the meshing phase and a more accurate global illumination.