Rendering CSG scenes with general antialiasing

Ray-tracing is one of the most popular techniques for rendering 3D images. Effects such as shadows, reflection, refraction and so on can be produced with this technique. However, raytracing is a point-sampling technique with well-known aliasing problems. In particular, small objects and small shadows can be hidden between rays and not be detected. No ray-tracing method, even using oversampling, can solve this problem entirely. The solution is to use an extension of ray-tracing in which the concept of the infinitesimal ray is replaced by that of the beam, which has a volume of the scene. Beam-tracing is more complex than ray-tracing: in particular because of the beam-object intersection computations. So beam-tracers are usually limited to polygonal objects. The method presented here is a beam-tracer with no explicit beam-object intersection computations; so it can be used for rendering CSG scenes with antialiasing.