A non-linear beam tracing technique that supports full non-linear beam tracing effects including multiple reflections and refractions for computer graphics applications. The technique introduces non-linear beam tracing to render non-linear ray tracing effects such as curved mirror reflection, refraction, caustics, and shadows. Beams are allowed to be non-linear where rays within the same beam are not parallel or do not intersect at a single point. Such is the case when a primary beam bounces off of a surface and spawns one or more secondary rays or beams. Secondary beams can be rendered in a similar manner to primary rays or beams via polygon streaming. Beyond smooth ray bundles, the technique can also be applied to incoherent ray bundles which is useful for rendering bump mapped surfaces.