Piecewise constant conic sections for accelerated volume density rendering

In order to accelerate the rendering of volumetric shadows, we propose a new technique which builds sets of conic volumes to approximate the shape of shadows in a participating medium. The novelty of our approach is notably the construction of the cone-sets, which are built with no knowledge of the underlying geometry of the scene. Instead, information collected during the construction of a global photon map is used to derive an estimate of the outline of the shadows in three dimensions. This information is then used in several different ways to speed up the rendering pass. The method shares many of the advantages proposed by photon maps such as viewpoint independence and decoupling from the geometry of the scene.