Methods for efficient sampling of arbitrary distributed volume densities

In recent years a number of techniques have been developed for rendering volume effects (haze, fog, smoke, clouds, etc.). Such techniques have been implemented for projective scanline renderers, ray-tracers and for radiosity. Roughly speaking, such a method depends on an illumination model which accounts for the light-material interaction, together with a sampling strategy for reading the data of the density field. The illumination models proposed in literature are quite complicated and require several time-consuming operations, such as exponential functions, roots and trigonometrical functions. Ray-tracing and radiosity evaluate the illumination model at every voxel of the density field. Since several hundred complicated calculations are necessary for each ray, such a rigorous evaluation is very time-consuming. On the other hand, methods proposed for scanline renderes solve the equations describing scattering and reflection of light analytically along each ray within a volume; thus, such methods do not account for arbitrary density distribution. The purpose of this paper is not to propose a new illumination model, but to compare several methods for efficiently sampling arbitrary distributed data, i.e. , efficiently distribute the samples within the sampling volume. We propose that several sampling strategies can be used to reduce the number of evaluations of the illumination calculations along a ray and, thus, reduce the rendering time needed. Such methods are well suited for scanline renderers but can be used with ray-tracers. We propose a Monte-Carlo approach and an approximative method with user-adjustable accuracy to sample the volume data.