This paper presents a fast approximation method to obtain the point hit by a reflection or refraction ray. The calculation is based on the distance values stored in environment map texels. This approximation is used to localize environment mapped reflections and refractions, that is, to make them depend on where they occur. On the other hand, placing the eye into the light source, the method is also good to generate real-time caustics. Computing a map for each refractor surface, we can even evaluate multiple refractions without tracing rays. The method is fast and accurate if the scene consists of larger planar faces, when the results are similar to that of ray-tracing. On the other hand, the method suits very well to the GPU architecture, and can render ray-tracing and global illumination effects with few hundred frames per second. The primary application area of the proposed method is the introduction of these effects in games.
This paper presents efficient algorithms for free path sampling in heterogeneous participating media defined either by high-resolution voxel arrays or generated procedurally. The method is based on the concept of mixing 'virtual' material or particles to the medium, augmenting the extinction coefficient to a function for which the free path can be sampled in a straightforward way. The virtual material is selected such that it modifies the volume density but does not alter the radiance. We define the total extinction coefficient of the real and virtual particles by a lowresolution grid of super-voxels that are much larger than the real voxels defining the medium. The computational complexity of the proposed method depends just on the resolution of the super-voxel grid and does not grow with the resolution above the scale of super-voxels. The method is particularly efficient to render large, low-density, heterogeneous volumes, which should otherwise be defined by enormously high resolution voxel grids and where the average free path length would cross many voxels.
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