Rather than using Monte Carlo sampling techniques or patch projections to compute radiosity, it is possible to use a discretization of a scene into voxels and perform some discrete geometry calculus to quickly compute visibility information. In such a framework , the radiosity method may be as precise as a patch-based radiosity using hemicube computation for form-factors, but it lowers the overall theoretical complexity to an O(N log N) + O(N), where the O(N) is largely dominant in practice. Hence, the apparent complexity is linear for time and space, with respect to the number of voxels in the scene. This method does not require the storage of pre-computed form factors, since they are computed on the fly in an efficient way. The algorithm which is described does not use 3D discrete line traversal and is not similar to simple ray-tracing. In the present form, the voxel-based radiosity equation assumes the ideal diffuse case and uses solid angles similarly to the hemicube.
Abstract. Radiosity in 3D scenes is usually computed using a discretization of the surfaces into patches. A discretization into voxels is possible, coupled with the use of discrete geometry. An algorithm for radiosity solving with voxels is introduced, lowering the theoretical complexity to an O(N log N ) + O(N ), where the O(N ) is largely dominant in practice, so that the apparent complexity is linear for time and space, with respect to the number of voxels in the scene. The method also fits in RAM and does not need disk storage. Instead of 3D discrete line traversal, a new algorithm is described to perform visibility computation. The voxel-based radiosity equation assumes the ideal diffuse case and uses solid angles similarly to the hemicube.
Global illumination that simulates realistic lighting environments makes use of bidirectional reflectance distribution functions (BRDF). Such a function is a surface property, describing how light is re-emitted after hitting this surface. The present paper details a representation of BRDF and radiance distributions, based on control points, that aims at performance. It uses spherical triangles for interpolation, least square mean or linear programming for optimal representation, and very fast rotation by precomputing control points reweightening. It has some more advantages for deforming an existing shape. This approach is compared to Spherical Harmonics, and outperforms this last one.
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