Efficient anti-aliased bump mapping

The naïve method of anti-aliasing bump mapping, using MIP maps, does not generate theoretically correct results due to the non-linearity of the bump mapping process. In some cases results can be improved by modifying the resultant average beam to take account of the angular spread of the vectors being averaged. More generally it is necessary to represent each texel in a MIP map by multiple vectors. The resulting structure can be thought of as a multiple surface. A previous attempt to do this encountered problems with excessive time being required to generate the MIP maps. We present a new method of multi-vector MIP map generation in which the vectors are obtained by a competitive learning process. This method is orders of magnitude faster. The multi-vector technique is also extended to environment map based bump mapping where it is shown to be visually superior to earlier techniques. The method can be readily incorporated into current and future graphics cards with low cost in memory and processing.