# A Survey of Non-linear Pre-filtering Methods for Efficient and Accurate Surface Shading

Rendering a complex surface accurately and without aliasing requires the evaluation of an integral for each pixel, namely a weighted average of the outgoing radiance over the pixel footprint on the surface. The outgoing radiance is itself given by a local illumination equation as a function of the incident radiance and of the surface properties. Computing all this numerically during rendering can be extremely costly. For efficiency, especially for real-time rendering, it is necessary to use precomputations. When the fine scale surface geometry, reflectance and illumination properties are specified with maps on a coarse mesh (such as color maps, normal maps, horizon maps or shadow maps), a frequently used simple idea is to pre-filter each map linearly and separately. The averaged outgoing radiance, i.e., the average of the values given by the local illumination equation is then estimated by applying this equation to the averaged surface parameters. But this is really not accurate because this equation is non-linear, due to self-occlusions, self-shadowing, non-linear reflectance functions, etc. Some methods use more complex pre-filtering algorithms to cope with these non-linear effects. This paper is a survey of these methods. We start with a general presentation of the problem of pre-filtering complex surfaces. We then present and classify the existing methods according to the approximations they make to tackle this difficult problem. Finally, an analysis of these methods allows us to highlight some generic tools to pre-filter maps used in non-linear functions, and to identify open issues to address the general problem.

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## BibTex references

@Article\{BN11, author = "Bruneton, Eric and Neyret, Fabrice", title = "A Survey of Non-linear Pre-filtering Methods for Efficient and Accurate Surface Shading", journal = "IEEE Transactions on Visualization and Computer Graphics", year = "2011", url = "http://maverick.inria.fr/Publications/2011/BN11" }