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We investigate current vertex normal computation algorithms and evaluate their effectiveness at approximating analytically computable (and thus comparable) normals for a variety of classes of model. We find that the most accurate algorithm depends on the class and that for some classes, none of the available algorithms is particularly good. We also compare the relative speeds of all algorithms.

: We have discovered a class of fractal functions that are differentiable. Fractal interpolation functions have been used for over a decade to generate rough functions passing through a set of given points. The integral of a fractal interpolation function remains a fractal interpolation function, and this new fractal interpolation function is differentiable. Tensor products of pairs of these fractal functions form fractal surfaces with a well-defined tangent plane. We use this surface normal to shade fractal surfaces, and demonstrate its use with renderings of fractal mirrors.