Linear-Time Approximate Spherical Gaussian Filtering

Blinn-Phong approximates a Gaussian distribution as the specular exponent increases [Lyon1993]. [Olano2010] has shown the following relation in terms of the angle $\theta$ between $n$ and $h$:

$\cos^{s}(\theta)\approx\exp\left(-\frac{s}{2}\tan^{2}\theta\right)$

This makes the spherical Gaussian blur an excellent and appropriate choice for generating environmental maps. By extending the Gaussian blur's separable property, it is possible to implement it in $O(K)$ (where $K$ is a kernel radius) for reasonably small $\sigma$ values.

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