## 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.## Related Works

## Pre-filtered Mipmapped Radiance Environment …