📁 Graphics

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 θ\theta between nn and hh:

coss(θ)exp(s2tan2θ)\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)O(K) (where KK is a kernel radius) for reasonably small σ\sigma values.

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