Spherical Gaussian approximation for Blinn-Phong, Phong and Fresnel

系统管理员 2022-07-12 17:38 102阅读 0赞

JUNE 3, 2012 [16 COMMENTS][]

Spherical Gaussian approximation for lighting calculation is not new to the graphic community\[4\]\[5\]\[6\]\[7\]\[8\] but its use has recently been adopted by the game developer community \[1\]\[2\]\[3\].  
Spherical Gaussian (SG) is a type of spherical radial basis function (SRBF) \[8\] which can be used to approximate spherical lobes with Gaussian-like function.  
This post will describe how SG can be use to approximate Blinn-Phong lighting, Phong lighting and Fresnel.

Why care about SG approximation ?  
In the context of realtime rendering for games, the SG approximation allows to save a few instructions when performing lighting calculations. For modern graphics cards, saving few ALU in a shader is not always beneficial, but for older hardware like one can find in the PS3, every GPU cycle counts. This is less true for XBOX360 GPU, which performs better with arithmetic instructions, though this optimization can still be beneficial. It can also be used to schedule instructions in a different (low loaded) pipe on SPUs to increase performance \[2\].

Part of the work presented here credits to Matthew Jones (from Criterion Games) \[9\].

## Different spherical radial basis function ##

The post talk about SG, but it is good to know that there is several different types of SRBF found in graphics papers.  
For completeness, I will talk quickly about SG and von Mises-Fisher (vMF) as this can be confusing.

SG definition can be found in \[4\]:  
![G(v; p,\\lambda,\\mu)=\\mu e^\{\\lambda(v.p -1)\}][G_v_ p_lambda_mu_mu e_lambda_v.p -1] where p ∈

[16 COMMENTS]: https://seblagarde.wordpress.com/2012/06/03/spherical-gaussien-approximation-for-blinn-phong-phong-and-fresnel/#comments
[G_v_ p_lambda_mu_mu e_lambda_v.p -1]: https://s0.wp.com/latex.php?latex=G%28v%3B+p%2C%5Clambda%2C%5Cmu%29%3D%5Cmu+e%5E%7B%5Clambda%28v.p+-1%29%7D+&bg=FFFFFF&fg=555555&s=0