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10.4.2 Gaussian Reflection

The Phong lighting equation, with its cosine raised to a power term for the specular component, is a poor fit to a physically accurate specular reflectance model. It's difficult to map measured physical lighting properties to its coefficient, and at low specularity, it doesn't conserve incident and reflected energy. The Gaussian BRDF is a better model, and with some simplifications, can be approximated by using the appropriate parameters in the Phong model. The specular phong term $K_s cos(\theta)^{spec}$ is augmented by modifying the $K_s$ and $spec$ parameters to a more complex and physically accurate form: $.0398(1.999 \frac{1}{\alpha^2})K_s cos(\theta)^{(1.999 \frac{1}{\alpha^2})}$ where $\alpha$ is a material parameter. See [25,103] for details on this equation's derivation, limits to its accuracy, and material properties modeled by the $\alpha$ parameter.