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# Torrance-Sparrow

Surface is modeled as consisting of multiple mirror-like microfacets rotated randomly. The specular component of light reaching the eye is said to come only from the facets that

$$s = \frac{DGF}{\langle N, E\rangle},$$

- $D$ distribution function of directions of microfacets, e.g. Gaussian $D_2(\alpha) = \exp{-(\alpha c_2)^2},$
where $\alpha$ is the angle from average surface normal; we're interested in facets pointing in direction of $H$, so we set $\alpha = \operatorname{arccos}\langle N, H\rangle$; large stddev $c_2$ yields surfaces that appear dull, and small values yield shiny surfaces;
- $G$ -- amount by which factes shadow and mask each other;
- $F$ -- Fresnel law's coefficients, the proportion of light incident on a facet that is actually being reflected, opposed to being absorbed.

The geometric term $G$ models microfacets as symmetric $V$-shaped grooves and does some trigonometry which I don't want yet to copy from written notes.