Schlick's approximation

In 3D computer graphics, Schlick's approximation, named after Christophe Schlick, is a formula for approximating the contribution of the Fresnel factor in the specular reflection of light from a non-conducting interface (surface) between two media.

According to Schlick's model, the specular reflection coefficient R can be approximated by:

R(\theta) = R_0 + (1 - R_0)(1 - \cos \theta)^5

R_0 = \left(\frac{n_1-n_2}{n_1+n_2}\right)^2

where $\theta$ is the angle between the viewing direction and the half-angle direction, which is halfway between the incident light direction and the viewing direction, hence $\cos\theta=(H\cdot V)$ . And $n_1,\,n_2$ are the indices of refraction of the two medias at the interface and $R_0$ is the reflection coefficient for light incoming parallel to the normal (i.e., the value of the Fresnel term when $\theta = 0$ or minimal reflection). In computer graphics, one of the interfaces is usually air, meaning that $n_1$ very well can be approximated as 1.

References

Schlick, C. (1994). "An Inexpensive BRDF Model for Physically-based Rendering". Computer Graphics Forum 13 (3): 233. doi:10.1111/1467-8659.1330233.

Schlick's approximation

See also

References