Schlick's approximation: Difference between revisions

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In 3D computer graphics, Schlick's approximation is a formula for approximating the contributions of Fresnel terms in the specular reflection of light from non-conducting surfaces.

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 half the angle between the incoming and outgoing light directions. If the light is reflected due to the law of reflection, this means that $\theta$ is the angle between the light direction and the normal. $R_{0}$ is the reflectance at normal incidence (i.e., the value of the Fresnel term when $\theta =0$ or minimal reflection) and $n_{1},\,n_{2}$ are the indices of refraction at the interface. In computer graphics, one of the interfaces is usually air, meaning that $n_{1}$ very well can be approximated as 1.

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 :<math>R(\theta) = R_0 + (1 - R_0)(1 - \cos \theta)^5</math>
 :<math>R_0 = \left(\frac{n_1-n_2}{n_1+n_2}\right)^2</math>
-where <math>\theta</math> is half the angle between the incoming and outgoing light directions. If the light is reflected due to the law of reflection, this means that <math>\theta</math> is the angle between the light direction and the [[Normal (geometry)|normal]]. <math>R_0</math> is the reflectance at normal incidence (i.e., the value of the Fresnel term when <math>\theta = 0</math> or minimal reflection) and <math>n_1,n_2</math> are the indices of refraction at the interface. In computer graphics, one of the interfaces is usually air, meaning <math>n_1=1</math>.
+where <math>\theta</math> is half the angle between the incoming and outgoing light directions. If the light is reflected due to the law of reflection, this means that <math>\theta</math> is the angle between the light direction and the [[Normal (geometry)|normal]]. <math>R_0</math> is the reflectance at normal incidence (i.e., the value of the Fresnel term when <math>\theta = 0</math> or minimal reflection) and <math>n_1,\,n_2</math> are the indices of refraction at the interface. In computer graphics, one of the interfaces is usually air, meaning that <math>n_1</math> very well can be approximated as 1.
 ==See also==