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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.^[1]

According to Schlick’s model, the specular reflection coefficient R can be approximated by: $R(\theta )=R_{0}+(1-R_{0})(1-\cos \theta )^{5}$ where $R_{0}=\left({\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right)^{2}$ where $\theta$ is half the angle between the incoming and outgoing light directions. And $n_{1},\,n_{2}$ are the indices of refraction of the two media 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.

In microfacet models it is assumed that there is always a perfect reflection, but the normal changes according to a certain distribution, resulting in a non-perfect overall reflection. When using Schlick’s approximation, the normal in the above computation is replaced by the halfway vector. Either the viewing or light direction can be used as the second vector.^[2]

References

^ Schlick, C. (1994). "An Inexpensive BRDF Model for Physically-based Rendering" (PDF). Computer Graphics Forum. 13 (3): 233–246. CiteSeerX 10.1.1.12.5173. doi:10.1111/1467-8659.1330233. S2CID 7825646. Archived from the original (PDF) on 2020-05-10.
^ Hoffman, Naty (2013). "Background: Physics and Math of Shading" (PDF). Fourth International Conference and Exhibition on Computer Graphics and Interactive Techniques.

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[1] Schlick, C. (1994). "An Inexpensive BRDF Model for Physically-based Rendering" (PDF). Computer Graphics Forum. 13 (3): 233–246. CiteSeerX 10.1.1.12.5173. doi:10.1111/1467-8659.1330233. S2CID 7825646. Archived from the original (PDF) on 2020-05-10.

[2] Hoffman, Naty (2013). "Background: Physics and Math of Shading" (PDF). Fourth International Conference and Exhibition on Computer Graphics and Interactive Techniques.

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+{{Short description|Lighting formula in 3D computer graphics}}
-In [[3D computer graphics]], '''Schlick's approximation''', named after Christophe Schlick, is a formula for approximating the contribution of the [[Fresnel equation|Fresnel factor]] in the [[specular reflection]] of light from a non-conducting interface (surface) between two media.<ref>{{cite doi|10.1111/1467-8659.1330233}}</ref>
+In [[3D computer graphics]], '''Schlick’s approximation''', named after Christophe Schlick, is a formula for approximating the contribution of the [[Fresnel equation|Fresnel factor]] in the [[specular reflection]] of light from a non-conducting interface (surface) between two media.<ref>{{cite journal | year = 1994 | title = An Inexpensive BRDF Model for Physically-based Rendering | journal = Computer Graphics Forum | volume = 13 | issue = 3 | pages = 233–246 |url=http://cs.virginia.edu/~jdl/bib/appearance/analytic%20models/schlick94b.pdf |archive-url=https://web.archive.org/web/20200510114532/http://cs.virginia.edu/~jdl/bib/appearance/analytic%20models/schlick94b.pdf |archive-date=2020-05-10  | doi = 10.1111/1467-8659.1330233 | last1 = Schlick | first1 = C.| citeseerx = 10.1.1.12.5173 | s2cid = 7825646 }}</ref>
-According to Schlick's model, the specular [[reflection coefficient]] ''R'' can be approximated by:
+According to Schlick’s model, the specular [[reflection coefficient]] ''R'' can be approximated by:
+<math display="block"> R(\theta) = R_0 + (1 - R_0)(1 - \cos \theta)^5 </math> where <math display="block"> 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. And <math>n_1,\,n_2</math> are the [[Index of refraction|indices of refraction]] of the two media at the interface and <math>R_0</math> is the reflection coefficient for light incoming parallel to the normal (i.e., the value of the Fresnel term when <math>\theta = 0</math> or minimal reflection). In computer graphics, one of the interfaces is usually air, meaning that <math>n_1</math> very well can be approximated as 1.
+In [[Specular highlight#Microfacets|microfacet model]]s it is assumed that there is always a perfect reflection, but the normal changes according to a certain distribution, resulting in a non-perfect overall reflection. When using Schlick’s approximation, the normal in the above computation is replaced by the [[Blinn–Phong shading model|halfway vector]]. Either the viewing or light direction can be used as the second vector.<ref>{{cite journal|last1=Hoffman|first1=Naty|title=Background: Physics and Math of Shading.|journal=Fourth International Conference and Exhibition on Computer Graphics and Interactive Techniques|date=2013|url=http://blog.selfshadow.com/publications/s2012-shading-course/hoffman/s2012_pbs_physics_math_notes.pdf}}</ref>
-:<math>R(\theta) = R_0 + (1 - R_0)(1 - \cos \theta)^5</math>
+==See also==
-:<math>R_0 = \left(\frac{n_1-n_2}{n_1+n_2}\right)^2</math>
-where <math>\theta</math> is the angle between the direction from which the incident light is coming and the [[Normal (geometry)|normal]] of the interface between the two media, hence <math>\cos\theta=(N\cdot V)</math>. And <math>n_1,\,n_2</math> are the indices of refraction of the two media at the interface and <math>R_0</math> is the reflection coefficient for light incoming parallel to the normal (i.e., the value of the Fresnel term when <math>\theta = 0</math> or minimal reflection). In computer graphics, one of the interfaces is usually air, meaning that <math>n_1</math> very well can be approximated as 1.
-In [[microfacet model]]s it is assumed that there is always a perfect reflection, but the normal changes according to a certain distribution, resulting in a non-perfect overall reflection. When using Schlicks's approximation, the normal in the above computation is replaced by the [[Blinn–Phong shading model|halfway vector]]. Either the viewing or light direction can be used as the second angle.<ref>{{cite journal|last1=Hoffman|first1=Naty|title=Background: Physics and Math of Shading.|journal=Fourth International Conference and Exhibition on Computer Graphics and Interactive Techniques|date=2013|url=http://blog.selfshadow.com/publications/s2012-shading-course/hoffman/s2012_pbs_physics_math_notes.pdf}}</ref>
-==See also==
-{{portal|Computer graphics}}
 * [[Phong reflection model]]
 * [[Blinn-Phong shading model]]