Schlick's approximation: Difference between revisions
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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: |
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<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> |
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: |
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:<math>\begin{align} |
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R(\theta) &= R_0 + (1 - R_0)(1 - \cos \theta)^5 \\ |
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\\ where \\ |
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R_0 &= \left(\frac{n_1-n_2}{n_1+n_2}\right)^2 |
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\end{align}</math> |
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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 [[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. |
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 [[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. |
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Revision as of 21:50, 30 September 2022
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: where where is the angle between the direction from which the incident light is coming and the normal of the interface between the two media, hence . And are the indices of refraction of the two media at the interface and is the reflection coefficient for light incoming parallel to the normal (i.e., the value of the Fresnel term when or minimal reflection). In computer graphics, one of the interfaces is usually air, meaning that 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]
See also
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 [cs.virginia.edu/~jdl/bib/appearance/analytic%20models/schlick94b.pdf the original] (PDF) on 2020-05-10.
{{cite journal}}: Check|url=value (help) - ^ 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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