本文详细介绍了SpecularTransmission的双向传输函数（BTDF）的推导过程，通过Fresnel方程和Snell定律解释了透射率与入射角的关系。此外，还讨论了SpecularTransmission类的实现，包括构造函数、f函数和Sample_f函数的工作原理，特别强调了在不同入射角度下透射效果的变化。
推导 specular transmission 的 BTDF
：
We will now derive the BTDF for specular transmission
Figure 8.8: The amount of transmitted radiance at the boundary between media with different
indices of refraction is scaled by the squared ratio of the two indices of refraction. Intuitively, this can
be understood as the result of the radiance’s differential solid angle being compressed or expanded
as a result of transmission.
a.
Consider incident radiance arriving at the boundary between two media, with indices of
refraction ηi and ηo for the incoming and outgoing media, respectively (Figure 8.8). We
use τ to denote the fraction of incident energy that is transmitted to the outgoing direction,
as given by the Fresnel equations, so τ = 1− Fr(ωi). The amount of transmitted
differential flux, then, is
If we use the definition of radiance, Equation (5.2), we have
Expanding the solid angles to spherical angles, we have
We can now differentiate Snell’s law with respect to θ, which gives the relation
（上面的这里其实就是对 Snell's law 进行微分
最低0.47元/天 解锁文章
扫一扫
1070
被折叠的 条评论
为什么被折叠?
到【灌水乐园】发言
