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help with Marschner hair

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Hi, am trying to make a hair shader based on the Light Scattering from Human Hair Fibers paper http://graphics.stanford.edu/papers/hair/hair-sg03final.pdf I'm stuck on what exactly i need to do in order to make a lookup table out of it and I am not sure I am on the right path. Np(p,&Phi)= &sumr A(p,h(p,r,&Phi))|2 d&Phi/dh (p,h(p,r,&Phi))|-1 According to the paper "Solving Eq:10 equation yields &gammai from which h is easily found" &Phi(p,γi) = ( (6pc)/∏ -2)&gammai - (8 pc/∏ 3)*&gamma3i + p*∏ p paths are 0 for reflecting, 1 for TT c = sin-1(1/η') So subsitituting p = 0 for Reflection yields &Phi(0,γi) = -2&gammai solving yields &gammai = 0? for TT p = 1 &Phi(1,γi) = ( (6 sin-1(1/η'))/∏ -2)&gammai - (8 sin-1(1/η')/∏ 3)*&gamma3i + 1*∏ now to get η' from appendix B of the paper which is kinda of confusing I think i need to use &Thetai η'(&Thetai) = sqrt(&eta2 - sin2(&Thetai))/cos(&Thetai) from that we can solve for &gammat &gammat = 3*c / ∏*γi - 4*c/∏3 * γ3i From there we have to find d&Phi/dh and then plug in &gammai, &gammat. So equation 3 &Phi(p,h) = 2p&gammat - 2&gammai + p∏ p=0 &Phi(0,h) =- 2&gammai //&Phir &Phi(1,h) = 2&gammat - 2&gammai + ∏ //&Phitt "We can determine the far-field intensity by tracing rays as they refract through a circle. Consider a ray incident on a unit circle at an offset -1 < h < 1 from its center h = sin &gammai angle of incidence h = η' sin &gammat angle of the refracted ray" Then use them to get the differential d&Phi/dh(p,h(p,r,&Phi)) and then I run into a brick wall here on differenting. Any help would be appreciated.

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