serge

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1. Hair revisited

Yes, a little mistake in my algebra. At least my heart is in the right place. As for the faster formula, I assume you are refering to the Snell's law approximation that is in the paper. Regarding the geometry you can send it to me. I'll see what I can do with it but I may need Jason's help for the conversion and he's out I think for the rest of this week. Cheers! and thanks again. Serge
2. Hair revisited

Well, let me bounce this off of you. It would seem to me that the actual ray that penetrates into the hair forms a right triangle with it's projection in the normal plane and the wall of the hair. The relationship between the radius and the length of the penetrating ray is 1 / cos(theta_t). So your corrected ray path length would go from 2*cos(gamma_t) to 2*cos(gamma_t)/cos(theta_t). And since theta_t=arcsin(eta)*theta_i the whole path length in terms of gamma_t and theta_i would be: 2*cos(gamma_t) / cos(arcsin(eta) * theta_i) What do u think? Serge
3. Hair revisited

Quite right. I'm just using the plain old external theta there too. I guess now would be time to take another look at the absorbtion formula given this and your other correction to it. Cheers! Serge
4. Hair revisited

Arno, Never saw the Schlick approximation before but I just got ahold of his paper from 1994 and intend to read it at some point. Looks like the approximation formula is in there and I can make an implementation from that. As for theta there looks to be one set of them in my calculations, all based on the exterior incident angles between the hair and the eye and the hair and the light. I don't have a seperate set for the interior of the hair. It was my impression that the exterior theta determines the effective index of refraction that is used to make the subsequent calculations possible in the normal plane of the hair. And that whatever calculations need to be made, including the fresnel calculations, could be done using this effective index of refraction. Why do you ask, have you found a need for the internal incidence angle? As for pictures, it would probably be best to get your hair sample (along with the lighting you used). Currently all of the tests that are being run are using models specific to the film project we are working on and I am not at liberty to post them (as much as I'd like to). Cheers! Serge
5. Hair revisited

Arno, Thanks for the resoponce. The absorbtion length error seems like something that would not have too bad of an effect on the operation of the model, though it certainly may throw off the relationship between the R, TT and TRT components As for the fresnel I didn't look that closely at his formula but understood the gist of the argument to be that at each reflection/refraction interface the light energy is partitioned between the relflection and refraction. And, in the course of making those calculations you have to use the effective index of refraction. Also, for each such interface you have to make sure at the next interface you include the properly diminished amount of light given the previous reflections and refractions. On a side note, I looked into the commonly published fresnel equations for the partitioning of energy between reflections and refractions and immediately ran into a physics issue I wasn't sure how to translate into the calculations commonly done in computer graphics. Specifically, the fresnel equations actually give seperate caluclations for the E and B (electric and magnetic) components of the light wave. I ultimately took the easy way out and simply used the fresnel calculation available in RSL and found the reflection coefficient and used one minus that as the refraction coefficient. Not entirely satisfying from a physical standpoint but it seemed an adequate approximation. I was wondering if you had any comment on how to properly apply the fresnel equation from physics into the realm of computer graphics, Cheers! Serge
6. Hair revisited

Hello Arno, Serge here. Just went through the joy of implementing the Marschener hair model as Jason has mentioned. I was curious what the nature of the mistakes were that you found. While I can't say I found anything in the paper the jumps out at me as a flaw I found I had to do a great deal of work to reconstruct the model from what was published. I was also wondering what you might have that is publically available from your VMV2004 presentation. While our first use of this shading model is basically for a dark haired actor being viewed and lit at a distance , I have no doubt that we will soon find the need for closeups. Cheers! Serge
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