Timeline for Why is the approximation valid, in the formula provided by Brian Karis?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14, 2018 at 17:11 | comment | added | user8469759 | Related question, just asked, dsp.stackexchange.com/questions/47180/… | |
| Feb 7, 2018 at 15:12 | comment | added | Sebastián Mestre | But since L_i will be precomputed from an image, it would be reasonable to use all data without importance sampling | |
| Feb 7, 2018 at 15:11 | comment | added | Sebastián Mestre | Any numerical integration techniques can be applied to either. The point is that they should approximate the integral. You can even do importance sampling with different importance distributions for each integral | |
| Feb 7, 2018 at 12:13 | vote | accept | user8469759 | ||
| Feb 7, 2018 at 12:12 | comment | added | user8469759 | Hi Again, just a last question. From the examples you gave me I have the feeling we are actually trying to split the integral and approximate those using montecarlo technique. The importance sampling is applied to the brdf one, while standard montecarlo integration seems to be applied for the $L_i$ term. Is this correct? | |
| Feb 6, 2018 at 17:38 | comment | added | Sebastián Mestre | I'd go as far as to say that this formula cannot be found if not by eye or by some sort of probabilistic analysis. And i don't have a strong enough grasp on probability to produce a proper derivation. Keep in mind that it is often said by CG professionals that "if it looks right, it is right" so rigorous proofs are not always needed. That is, unless you are doing scientific research | |
| Feb 6, 2018 at 17:34 | comment | added | Sebastián Mestre | The two functions are $f_r$ and $L_i$. I say they are not correlated because the brdf shouldn't depend on the environment | |
| Feb 6, 2018 at 17:28 | comment | added | user8469759 | Also you mention "the two functions are not correlated", which functions? And why are you saying they're not correlated? | |
| Feb 6, 2018 at 17:18 | comment | added | user8469759 | I know I'm being annoying but I still have few unclear points... First $f_r$ is actually $f_r(l,v)$, the integral is computed over the hemisphere parametrized wrt $l$ (here $v$ is fixed). If $f_r(l,v)$ is low frequency (in signal processing terms) that means, I guess, that $$f_r(l,v) = \sum_{k=0}^{N-1} \alpha_k(v) \psi_k(l)$$, I'm assuming that $psi_k$ are spherical harmonics on the unit sphere. Is this interpretation correct? I know you said you don't know the derivation, but I'm trying to work out a bit of rigour for that formula. | |
| Feb 6, 2018 at 17:11 | history | answered | Sebastián Mestre | CC BY-SA 3.0 |