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10 votes
Accepted

In a physically based BRDF, what vector should be used to compute the Fresnel coefficient?

In Schlick's 1994 paper, "An Inexpensive Model for Physically-Based Rendering", where they derive the approximation, the formula is: $$F_{\lambda}(u) = f_{\lambda} + (1 - f_{\lambda})(1 - u)^...
RichieSams's user avatar
  • 3,782
8 votes

In a physically based BRDF, what vector should be used to compute the Fresnel coefficient?

The Fresnel coefficient should be evaluated using $H$, not $N$. You wrote, I have trouble seeing why we can still use that formula in a BRDF, which is supposed to approximate the integral over all ...
Nathan Reed's user avatar
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7 votes
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Why random monte carlo sampling instead of uniform sampling?

Sample locations with a uniform pattern will create aliasing in the output, whenever there are geometric features of size comparable to or smaller than the sampling grid. That's the reason why "...
Nathan Reed's user avatar
  • 25.1k
6 votes

Why random monte carlo sampling instead of uniform sampling?

Monte Carlo methods rely on the law of large numbers, which states that the average of a random event repeated a large number of times converges toward the expected value (if you flip a coin a ...
Julien Guertault's user avatar
5 votes
Accepted

How to compute the following integral over a polygon?

Triangulate the Voronoi cell then write the integral as a sum over the triangles: $$\int_{\Omega}\|P - Pi\|\,dP = \sum_{k=1}^{N}\int_{\Delta_k}\|P-P_i\|\,dP.$$ Write the integration over the ...
lightxbulb's user avatar
  • 2,226
3 votes
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Why does the integral of NDF over a solid angle equals the area where micronormals belong to that angle?

$D(\omega)$ is defined as the area ($m^2$ unit in the numerator) of the microsurface with normals pointing in the direction $\omega$. $\mathcal{M}'$ is defined as the portion of the microsurface with ...
John Calsbeek's user avatar
3 votes
Accepted

PBR : Understanding the right part of Split sum integration of specular IBL

1)What is the V vector? How did they compute that It's the vector toward the camera (view vector), i.e. direction of the reflected ray. The lookup table they're building is parameterized in terms of ...
Nathan Reed's user avatar
  • 25.1k
3 votes

Integral over cosine weighted sphere cap/cone

As I was referencing PBRT, here are the functions I ended up with: ...
B_old's user avatar
  • 203
2 votes
Accepted

Integrating BRDF using Importance Sampling

Think of this way: when integrating uniformly over the hemisphere, it's like you are importance-sampling with a constant pdf of $1/2\pi$. The multiplication by $2\pi$ at the end, then, can be seen as ...
Nathan Reed's user avatar
  • 25.1k
1 vote
Accepted

Where does sin(theta) go in estimators of The Rendering Equation?

Assume you want to estimate the following integral: $$I = \int_{\Omega} f d\mu$$ over the set $\Omega\subseteq \mathbb{R}^n$. Suppose you are given a bijective and continuously differentiable ...
lightxbulb's user avatar
  • 2,226
1 vote

Where does sin(theta) go in estimators of The Rendering Equation?

Your second equation is estimated with respect to solid angle $\Omega$, and the Jacobian of the transformation from spherical coordinates to solid angles is equal to $\sin\theta$. Since $\mathrm{d}\...
Hubble's user avatar
  • 344
1 vote

PBR : Understanding the right part of Split sum integration of specular IBL

I recommend to ignore my post (however I consider papers that I've sent valueable) and read post of Nathan Reed, which is much better in explaining this problem! I'm still a junior when it comes to ...
DirectX_Programmer's user avatar
1 vote
Accepted

Adding two fogs

After some research i think i have final answer. General fog equation looks something like this: $$ L(t)=L_p\color{red}{T(t)} + \int_0^t\color{blue}{T(x)}\color{green}{\sigma(x)L(x)}dx $$ ...
Derag's user avatar
  • 596

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