9 votes
Accepted

Reasons of the assumptions for the microfacet distribution function?

It's a geometric assumption like the other two. Consider a flat macrosurface. Its projected area in any direction $v$ is just $v\dot\ \hat N$ times its area (where $\hat N$ is the surface normal). In ...
Dan Hulme's user avatar
  • 6,770
8 votes
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Understanding Jump Flooding Algorithm (JFA) for Voronoi Diagrams

I think that there is a bit of confusion in terminology. My understanding is that only the initially colored points, before step 1, are called seeds. Maybe this helps clarify the algorithm as well. ...
StinkySkunk's user avatar
7 votes
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Role of PDF of Uniform Random Sampling in a path tracer

Firstly, as @trichoplax correctly pointed out, your randomPoint function calculates a point in a cube, then uses rejection sampling to return all points that are inside a unit sphere. In order to ...
RichieSams's user avatar
  • 3,732
5 votes
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2D sampling with multidimensional transformations

I'm not sure I've correctly understood the question, but here goes. You're trying to sample directions uniformly, so you've got $p(\omega)$, which is the probability of getting a particular direction....
Dan Hulme's user avatar
  • 6,770
4 votes
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Why map Hammersley 2D set's (u,v) to sphere's (θ, φ) coordinates (and not to (φ, θ) )?

You can of course, as you suggested, map (u, v) to (φ, θ). Unfortunately, it does not solve the problem for 5 points: I've changed Holger Dammertz' code a bit (switched u and v), and you see that the ...
David Kuri's user avatar
  • 2,293
3 votes
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Troubleshoot half vector sampling from a distribution (cook-torrence, trowbridge-reitz, etc)

The general idea for sampling half vector based distributions is that you generate $H$ and then compute $w_i$ by reflecting $w_o$ about $H$. This is so $H$ will be the half vector of your $w_i$ and $...
Olivier's user avatar
  • 1,585
3 votes
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Relationship between roughness and BRDF

Most normal distribution functions (NDFs) are parametrized by some variable (tipically $m$ or $\alpha$) that determines the "roughness" or "spikiness" of the NDF (this is often meant to be the rms ...
Sebastián Mestre's user avatar
3 votes
Accepted

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
2 votes

Visualize the output of a Trowbridge-Reitz Half Vector Sampling Function

So for anyone who was interested - after studying the source material by Walter, I became convinced the error had to be in the rotation of the slopes back into "normal shading space". PBRT does this ...
Steve's user avatar
  • 73
2 votes

Relationship between roughness and BRDF

for each point $p$ in theory we have a 3D function that tells us the orientation in a given direction You have missunderstood this. $D$ is a Normal Distribution Function (or short NDF), so it doesn't ...
Tare's user avatar
  • 1,541
2 votes
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What does GGX stand for?

According to E. Heitz (Sampling the GGX Distribution of Visible Normals) it stands for "ground glass unknown". I am not sure what the word unknown means though. By the way, it is equivalent ...
Aleš Koblížek's user avatar
2 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
  • 183
1 vote
Accepted

Equally distribution on triangle surfaces

Barycentric coordinates need to sum to 1.0, so pick two of them (say $u, v$) randomly from [0, 1] and then set the third as $w = 1 - u - v$. This will give you random points that are evenly ...
Nathan Reed's user avatar
1 vote

Using Monte carlo on Rayleigh scattering

For sampling a uniform volume you use the mean free path of a photon: float dt = -logf(1.0f - Xi) / uT; where: Xi is a random variable in [0, 1] uT is the ...
Kara's user avatar
  • 11
1 vote

Why map Hammersley 2D set's (u,v) to sphere's (θ, φ) coordinates (and not to (φ, θ) )?

The "Uniform Mapping" here is incorrect. It does not transform to a uniform distribution on the sphere. Very very bad me. I misread the equation AND I didn't even consult my own reference [...
MB Reynolds's user avatar

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