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Questions tagged [distribution]

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4
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2answers
194 views

Relationship between roughness and BRDF

In a BRDF $f_r$, assume Cook-Torrance model, we have a microfacets distribution $D$. This distribution essentially models the rougheness of the material as far as I've understood. Given a direction $v$...
9
votes
0answers
295 views

Using Monte carlo on Rayleigh scattering

Update I am editing and posting this question in a different way; this time from the point of view of Nishita paper. Sunlight gets scattered at P and attenuated before reaching Pv. Therefore ...
7
votes
1answer
133 views

2D sampling with multidimensional transformations

I'm currently learning mathemetical concepts of distribution and the way to use them in a ray tracer with the book "Physically Based Rendering". Let's start by uniformly sampling an hemisphere: As ...
4
votes
1answer
163 views

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

I am attempting to visualize the raw output from PBRT's half-vector sampling function, based on the trowbridge-reitz distribution. I'm isolating only the distribution and the associated functions ...
4
votes
1answer
126 views

Troubleshoot half vector sampling from a distribution (cook-torrence, trowbridge-reitz, etc)

I am learning ray tracing and the mathematics behind it. I have a working monte-carlo raytracer I am experimenting on. I have gotten past pure diffuse BRDFS, area lights, acceleration structures, ...
7
votes
1answer
1k views

Understanding Jump Flooding Algorithm (JFA) for Voronoi Diagrams

I'm having trouble understanding the JFA. As far as I understood the algorithm, it walks log(n) times through every pixel (no matter if it is a seed or not) and looks at that pixel's neighbors in $(x+...
5
votes
1answer
720 views

Role of PDF of Uniform Random Sampling in a path tracer

I am trying to implement my own path tracer but before arriving to the question I want to give you a short overview: In the implementation of the rendering equation I use some particular technique in ...
5
votes
1answer
91 views

Why does the integral of NDF over a solid angle equals the area where micronormals belong to that angle?

In Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, Section 2.2, Mr Eric Heitz defines the distribution of normals as: And then, he goes on with the following assertion: I ...
5
votes
2answers
551 views

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

As explained in Holger Dammetz page Hammersley Points on the Hemisphere, the 2D coordinates (u,v) are usually mapped to the spherical coordinates (θ, φ). As a result, the coordinate "uniformly ...
11
votes
1answer
142 views

Reasons of the assumptions for the microfacet distribution function?

The paper Microfacet Models for Refraction through Rough Surfaces (among others) reminds us the following assumptions about the microfacet distribution function D: Microfacet density is positive ...
8
votes
1answer
101 views

Is there an established method of approximating dust distribution on surfaces?

Intuitively, dust settles onto surfaces at a higher rate in areas where the air flow is slower. This means instead of a surface gathering an even layer of dust, there will be more in corners - corners ...