Questions tagged [distribution]
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PBRT - Transforming between Distributions (Section 2.4)
In the 4th edition of "Physically Based Rendering" here:
pbrt book 4th ed Section 2.4
in Section 2.4 "Transforming between Distributions", it is said "Suppose we are given a ...
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What does GGX stand for?
Many render engines implement the microfacet model for rendering surfaces that are rough, metallic, and/or transparent, a concept first published in "A Reflectance Model for Computer Graphics&...
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Integral over cosine weighted sphere cap/cone
I'm not sure I have the right terminology, but in rendering it can be useful to draw cosine weighted samples from a hemisphere. In this case the integral (over the weights) is Pi.
Now I don´t want to ...
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Equally distribution on triangle surfaces
I would like to implement a random placement for objects like trees stones etc. on a triangles surface.
The important part is to have an equally probability to place an object on this surface. That ...
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An equation about PDFs and differentials in the book of pbrt-v3
Why does the equation at the bottom of the following page hold?
http://www.pbr-book.org/3ed-2018/Monte_Carlo_Integration/Transforming_between_Distributions.html
$p(\theta,\phi)d\theta d\phi=p(\omega)...
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GPU Procedural placement - Creating evenly distributed sampling points
I am working on a procedural placement system on the GPU, inspired by the work done by Guerrilla Games in Horizon Zero Dawn:
https://www.guerrilla-games.com/read/gpu-based-procedural-placement-in-...
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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 $v$...
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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 ...
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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 ...
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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 ...
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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, ...
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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+...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
