Questions tagged [distribution]
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17 questions
1 vote
1 answer
150 views
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 ...
- 213
2 votes
1 answer
201 views
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 ...
- 203
0 votes
0 answers
94 views
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)...
- 591
2 votes
2 answers
2k 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 $v$...
- 596
7 votes
1 answer
273 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 ...
- 73
2 votes
1 answer
318 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, ...
- 73
8 votes
1 answer
2k 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 ...
- 355
4 votes
2 answers
1k 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 ...
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