# 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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### 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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