Questions tagged [integral]

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4
votes
1answer
58 views

Adding two fogs

When calculating fog along the ray we have two main part- transmittance and scattering. What happens when we have two different fogs? With different extinction and color? Both extinction and color ...
8
votes
2answers
583 views

Why random monte carlo sampling instead of uniform sampling?

Why is it that it's so common to use monte carlo randomized sample locations, instead of uniform sampling? I'm assuming that taking randomized samples gives some benefit but I don't know what they ...
10
votes
2answers
1k views

In a physically based BRDF, what vector should be used to compute the Fresnel coefficient?

The well known Schlick approximation of the Fresnel coefficient gives the equation: $F=F_0+(1 - F_0)(1 - cos(\theta))^5$ And $cos(\theta)$ is equal to the dot product of the surface normal vector ...
4
votes
1answer
93 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 ...