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Questions tagged [integral]

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13 votes
2 answers
3k 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 ...
Julien Guertault's user avatar
8 votes
2 answers
1k 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 ...
Alan Wolfe's user avatar
  • 7,801
5 votes
1 answer
190 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 ...
wip's user avatar
  • 1,861
3 votes
1 answer
138 views

How to compute the following integral over a polygon?

I am implementing an algorithm which requires me to compute the following integral, $$\int_{Poly(P_i)}||P-P_i||^2 dP$$ where $P_i=(X_i, Y_i)$ is a point in 2D and $Poly(P_i)$ is a polygon containing $...
Student's user avatar
  • 133
3 votes
1 answer
87 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 ...
Derag's user avatar
  • 596
2 votes
3 answers
1k views

PBR : Understanding the right part of Split sum integration of specular IBL

This is the website I am learning from. In the specular part of IBL this is the split sum approximation Now the left part of the equation I have asked in This post and I have understood everything ...
Sync it's user avatar
  • 179
2 votes
1 answer
126 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 ...
B_old's user avatar
  • 203
1 vote
1 answer
516 views

Integrating BRDF using Importance Sampling

I read some articles about BRDF integration with and without importance sampling and I don't understand one thing in equations. If we integrate a BRDF over hemisphere with uniform sample direction ...
Emil Kabirov's user avatar
1 vote
0 answers
52 views

Measure for volumetric rendering equation

Recently I've been digging deeper into the volumetric rendering (volumetric path tracing, to be specific). I already know that for surface rendering, there are two commonly used measures (reference ...
Enigmatisms's user avatar
1 vote
0 answers
54 views

The ploygon width parallel to the x axis as a function of the y ordonate?

Considering a polygon with n vertices as input. I need to calculate the integral of the form \[\int_A p(y) dA \] where $p(y)$ is a piecewise polynomial function of $y$. May be if I could find the ...
Hafid Boukhoulda's user avatar
0 votes
2 answers
139 views

Where does sin(theta) go in estimators of The Rendering Equation?

Consider this equation, where we have a surface integral over hemisphere with Lambertian BRDF and cos(theta) from The Rendering Equation: $$ \int_{0}^{2\pi}\int_{0}^{\frac{\pi}{2}}\frac{albedo}{\pi}...
Ocelot's user avatar
  • 125