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Sampling Area Lights

2022-07-01 02:31:00 【Crazy rotten ball】

Overview

This is just an introduction AreaLight Sampling of , The following default Light All are Area Light,Delta Light Not within the scope of this article .

Purpose ： stay path tracing in ,Sampling Lights Is not intended to obtain a certain direction of a certain light source radiance, But to It is estimated that At present path The intersection of is generated by all light sources of the whole scene irradiance.

sample ： Any estimation is made through a sample , So in Sampling Lights Sample in , Is the current path From the intersection of One way .

Integrals over Area

Due to the calculation of the area of the light source irradiance It's a lot easier than calculating the integral in the hemispherical direction of a point , therefore irradiance The area of the light source can be used as the integral for the calculation of .

Relation between area and solid angle ：

As can be seen from the above figure dA and dω The relationship between ：

$\rm d\omega = \frac{\rm dA \cos \theta}{r ^2}$

Sampling Light Source

As mentioned earlier , After sampling to a light source , We need to estimate the total of this light source irradiance,irradiance Is obtained by integrating the solid angles in the hemisphere . According to Monte Carlo method , We need to know the direction from this light source to a point pdf, Finally participate in bsdf Calculation of .

Here are the specific steps for sampling light sources .

1） Because the scene may have too many lights , According to the light source distribution （ Or you can use uniform sampling ） sampling , It is necessary to calculate the pmf.

2） Sample a specific face of the light source , Calculate the position of the face in the light source pmf.

3） Randomly sample a point on the face , And generate rays with the illumination points for visibility detection first .

4） If this direction is visible , Calculate the direction pdf.

In the direction of light pdf The following is derived ：

Sampled by AreaLight The area of the face of is A, The direction is ω, because pdf(ω) The integral of is 1, We have ：

$\int pdf(\omega)\rm d\omega = 1$

according to dω and dA The relationship between , The above integral can be converted from direction to point integral ：

$\int _A pdf(\omega) \frac{\cos \theta}{r ^2}\rm dA=1$

So we can get ：

$pdf(\omega) \frac{\cos \theta}{r ^2} = \frac{1}{A}$

$pdf(\omega) = \frac{r^2}{\cos \theta A}$

Put the last one pdf do irradiance Estimation .

One principle must be understood ： What is the sample , It is necessary to calculate the pdf, For example, if the sample is a dot , that pdf That's the point pdf, The sample is the direction , So that's the direction pdf.