# Directly Sampling an Area Light

So in my path tracer I sample both some bounce ray given an importance function for the current BRDF, and if applicable (reflection is non-specular) I directly sample all light sources (for my application, I am guaranteed to have very few).

I recognize however, that directly sampling the light each time needs to be considered carefully, as we are no longer uniformly sampling our importance function. But my hope is that by doing it this way the variance of the samples can be decreased and the image can converge faster.

My understanding though is that we would need to directly calculate the radiance from the light separately which would require three things:

1. Have the light source defined in terms of luminosity (in units of $$W$$)
2. Calculate the emitted irradiance of the light by dividing the luminosity (total power output) by the surface area (in units of $$[W\cdot m^{-2}]$$)
3. Calculate the radiance incoming at that point by dividing the irradiance by the solid-angle subtended by the light source (units of $$[W\cdot sr^{-1}\cdot m^{-2}]$$

This seems like it would work fine so long as the following is true:

• The solid-angle subtended by the light is easy to calculate.

Thankfully, for my purposes, my lights are always going to be either spheres or rectangles and so calculating the solid-angle they subtend is not terribly complicated, but if some arbitrary complex geometry was used as a light, it would be far more complicated then, no?

Beside that point of mild confusion, is the rest of what I outlined sensible?