Is this necessarily better than the previous method if we have tons of light sources? It may be more complex to account for a lot of sources than just trying to sample the amount of light coming in at points on the hemisphere.
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This is just a change of the variable to integrate on in the integral, and integrate only from the area over the light source instead of the entire hemisphere, because solid angles outside the light source area contributes an irradiance of 0.In sampling in Monte Carlo integration, however, this greatly reduces the variance of the samples.
Is this necessarily better than the previous method if we have tons of light sources? It may be more complex to account for a lot of sources than just trying to sample the amount of light coming in at points on the hemisphere.
This is just a change of the variable to integrate on in the integral, and integrate only from the area over the light source instead of the entire hemisphere, because solid angles outside the light source area contributes an irradiance of 0.In sampling in Monte Carlo integration, however, this greatly reduces the variance of the samples.