Details on radiance caching

[tom94]

Details on radiance caching

[Tom94]

Hi Shilin,

intuitively speaking, our ultimate goal is to sample each quad of the DTree proportional to the incident "energy" that flows through it. So we want to store said "energy" within each quad. What I mean by "energy" is the integral of radiance over the quad's solid-angle footprint. This is where woPdf comes in: we estimate that integral via Monte Carlo and woPdf is the solid-angle PDF we use for importance sampling.

You raise a good point on whether the units of this integral truly are "irradiance"---this is actually a slight abuse of notation and the cosine factor is indeed missing. The integral has units of flux per projected surface area as opposed to Wikipedia's definition of irradiance as flux per _un_projected surface area. Hence the discrepancy of the cosine factor (to convert between projected and unprojected area). In the code, projected area fits better into the framework of radiance, as it makes converting back to radiance easy: assuming piecewise-constant radiance across quads allows dividing each quad's energy by the quad's solid-angle footprint to obtain the learned radiance.

Lastly: irradiance and radiance are not only related by a cosine factor. They're related by an integral and a cosine factor. If you combine your formulas, you get dE / dw_i == L_i * dot(w_i, n). Integrate on both sides to get E == int(L_i * dot(w_i, n) dw_i).
woPdf takes care of the integral and I omit the cosine factor as mentioned above, because energy per projected area is more convenient than energy per area. :)

Cheers!

[ShilinC]

Thanks for your quick response! Very nice explanation.