The way I see it, the derivation in the link is a special case for a small circular area light. Small means small enough (as seen from the surface) that you can assume the fr*cos term is constant over the projected area and take it out of the integral. For this case it's correct, but I'm pretty sure you cannot generalize this to arbitrary lights.

But, as Bacterius said, for _direct_ illumination from delta lights, you can always pull the pi into the light's intensity. Example:

Consider a point light 1 unit above a surface normal to the light. Let's say the light causes an irradiance of E=1 at the surface point closest to the light. For a diffuse BRDF we get for every direction

L_o(wo) = fr*E.

Case 1: With fr = 1 we get L_o = 1 for every direction. The radiant exitance (Lo*cos integrated over hemisphere) is M = pi. So we have M>E which means we reflect more than came in.

Case 2: With fr = 1/pi we get exactly M=E, which is correct.

Of course, in case 1 you can always say "My light source was really causing E=1*pi and my BRDF was really 1/pi". You'll get the exact same image (if only direct illumination from this point light is considered), but you safe a division by pi.

Bottom line:

In my opinion, the pi should always be there. But if you're only doing direct illumination from delta lights and every multiplication counts, you can pull the pi into the light sources. But that's only my personal opinion, so you should take it with a pinch of salt.

EDIT: Of course, if you decide to "pull pi into the light source", you have to multiply _every_ BRDF by pi. (And every BRDF component, e.g. if you only remove pi in the diffuse term, you'll obviously shift the balance between diffuse and glossy.)

**Edited by macnihilist, 12 January 2013 - 04:20 AM.**