Raytracing: Distributed Lighting Approximation?

if you're talking about area lights, it's really not possible to reduce it to a point light to close approximation, this is evident by the fact that a diffuse area light doestn' even shoot energy in all directions equally. there are analitical formulas for the lighting of an area light A and a differential surface element dA. I could derive a few if you want, but they do not take into account occulsion. area lights can be approximated by a bunch of point lights distributed about the area, but this is still an approximation. I can't see how a area light can be approximated with just one point light... the only techniques I know of to simulate area lights without distributed sampling is

1) use a bunch of point lights distributed about the area
pros) cheap, only need to send n shadow rays for n point lights
cons) noticebale banding in shadows if too few points are used
doesn't accuratly represent diffuse illuminating surfaces.


2) use analitical formulations
pros) very cheap, just a formula you plug the angle, distance b/w light and
point to shade in.
cons) need to add distrubuted features to or some how fake shadows, as this
doesnt take it into account, it assumes unocculed sufraces.

come to think of it you could probably approximate a diffuse area surface with a point light with a certian power, but you'd still have to fake area lighting, if you have a complex light where radiance vaires widley with angle, a point light would be unacceptible, a point light has constant radiant intensity for every direction, if your light doesnt' have this property, how could you approximate it? I guess you could use say spherical hoarmonics to build a function of out going direction and make the light a point use the harmonic to scale the outgoing light in that direction.
Tim

Well, the point light doesn't have to be at the same position every time it is sampled.

that's true, but if your sampling jittered points, what is the difference between this and distributed tracing? I mean from a visibility standpoint, it is, after all what make area lighting expensive, that is the visibiliity determination.