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funfun
02-09-2004, 05:14 PM
I am a little bit confusing about some rendering equations with integration and summation.
The symbol (a big graceful S wih a little ohm ) indicates an integral over a hemisphere of all directions.
Is that mean I have to add up all (say, radiance/irradiance) from any direction over the hemisphere.?
If this is right, why not using summation(big sigma)? could someone explain their difference?
thanks

playmesumch00ns
02-09-2004, 06:05 PM
It's basically down to the notation.

Summation implies you are adding up a group of discrete terms, whereas what you "really want to do" is to integrate your illuminance function over the sphere of all directions.

How you sample that illuminance function is up to you... but if you're thinking about only sampling light sources, then you'll just want to loop over the light sources in the scene and sum their contributions. Alternatively, you can do monte carlo integration and basically just shoot a bunch of rays off to see how bright a particular direction is then average them.

edit---you also have to divide by the surface area of the unit sphere, i.e. 4*pi

funfun
02-09-2004, 06:49 PM
**pls remove the post, the "delete now" does not work at all.

How come my post disppeared until 24 hours later!!!

funfun
02-10-2004, 10:33 AM
pls remove this post

funfun
02-10-2004, 10:35 AM
Thanks.
Is that mena, only radiosity will use integral as it needs to sample the radiance and irradance emitted from light and other surface, but other shading such as phong shading will use Summation since they only concern the lighing in the scene and no sampling needed?

one more :
http://home.netvigator.com/~gumfx/images/sum.jpg

when it needs to convert to integral? I don't quite understand "When considering the continuous hemisphere of all outgoing reflected directions..."

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