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From: nujy@vax5.cit.cornell.edu
Newsgroups: comp.graphics
Subject: Re: good radiosity question
Message-ID: <1991May4.142920.4479@vax5.cit.cornell.edu>
Date: 4 May 91 14:29:20 EDT
References: <20917@ogicse.ogi.edu>
Distribution: comp
Organization: CIT, Cornell University
Lines: 52

In article <20917@ogicse.ogi.edu>,
aburke@ogicse.cse.ogi.edu (Andrew Burke) writes: 
> 
>> 	I have written a combination radiosity/raytracing rendering system
>> (whew!) and I'm somewhat confused on one point: I have a scene of 5 walls,
>> 10x10, with a light 3x3 pointing at one of the walls.  Now with 90% diffuse
>> surfaces, the relative energy out of the wall *behind* the light (i.e. light
>> left the lightsource, hit the wall in front, and was re-radiated to the back
>> wall, and re-radiated again) is about 1/1000 the energy leaving the light.
>> This seems wrong. ...
> 
> I have basically the same problem. I've read all the papers, scratched a 

I don't think this is a problem.  I don't have my radiosity stuff with me
but I think I can remember enough to go through this example.

First, lets assume that each wall is a single polygon and we find the form
factor at the center of it.  If we approximate the receiving polygon as a 
disk (of diamter 10), get the solid angle of the projected disk on a sphere
surrounding the center of the emitting polygon, and divide by 2PI, we get
a form factor of (2-sqrt(3))/2.  Multiplying this by 4/PI gives an
approximate form factor of a 10x10 polygon of:  (4 - 2*sqrt(3))/PI.  This
is about 0.17.

I'll denote the intensity of the light leaving the source as I (for a total
emitted energy of 9I = 3*3*I).

The energy falling on the receiving polygon is (I think):

   Er = Is * As * Brs

where Is is the intensity of light leaving the source, As is the area of
the source and Brs is the form factor for the source and receiver.  Plugging
in the numbers:

  Er = I * 9 * (0.17) = (1.53)I

On the next step,  Is = (1.53)I * (0.9) * (1/100) = 0.0138I.  The 0.9 is
for the reflectance of the surface, and the (1/100) for its area.

  Er = (0.0138I) * 100 * (0.17) = 0.235I.

The intensity leaving this surface is Is = (0.235I) * (0.9) * (1/100) =
0.0021.  So your problem isn't really an error, the numbers do come out
right.  In fact, if we obtain a more accurate form factor by integrating
form factors over differential areas over the entire source polygon, the
result is more like 0.00087I, even smaller than was indicated! 
-Chris

  Chris Schoeneman                  |  "I was neat, clean, shaved, and sober,
   nujy@vax5.cit.cornell.edu        |    and I didn't care who knew it."
                                    |               - Raymond Chandler