Soccerman, let me try to answer your question.
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oh? so you're saying that Raytracing won't work in that way? even though it's basically the same thing? I thought that raytracing would reflect off of any surface, and therefor would illuminate surfaces that aren't lighted with direct light from a light source..
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First, raytracing is NOT the same as radiosity.
Let me try to explain how raytracing and radiosity work, so you can know the difference
between the two.
RAYTRACING
It renders perpixel. For each pixel, it fires a ray from eye (or camera) to the object.
If the point intersecting the ray on the object is reflective (i.e. mirror), it bounces this ray.
On the other hand, if point on the object is refractive (i.e. crystals or transparent objects),
it will generate refraction ray (into the object).
This is done recursively until all ray hit blank or a certain depth (reflection or refraction
depth) has been reached.
Thus the color of the pixel is calculated by the SUM of
1. reflection ray if exist
2. refraction ray if exist
3. color of objects and light intensity
RADIOSITY
It renders per polygon (or subpolygons). The scene is divided into polygons or patches.
For each polygon, it will calculate which other polygons can be seen from this polygon
(basically calculating form factor in technical term).
Once the form factor for each polygon has been calculated (this is the computation expensive,
imagine if you have 10,000 polygons in a scene, you need to calculate for each polygon,
intersections and the visibility with other polygons), then it can calculate SHOOTING and GATHERING energy.
First, it starts from light source, light source will shoot energy (SHOOTING) to all patches that it
is visible to (from the form factor).
Next, All the polygons that receive energy from light source will save some energy (GATHERING) and
shoot (SHOOTING) the remainder of the energy to other polygons that its visible to.
This is done until no more energy change in each polygon or it has reached a STABLE energy

Like
temperature in the room doesn't change after a while once you turn on the heater
(it doesn't automatically reach the stable temperature).
Then using this energy (or light intensity) for each polygon, we render the scenes.
If you want to render scenes outdoor, or scenes with lots of mirrors, or one with lots
of crystal objects, raytracing is best.
If you want to render INDOOR scene, hospital rooms, or any indoor scenes, radiosity is better
than raytracing.
One of the strength of radiosity is generating very soft shadows, if you see around you (assuming
you are indoor), you can noticed shadows everywhere, and most of them are very soft and don't
have hard edges. Raytracing can't NEVER generate this kind of shadows, all images generated
by raytracing is VERY SHARP and flashy.
Now do you see the difference ?
I know a lot of radiosity and raytracing, because I have implemented both rendering systems.
Raytracing and radiosity are called Global Illumination rendering techniques, because to render
one object, it accounts for all other objects in the scenes.