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<CENTER><B>3D</B></CENTER>
Creating a cutting-edge engine<BR>
<A HREF="Engine01.shtml">01 - Design document</A><BR>
<A HREF="Engine02.shtml">02 - Overall structure</A><BR>
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<A HREF="Engine03.shtml">03 - Binary Space Partitioning</A><BR>
<A HREF="Engine04.shtml">04 - Constrctive Solid Geometry</A><BR>
<A HREF="Engine05.shtml">05 - Portals</A><BR>
<A HREF="Engine06.shtml">06 - Possible Visible Set</A><BR>
<A HREF="Engine07.shtml">07 - Radiosity lighting</A><BR>
<!--A HREF="Engine08.shtml"-->08 - Mirrors</A><BR>
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<!--A HREF="Dictionary.shtml"-->Dictionary of 3D terms</A><BR>
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<!--A HREF="GeneticAlgorithm.shtml"-->A Genetic Algorithm</A><BR>
<A HREF="Line01.shtml">Line drawing</a><BR>
<!--A HREF="Line02.shtml"-->Line clipping</a><BR>
<!--A HREF="Line03.shtml"-->Line antialiasing</a><BR>
<!--A HREF="Line04.shtml"-->Line thickening</a><BR>
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<font face="arial"><b>07 - Radiosity lighting</b></font>
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Radiosity lighting is one of those things that makes everybody sit up and say "oh, my." With a good
level designer and a good texture artist radiosity can really look cool. Even if you're doing it all
by yourself and you have no artistic talent at all, radiosity can still make any level look better.
Radiosity is to 3D what mayonnaise is to a smoked turkey and roast beef sandwich with lettuce...and
tomato...excuse me, I'll be right back.<br>
<br>
Moo can cobe a fimple *gulp* You can code a simple radiosity calculator in a very short period of time.
The only drawback is that the complexity of your calculator is inversely proportional to the speed at
which it runs. I think that's one of Murphy's laws. The first step to setting up a radiosity
calculator is to have an engine that can render light maps. "Ah, but if you don't have light maps, how
can you tell if it's rendering them?" Use a hex editor and make some really simple grey scale light maps
by hand to test. There is one major decision to make at this point and it is: how detailed will your
light maps be? Quake had a maximum resolution of (I think) 32x32 which worked great until you had sharp
contrasts on a big wall, it looked like a set of 'z's running down the wall. You can opt for larger
light maps or (if you're feeling up to it) you can make different sized light maps for different polygons.
Who knows, two or three different sizes might actually save you some memory.<br>
<br>
<center><img src="0706.jpg" width="428" height="128" border="0" alt="texturemaps and lightmaps"></center>
<br>
Once you've got light maps working you've got a foundation to test on, so you can start writing the
calculator. I'm going to break each of the major concepts into separate groups, take your time to eat
a sandwich or something between them 'cause it's heavy stuff.<br>
<br>
<hr>
<b>The Radiosity Equation</b><br>
<br>
The concept of radiosity is pretty easy. The reason more people haven't implemented it is because almost
know one who understands it wants to talk about it, probably because they've all got high pay, high stress
jobs that keep them far too busy. Sounds to me like someone's bought their silence, probably some of
those same guys who claim the whole Roswell thing was to keep Stalin scared the US had UFOs technology.
Oh yeah, it's all so clear to me now...<br>
<br>
...My point being that once you get past all the integrals and the differential areas and a whole bunch of
other fancy lingo it breaks down to this: For every point on every surface everywhere in the world find
the total amount of light incident at that point. By incident I mean find all the light that is
<i>absorbed</i>, <i>reflected</i> or <i>emitted</i> at that point.<br>
<br>
Think about that for a minute: if you're going to find every point on every surface blah blah blah, how
big are your points? I mean if they're infinitely small points then it would take forever to solve the
equation. Uh oh. The solution is to break each surface into finite, bite size pieces called
<i>patches</i> and average the light incident in each patch. Once all the calculations are done the the
patches can be converted back to light maps and voila!<br>
<br>
Before I show you how to figure out how much light travels from patch i to patch j there's one more very
important point to touch on. As I said, radiosity works by finding the amount of light incident at
every point everywhere in the world <b>BUT</b> it is supposed to find these values <i>simultaneously</i>.
Stay calm, it's not as bad as you might think. When radiosity calculations were first invented there was
a brute force solution - given that you had n patches you could build an n<sup>2</sup> matrix and (slowly)
solve it until your first row or column had the light values at every point. In today's world of highly
complex geometries and the ever greater push to wow people with high polygon counts, a matrix just isn't a
practical solution.<br>
<br>
Thus <i>Progressive Refinement</i> came to be. The idea works like this: Find the patch giving off the
most light and send it's light to all the other patches. Repeat until the brightest patch is giving off
less than some really small value. This means we have to keep track of both the radiosity (light incident)
and the delta radiosity (amount of light being reflected) of each patch.<br>
<br>
But is there anything else we need to keep track of? Take a look at the wall for a second. What is it
you're seeing? The light hitting the wall or the light being reflected? If you said reflected, give
yourself a back on the back. Careful, you don't break the arm! If we denote a patch n's radiosity as
<b>B<sub>n</sub></b> then our equation so far is<br>
<br>
<center><img src="0701.jpg" width="125" height="100" border="0" alt="Beginnings of the radiosity eqn'"></center>
<br>
Where Pj is the amount of reflected light, some value in the range (0...1). No sweat, right? Well, this
equation would only work if every patch was exactly the same size, shape and distance apart. First of all,
we can (for the most part) ignore a difference in shape but size is crucial. If you shine a light the size
of a pin near a wall you'd see almost no change on the wall. However the opposite is also true, if you held
a pin sized dot near a well lit wall, you'd see the dot very clearly. If we denote the area of a patch n as
<b>A<sub>n</sub></b> then we've now got<br>
<br>
<center><img src="0702.jpg" width="225" height="100" border="0" alt="Radiosity eqn' continued..."></center>
<br>
Much better, but it still needs work. What we're missing is the <i>Form Factor</i>, the most powerful part of
the process. If we weren't using patches, the form factor equation would look like this:<br>
<br>
<center><img src="0703.jpg" width="375" height="110" border="0" alt="Form factor eqn'"></center>
<br>
Yikes! Thankfully we're using patches so we can take out all the integrals and simplify to<br>
<br>
<center><img src="0704.jpg" width="275" height="75" border="0" alt="Simpler form factor eqn'"></center>
<br>
Where
<ul>
<li><b>cos( theta i ) * cos( theta j )</b> is the angle between the normals of the planes of each patch. This
will make sure that a patch in front of a light source gets more light than one that's way off to a side. It
will also make sure that a patch that faces directly into the light will get more light than a patch that's
turned away.
<li><b>pi * r<sup>2</sup></b> accounts for the distance between the two patches. The further away, the dimmer
the light.
<li><b>H( i, j )</b> is the visibility between patches i and j. If there is no line of sight between i and j then
H( i, j ) would be 0. If there was full visibility between the two then H( i, j ) would be 1. Naturally, H( i, j )
can be some fraction in the range [0...1] if the line of sight is partially occluded (blocked)
<li><b>dAj</b> is the area of patch j.
</ul>
So our final patch to patch radiosity equation is<br>
<br>
<center><img src="0705.jpg" width="260" height="100" border="0" alt="Radiosity eqn' continued..."></center>
<br>
I know that seems weird multiply by dAj in the form factor and then dividing by dAj back in the main part of the
radiosity equation but that's the way it goes. Personally, I'd just simplify and remove both references. Note that
no one I spoke to would give me a straight, concise answer on what dAj was supposed to be in the form factor so it
could be that I've totally screwed this up but if that were true my code wouldn't be working, would it? (:<br>
</font>
<pre>
<font color="green">/* Pseudocode for a simple radiosity calculator loop.
* I highly reccomend using doubles everywhere, you
* will need the extra precision.
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