Author : Paul Nettle
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are used to decrease the amount of energy shot from one patch to another. The greater the angle, the less energy is transmitted. Our hemicube gives us part of this information by only telling us (in an indirect way) how much of an angle the destination patch is relative to us. But we also need to take the shooter’s relative angle into account as well. It’s much like Lambert shading. As the surface turns away from the light, the surface receives less light. We’ve got this information (indirectly) in the hemicube frame buffer. But our light source is also an area, which means it can turn, too. So we’ll need to take its angle into consideration before we shoot any energy to anybody.
The hemicube has a wonderful mechanism for this. It’s called the "delta form factor." This is simply a table of values. It is the same resolution as the surface of the hemicube and it contains values that are used to scale the amount of energy that each hemicube pixel can transmit. The values in this table associated with the center pixels of the top face have the highest value, and the values fall off as they get near the edges of the hemicube face. The reason for this is simple. The values associated with the center of the hemicube face have the highest value since anything rendered to this area of the "screen" will be directly in front of the hemicube (i.e. the least incident angle.) The values in the table associated with the edges of the hemicube face are at a 45-degree angle, so they are considerably less than those found near the center.
There is a very specific calculation for the "delta form factor" table which can be found in most radiosity references.
To finish up our hemicube explanation, we need to pull it all together.
Rather than shooting light from the source patch to the destination patches, we do this through each pixel in the hemicube’s frame buffer (remember, we’ve stored patch IDs in there so we can reference them later, and THIS is later :-). Visiting each hemicube pixel, we simply scale the amount of the shooter’s total radiative energy by the delta form factor associated with that pixel. This means that each patch will receive a little bit of energy for each pixel it resides in, in the hemicube’s frame buffer. Each of these partial energy transmissions to an individual destination patch will all add up to the proper amount of total transmitted energy, just like magic.
How do we know that we’ve transmitted all the energy from the shooter? Well, if you add up all the delta form factors for the hemicube, you’ll find they add up to 1.0. This is a good test, by the way, to make sure your hemicube delta form factor table is correct. Remember to account for error, so the value might not equal exactly 1.0, rather something very close.
A typical hemicube resolution might be 128x128. However, you may decide to go with a higher resolution. Either way, remember this: each pixel in the hemicube’s delta form factor table contains a very small fractional value. You should consider using doubles to store these values as they can get VERY small.
To save confusion, I purposely neglected to mention a few things. Each hemicube has five sides. I only described the process for rendering the top face. The remaining half-faces also require rendering, but the process is identical to that of the top face. Don’t worry, your radiosity references will cover how to calculate the delta form factors for ALL faces of the hemicube. And don’t forget that when you run your little test that adds up all the delta form factors to a result of 1.0, you’ll need to include ALL of the delta form factors, not just those for the top face.
In closing, I should mention that there are issues with hemicubes (like aliasing artifacts under certain circumstances.) There are some solutions to these issues as well as totally different techniques. But hemicubes are a great place to start your radiosity adventures.
Recommended References
"Advanced Animation & Rendering Techniques" by Watt & Watt
"Computer Graphics Principles & Practice" by Foley, vanDam, Feiner & Hughes
"Radiosity: A Programmer's Perspective" by Ashdown
"Radiosity and Realistic Image Synthesis" by Cohen & Wallace
"Radiosity and Global Illumination" by Sillion & Puech
Personally, I originally learned the concepts & fundamentals of radiosity from "Advanced Animation & Rendering Techniques." I learned enough to get my first radiosity processor up and running. Since this book has such a wealth of other information, I highly recommend it for first-timers on the subject. From there, you can graduate to any of the other references listed. If you make it to the more advanced stuff, you’re welcome to visit my site and grab some research papers on the subject.
- Paul Nettle
- midnight@grafix3d.tzo.com
- http://www.grafix3d.tzo.com
also
- kage@terminalreality.com
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