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Listing 60.1 isn’t very long or complex, but it’s somewhat more complicated than it could be because it’s structured to allow visual display of the ongoing compilation process. That’s because Listing 60.1 is actually just a part of a BSP compiler for Win32 that visually depicts the progressive subdivision of space as the BSP tree is built. (Note that Listing 60.1 might not compile as printed; I may have missed copying some global variables that it uses.) The complete code is too large to print here in its entirety, but it’s on the CD-ROM in file DDJBSP.ZIP.

### Optimizing the BSP Tree

In the previous chapter, I promised that I’d discuss how to go about deciding which wall to use as the splitter at each node in constructing a BSP tree. That turns out to be a far more difficult problem than one might think, but we can’t ignore it, because the choice of splitter can make a huge difference.

Consider, for example, a BSP in which the line or plane of the splitter at the root node splits every single other surface in the world, doubling the total number of surfaces to be dealt with. Contrast that with a BSP built from the same surface set in which the initial splitter doesn’t split anything. Both trees provide a valid ordering, but one tree is much larger than the other, with twice as many polygons after the selection of just one node. Apply the same difference again to each node, and the relative difference in size (and, correspondingly, in traversal and rendering time) soon balloons astronomically. So we need to do something to optimize the BSP tree—but what? Before we can try to answer that, we need to know exactly what we’d like to optimize.

There are several possible optimization objectives in BSP compilation. We might choose to balance the tree as evenly as possible, thereby reducing the average depth to which the tree must be traversed. Alternatively, we might try to approximately balance the area or volume on either side of each splitter. That way we don’t end up with huge chunks of space in some tree branches and tiny slivers in others, and the overall processing time will be more consistent. Or, we might choose to select planes aligned with the major axes, because such planes can help speed up our BSP traversal.

The BSP metric that seems most useful to me, however, is the number of polygons that are split into two polygons in the course of building a BSP tree. Fewer splits is better; the tree is smaller with fewer polygons, and drawing will go faster with fewer polygons to draw, due to per-polygon overhead. There’s a problem with the fewest-splits metric, though: There’s no sure way to achieve it.

The obvious approach to minimizing polygon splits would be to try all possible trees to find the best one. Unfortunately, the order of that particular problem is N!, as I found to my dismay when I implemented brute-force optimization in the first version of my BSP compiler. Take a moment to calculate the number of operations for the 20-polygon set I originally tried brute-force optimization on. I’ll give you a hint: There are 19 digits in 20!, and if each operation takes only one microsecond, that’s over 70,000 years (or, if you prefer, over 500,000 dog years). Now consider that a single game level might have 5,000 to 10,000 polygons; there aren’t anywhere near enough dog years in the lifetime of the universe to handle that. We’re going to have to give up on optimal compilation and come up with a decent heuristic approach, no matter what optimization objective we select.

In Listing 60.1, I’ve applied the popular heuristic of choosing as the splitter at each node the surface that splits the fewest of the other surfaces that are being considered for that node. In other words, I choose the wall that splits the fewest of the walls in the subspace it’s subdividing.

### BSP Optimization: an Undiscovered Country

Although BSP trees have been around for at least 15 years now, they’re still only partially understood and are a ripe area for applied research and general ingenuity. You might want to try your hand at inventing new BSP optimization approaches; it’s an interesting problem, and you might strike paydirt. There are many things that BSP trees can’t do well, because it takes so long to build them—but what they do, they do exceedingly well, so a better compilation approach that allowed BSP trees to be used for more purposes would be valuable, indeed.

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Graphics Programming Black Book © 2001 Michael Abrash