Practical Analysis of Optimized Ray-Triangle Intersection
Tomas Möller
Department of Computer Engineering, Chalmers University of Technology, Sweden.

Being a sucker for fast intersection tests, I just had to try to optimize Trumbore's and my ray-triangle intersector presented in journal of graphics tools (JGT) in 1997. Eric Haines and I turned this (and some other optimizations for the 2D case) into a little article for Dr. Dobb's Journal. However, there was not space enough to discuss all details, therefore this page exists.
First of all, I thought that it would be interesting to see what happens with the intersection time as the number of hits increases from 0% to 100%. Second, as we said in our JGT article, the division (after all, the division is pretty expensive, which is why we care about it) might be pushed away later in the code, by doing different tests depending on the sign of the determinant. So, I implemented this, and I believe that the code is even cleaner now (for example, just take away the "else if" and you have a test for backface culling) Third, I tried alot of different ways to order the computations in the code, and finally settled on three different versions:
1) Having the divide at the end.
2) Having the divide early in the code.
3) Having the divide early in the code plus move a cross product out from the "if-else if"-case.
(Version number 0 is simply the original JGT code).
The code for these four versions is available below. I run my test program (compiled with "gcc -O2") on three different computers: an SGI Octane with an R10K 175 MHz, a Sun UltraSPARC-IIi 333 MHz, and on a Linux PC with a Pentium III 700 MHz. To make the test and the timings reasonable (at least in some ways), I first randomized 1000 different ray-triangle pairs and put these in a list. Then I started the clock for the first optimization, and run through the list 10,000 times, and then stopped the clock. Doing it this way, I think I avoid branch prediction performance hits, which I may get if I repeat the same test for one ray-triangle pair 10,000 times in a row (and then the next pair, and so on). All this was done for all four versions of the code.

raytri.c: the code for all four different version of the ray-triangle intersection routine.

Diagrams and discussion:

For this particular UltraSPARC (from Sun), it is obvious that the divide instruction should be placed early in the code, and that thus, Sun are pretty good at issuing instructions in parallel, i.e., starting the divide instruction and then issuing other instructions in parallel while the division is being computed. Then, when the result from the division is needed, the result may already be computed (or at least close to being computed). For this CPU, I'd probably choose optimization 2, but optimization 3 has similar performance. Optimization 2 is about 12-23% faster for this test (and it's faster the fewer intersections as one can expect) than the original jgt code. Also, note that optimization 1 is almost always the slowest (and not the original JGT code).

This was the slowest CPU I tried it on, and if I were to choose one routine for this CPU, I would go with number 1 (which was slowest on the UltraSPARC). It's interesting to see that there really isn't that much of a difference between having the division early (optimization 2,3) or late (optimization 1). Optimization 1 was about 7-20% faster than the original jgt code.

For the Pentium III, optimization 1 is the way to go. This was not, however, what I expected. I thought that the Pentium III would issue the division in parallel, but it looks like it does not (at least not very well). Optimization 1 is 10-33% faster than the original jgt code.
Last update by Tomas Möller on June 15, 2000