uutee
08-22-2003, 03:20 PM
Hi,
Recently I've studied low-discrepancy point sets for quasi-Monte Carlo integration.
The Halton-Hammersley sequence was trivial to implement. I have one side question about it, though: in computer graphics (solving rendering equation) we do integration for each pixel in the image. If the first dimension of the quasi-random vector is always evenly distributed (as it is in Hammersley set), won't this cause aliasing? I thought jittering the first dimension could solve this problem, but I don't know if pure Halton sampling is better in that case... what do you people think?
And the second question is about Halton-Hammersley-Wozniakowski algorithm. I've heard Mathematica uses it, but I've never seen a description of the algorithm. Does anyone happen to know it?
- Mikko Kauppila
Recently I've studied low-discrepancy point sets for quasi-Monte Carlo integration.
The Halton-Hammersley sequence was trivial to implement. I have one side question about it, though: in computer graphics (solving rendering equation) we do integration for each pixel in the image. If the first dimension of the quasi-random vector is always evenly distributed (as it is in Hammersley set), won't this cause aliasing? I thought jittering the first dimension could solve this problem, but I don't know if pure Halton sampling is better in that case... what do you people think?
And the second question is about Halton-Hammersley-Wozniakowski algorithm. I've heard Mathematica uses it, but I've never seen a description of the algorithm. Does anyone happen to know it?
- Mikko Kauppila