I've been slow to write the last couple of parts on my untangling series as I've been pretty busy lately. Among other things I've finally got around to submitting a couple of graphics related papers (that I actually wrote ages ago) for publication. Not sure they'll get accepted but there's no harm trying. I'll probably write blog posts about these in the near future now that I have permission from my employer to talk about them.
Note: Neither of these are anything I actually use at work. Well, I've used the adjoint one a tiny bit. The latter is in the spirit of computational geometry papers: it demonstrates an algorithm that runs (asymptotically) in the fastest possible time, but in practice you'll probably want to use an approximation that looks just as good. I was amazed I was able to find a practical application for a result that came out of toric varieties, but it's going to be tough on the reviewers as there seem to be so few people in the graphics world who know about multidimensional DSP techniques.
Two Tricks for the
Price of One: Linear Filters and their Adjoints
Fast and Exact
Convolution with Polygonal Filters
Of course, straight after submitting I noticed a bunch of pieces missing from some expressions. In places designed to help disambiguate things for the reviewers as well. Ho hum.
I also recently presented a very short presentation at the "Stupid Rat Tricks" part of the Renderman User Group: quine.sl: a self-shading shader. (For more on RSL see Wikipedia.) The source is available here. I don't think the company lawyers fully appreciated that this shader now allows their handiwork to be used like a texture map.
My presentation was completely blown away by the guy who implemented a large part of the Renderman interface completely in bourne shell. I can't think of a stupider thing than that! :-)
Back to untangling in the next post.
Update: I added a Mathematica 5 notebook illustrating the transfer functions in the polygonal filter paper.
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