Cutting Up Curved Things
campedersen.com
campedersen.com
Now of course triangles are usually the most practical way to render objects but it just bugs me when someone says something like “Every smooth surface you've ever seen on a screen was actually tiny flat triangles” when it’s patently false, ray tracing a sphere is pretty much the Hello World of computer graphics and no triangles are involved.
Edit: for CADs, direct ray tracing of NURBS surfaces on the GPU exists and lets you render smooth objects with no triangles involved whatsoever, although I’m not sure if any mainstream software uses that method.
Algorithms that can solve these triangulations with no additional resource usage are widespread nowadays, but they were a tough problem in the 70s and 80s.
The trick is to maximise the minimum angle inside all triangles, so that no triangle has a very small angle, in combination with carefully choosing the starting points for the triangulation.
We had no AI policy at the time so I had to read up on CDL and implement it by hand. The concept is straight-forward and I also targeted regularity as acceptance criteria for the mesher, but making it optimal was hard.
I ended up having to park it after the ticket ran out of time, but now we have an AI policy this was the first problem I gave it. What it put out was similar but better structured and more informed.
I worry a little that AI will stunt our problem-solving in 20-30 years, we still need new algorithms, even when ML is capable of producing a model that can do the same thing. But right now it's much better at the things we've already done than we are.
Instead of going meta about their strategies for identifying their tasks and reasoning about them, they currently stick to one conception of the task and try different tactics for implementing different strategies for solving it within that conceptual frame.
Furthermore, they don't seem to have a reliable way to ask themselves if they're taking too long to do something that should be easy yet. Maybe one in fifty times the latest agents will say "This is taking too long, let's step back and look up how other people do it," but humans do that for most human tasks.
I don't think appropriate use of some, but not too much, meta-reasoning and meta-meta-reasoning on the fly will be easily solved without some kind of mental parallelization advance, which might come tomorrow but might not come for two or more years.
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As for society, we need an AI takeover for the simple reason that we're facing real bad shortages of diesel fuel and days of agriculture-suitable weather in the next decade, which makes the former the less bad outcome. Given that AI will outcompete humans for all economic roles in such a scenario the only way it can happen humanely is human preservation through uploading or as pets.
Literally every other option is on a spectrum of negative outcomes from extinction to Greer's 2013 essay on the ten-billion year future.
Well done!!
<3