TIL (from http://tom94.net , who is not on twitter afaik) if you interpolate camera matrices in log space, the center of rotation is preserved. this is awesome for smoothing camera paths and I cant believe I didnt do this before. may this tweet make you less dumb than me
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Replying to @mmalex
Log space interpolation isn't shortest-path, however, so it is important to understand what you give up by using exponential maps. Direct matrix interpolation always obeys shortest path, as do quaternion lerps/slerps, but exponential maps diverge.
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Replying to @cmuratori @mmalex
You can see the original diagrams I made here: https://caseymuratori.com/blog_0002 It is unfortunate that these are literally two decades old, because that means I am _way_ over the hill now :(
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Replying to @cmuratori @mmalex
But anyway, as you can see from the blue arc, expmaps are really pretty janky. Depending on what you're doing, that may not matter, but never assume it's doing the proper torque-minimal path, because it generally doesn't!
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Replying to @cmuratori
thankyou for the detailed exposition! yeah i was pointed at your (hilarious, on point) rant with charles and jonathan and it’s linked in other threads… cant believe i missed this slice of graphics history first time round!
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Replying to @mmalex
Supposedly there is another slice that I was too busy with other projects to be a part of, but, I got a bunch of emails about it. I believe some grad students later proved that exponential map also isn't constant speed. But don't quote me on that.
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Replying to @cmuratori @mmalex
If that's accurate then they are "the worst of all worlds" - non-constant speed, non-torque minimal :( If you're studying this stuff now I can try to dig up the emails for you...
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Replying to @cmuratori @mmalex
OK found it - it's actually just in the dual quaternion blending paper!pic.twitter.com/uGUaKq304Z
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Replying to @cmuratori @mmalex
It's Appendix B in this: https://www.cs.tcd.ie/publications/tech-reports/reports.06/TCD-CS-2006-46.pdf …
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Anyway, yeah. The exponential map has a lot of serious drawbacks. Buyer beware :)
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