Hi there,
I’m looking for practical applications of exterior calculus.
I’m interested in applications not too far from graphics development.
Regards
For Discrete exterior calculus there are plenty. This is actually why I’ve been learning GA! I skim these great papers using DEC and then put it on the “Read after you’ve learned DEC” pile. GA seems like a better system, although I’m starting to see it as just different and not better.
Most papers by these two are really great, and use Exterior Calculus extensively.
https://www.cs.cmu.edu/~kmcrane/
https://page.math.tu-berlin.de/~chern/projects/
Also from this group
http://www.geometry.caltech.edu/pubs.html
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How about geometric calculus (GC)? Do you consider it a better system?
(I’m new in GC. I recently heard of a saying that GC is a rewriting of tensor/Ricci calculus.)
Just different. The way “duality” and “metric” are handled is quite different in perspective and possibly in theory. I am not a mathematician and still learning this stuff. I’ll need to actually solve some non-trivial problems with them to form an opinion.
Initially k-forms and the musical isomorphisms seemed to me to be unnecessary, since they aren’t needed in GC. Now I kind of like them because they seem to make duality and measurement much more explicit. You are measuring one thing against another when you apply a k-form. The measurement function is dependent on your k-form.
However with GC you should be able to do things like, using dual quaternion valued functions on a surface quite easily ( I assume ). That’s cool!
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