people seem to always talk about gimbal lock as a reason to use quaternions over euler angles, but it seems like they're also a more natural fit for physics (esp. torque) and relative rotation (i.e. a space ship turning around its own z axis).
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we could have settled on the more natural vector algebra that includes quaternions, but unfortunately they were dubbed "a positive evil of no inconsiderable magnitude" before it caught on 😔
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Yeah, I'm trying to learn about clifford/geometric algebra more. It seems really nice! Sadly we have a huge amount of stuff on linear algebra, but not much on clifford algebra. Apparently it's really handy for spacetime computations, and greatly simplifies many things in physics.
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I think if's fine for people to learn LA first, given the wider resources available, but I would love to see more stuff on GA. Perhaps with less of the fervor too - I think at times people see that as a tad off-putting.
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if you haven't already come across it, bivector.net/doc.html has some nice resources & links!
i definitely think LA is more than fine to learn first on its own. but it's hard for me to place where exactly GA would land in an ideal curriculum bc it's very broadly applicable!
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Oh cool! Will have a look at this. Do you know of any resources about using GA in the context of spherical navigation? Or would that be pretty natural to me after I'd grasped more than just the basics?
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can't say i have sources on hand for that specifically, but it certainly does seem like it'd be very workable with just rotors when you get down to it!
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Yeah, I'm at the stage where I'm convinced by the motivations, but just probably need to work through the material slowly and see if I can piece it together properly.
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Would like to be able to locate entities on the surface of a planet, then be able to work with great circle paths along the surface. Like figuring out how to steer things along the surface without having to resort to bearings from some north-pole location.
Perhaps a spherical flocking thing would be fun to play around with… hmmmm! 🤩
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that'd be super interesting to see!
if you use unit vectors as your representation for points on the sphere, then by taking two points' geometric product, you get a rotor as both the repr of the rotation delta between them, as well as the operator that does the actual rotation!
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you could do this with vectors by getting the vector pointing at your goal, projecting it onto the normal at current position, then subtracting that out (giving you the planar component).
breaks for the point on the opposite side of the sphere
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