Viewing profile — enkimute

fixed it. mea culpa.

Thank you, appreciate that!

Apologies. Had that joke sitting around for waaaay to long. Not that great in retrospect :D

don't foget the fantastic Sudgy 'A swift introduction to projective geometric algebra' : https://www.youtube.com/watch?v=0i3ocLhbxJ4 and ofcourse the go-to reference https://bivect…

For specifying animations, you should work in the quaternion lie algebra, not in the group as you suggest. There you can represent 1620 degrees without any problem. Furthermore, in…

done. mea maxima culpa.

There's no smoke. But there surely are mirrors. (Group theory joke)

These are also called the planar quaternions and are the even subalgebra of 2D PGA. I use and explain these (and their nD generalisations) in my SIBGRAPI 2021 talk on kinematics an…

Not the same concrete example, but one where I do find the Geometric Algebra version substantially more insightful, is the treatment of rigid body mechanics in the geometric algebr…

Every Lie algebra is a bivector algebra (see 'Lie groups as Spin groups' http://geocalc.clas.asu.edu/pdf/LGasSG.pdf ). Additionally the GA formalism enables closed form solutions f…

They were designed with touchscreens in mind - I agree tho that it didn't work out exactly as I wanted. Someone did make a playthrough video of it : https://www.youtube.com/watch?v…

Thanks for this background info. I also agree with your assessment - so far its just gotten some giggles and maybe even some extra attention from students who are not always easy t…

> You're generating code that relates to a certain algebra, likely for providing API for doing calculations based on that algebra (so an algebra library). Why would you call that '…

A bias towards 'vectors must be points' crops in as an unwritten legacy axiom, leading to a broken correspondence with Group theory (which again cannot be turned around, discrete s…

The grade 1 element is not the normal vector of the plane, it is the plane itself (as a homogeneous linear form, it includes the distance from the origin as an extra coefficient, w…

Chris Doran, while not officially in academia, is still very much actively researching these topics and regularly publishes. (he is also a member of the bivector community, very ap…

close? https://enkimute.github.io/ganja.js/examples/coffeeshop.html

Geometric Algebra for Physicists : https://www.amazon.com/Geometric-Algebra-Physicists-Chris-Do...

Absolutely : Algebraically we can always use the Hodge dual and its inverse to move to/from k-vectors from/to n-k vectors. Geometrically we can always say two points define a line …

That is correct - matrices are the natural companion of the general linear group. The GA representation exists, and is called 'the mother algebra', for general 4x4 matrices the GA …

> But to really make it popular and understandable, a "simple" version of GA that handles translation, rotation & non-uniform scaling would really help, without the group theory co…

Take a look at Klein : https://www.jeremyong.com/klein/ (arm implementation is coming) Its geometric product between motors is the equivalent of the 4x4 matrix product. Although th…

a selection: - no closed form exponential/logarithm (i.e. cant interpolate) - no numerical stability for subgroups (i.e. need Gramm-Shmidt, SVD) - no covariant transformations (i.e…

I fully agree, for practical examples (no-install, web-browsable, interactive), check out the dozens of examples in the ganja.js coffeeshop: https://enkimute.github.io/ganja.js/exa…

Ok, standard 4x4 matrices also implement a projective (aka d+1) model. (the 'w' coordinate is just the projective coordinate). So no difference with GA in that respect. Setting up …