
BiVector: Community for Geometric Algebra for CGI, Vision and Engineering - adamnemecek
https://bivector.net/
======
adamnemecek
The community is brand new. It's managed by Steven De Keninck (enkimute), the
author of the ganga.js framework
([https://github.com/enkimute/ganja.js](https://github.com/enkimute/ganja.js)).

Check out some examples

[https://enkimute.github.io/ganja.js/examples/coffeeshop.html...](https://enkimute.github.io/ganja.js/examples/coffeeshop.html#pga2d_points_and_lines)

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outlace
Why isn’t geometric algebra more popular when it is described glowingly as
“the most powerful language for mathematical physics”? (Honest question)

~~~
chombier
Apart from the exterior algebra part, there is little added value to using
geometric algebra compared to other representations.

My guess is that most applications don't really need exterior algebra, or at
least they would not benefit much from the nice unified representation it
provides.

~~~
jacobolus
> _there is little added value to using geometric algebra compared to other
> representations_

This is not right in my experience. When trying to solve geometry problems I
find that working out the details in terms of the GA formalism typically saves
big piles of work compared to other formalisms (such as matrices, differential
forms, trigonometry, analytic geometry, ...).

The biggest features are (a) access to a concept of “multivectors”, and (b)
access to a concept of vector division.

Mathematicians use these concepts all the time in the planar setting by
pretending that points and vectors are just funny kinds of complex numbers,
and eliding the semantic differences between these different types of objects.
Similarly for the use of quaternions in 3D (though this is less common
nowadays than complex numbers).

But multivectors and vector division are very powerful tools in more general
settings.

What sometimes ends up happening is I try to solve a problem using my (more
extensively trained) understanding from standard undergraduate math courses
and other standard textbooks, flail around with a bunch of horrible fiddly
algebra for a while, then decide to redo my work in terms of GA and end up
with like 4–5 lines of simple manipulation replacing a page of messy work.

And I am by no means an expert. There are many extremely convenient
(multi)vector identities which I have not properly learned and end up
laboriously working out for myself while solving geometric problems. If I had
spent more time doing guided exercises I am sure I could be still much more
efficient.

~~~
chombier
I completely agree: for pen/paper computations it is probably hard to beat.

I was more referring to computer applications, where once you've coded data
structures for point/lines/planes/etc you don't really care _how_ they're
implemented.

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martinhath
Also see slides[0] from a recent course at SIGGRAPH2019 that Steven De Keninck
and Charles Gunn held.

[0]:
[https://slides.com/enkimute/siggraph/](https://slides.com/enkimute/siggraph/)

~~~
Iwan-Zotow
Do you recognize that BiVector are Steven De Keninck and Charles Gunn ?

~~~
enkimute
Hi (Steven here) - biVector.net is an effort from active researchers from
Cambridge, UPEM Paris, UVA Amsterdam, and a couple of others. (as well as the
developers for some modern, actively maintained GA libraries).

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vecplane
Nice visualizations on the homepage! Cool that one is interactive, but some
hijack the scroll event and the right-click menu.

Also the super light contrast on the de-emphasized text makes a lot of the
content hard to read.

