BiVector.net – Geometric Algebra for CGI, Vision and Engineering | Hacker News Reader

BiVector.net – Geometric Algebra for CGI, Vision and Engineering

bivector.net

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If you enjoy geometric algebra, you might like my Julia language implementation

Grassmann.jl (features on bivector.net)

https://github.com/chakravala/Grassmann.jl

What a beautiful subject. A framework that manages to incorporate the complex numbers, quaternions, and vector algebra - all from a unified perspective. Is there a textbook that uses this framework to present “all of physics,” similarly to what you can find for some other frameworks (e.g. Lie groups/algebras)?

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

Looks interesting, thanks. (Too bad, as one of the reviewers notes, “author has given up on theoretical physics and now runs a software development company specializing in lighting/shading routines for video games”...)

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 approachable and happy to help out with questions).

Anthony Lasenby, professor astrophysics and cosmology at Cambridge, is also absolutely still actively researching and publishing, all in the mindset of the GA4Physicists book. (See a recent (feb 2020) lecture of him here : https://www.youtube.com/watch?v=x7eLEtmq6PY&t=7s )

(GA4P is considered one of the few comprehensive and up to date treatments of geometric algebra, not just in physics).

It look like Chris Doran's company was acquired by Arm, and that he is back in academia as a fellow at Sidney Sussex College: https://www.sid.cam.ac.uk/people/dr-chris-doran

As a school kid (14? 15?), I won a prize to go to Birmingham University (UK) each Saturday morning for a term, to do a maths course. The teachers took turns in taking me and another to the course. One of the things I remember doing was playing with all kinds of geometrical transformations of triangles (e.g. bisect each of the edges to get the circumcentre and then add a circle which had that centre. As you adjusted the shape of the triangle everything updated in real time). It was running on what must have been a mainframe. This was my first (and only?) experience of using a mainframe. I remember being rather unimpressed with the mainframe, since it hung and crashed once. The interface was also a bit crap. As all of the students started doing this work, the mainframe started to struggle and slow down! These libraries look to be able to do similar stuff which is very cool.

I had fond memories of that, and was a reason I got into Computer Science and Maths. I wanted to recreate it, but I've never really tried to do it. These libs look like they could be just the thing.

Something like this? https://www.mathsisfun.com/geometry/triangle-centers.html

EDIT: Or maybe more like this with all the optional lines and circles turned on. https://stage.geogebra.org/m/bm27Qwk5#material/ZvKsNnvv

> As you adjusted the shape of the triangle everything updated in real time). It was running on what must have been a mainframe.

I think it was probably a minicomputer, not a mainframe. Good interactivity was pioneered by minicomputers and traditionally not associated with mainframes.

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

You guys should join the bivector discord channel https://discord.gg/vGY6pPk.

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