Geometric Algebra for Computer Science

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1. flubertNov 2020
   >lack of practical examples

   Maybe check out: Geometric Algebra For Computer Science

   https://geometricalgebra.org/

   ...there's at least a chapter on a ray tracer, if that is practical enough.

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2. SAI_PeregrinusFeb 2020
   In addition to gibsonf1's recommendations (not books), the following books are good. The first 2 are more pure introductions to the math, the third is applying it to physics, the fourth to CS.

   Linear and Geometric Algebra, by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/laga/

   Vector and Geometric Calculus, by Alan Macdonald: http://www.faculty.luther.edu/~macdonal/vagc/index.html

   Application to physics: New Foundations for Classical Mechanics by David Hestenes: https://books.google.com/books/about/New_Foundations_for_Cla...

   Geometric Algebra For Computer Science by Dorst, Fontijne, and Mann: http://www.geometricalgebra.net/index.html

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3. erichoceanJan 2020
   > finally there's the 5D conformal GA, which is supposed to not have all this nastiness, but it's hard to find anything resembing practical on it

   Give Versor[0] a try. Implementation is fast, solid, with lots of example code. I'm no math genius, but it makes sense to me. The book Geometric Algebra for Computer Science was also helpful.

   Pablo (Versor developer) has some nice videos and write-ups on it too.

   That said, I totally agree that GA in general is WAY too abstract. I don't give a shit about the intricacies of the math, what I care about are access to geometric objects that behave normally, where it takes very little code to go from "this is what I want to do" to "okay, it's doing it." Make me a circle from these three points, then rotate it by this much about this line—that kind of thing. I want the simple stuff to be stupid simple, and so far, Versor has been sufficient.

   [0] http://versor.mat.ucsb.edu/

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4. hugohadfieldJan 2020
   I agree with a lot of what you have said here about GAs ease of use for newcomers, people change notation continuously across papers and there is a lack of material to go from nice basic theory and examples to practical applications. I started using the Clifford package https://clifford.readthedocs.io/en/latest/ because it was one of the only GA libraries that actually had documentation (thanks to Alex Arsenovic) and I could work out how to use as well as interfacing with numpy and the rest of the scipy stack. Documentation across all libraries is definitely still a problem and the difficult learning curve is compounded by the fact that there are basically no undergrad courses on GA (I know of only one in the world atm at the BNU Brno taught by Petr Vasik) and most of the existing material is targeted at mathematicians or physicists. Leo Dorst's Geometric Algebra for computer science does attack a lot of practical problems and is definitely worth digging into, as are the various PhD theses which focus on GA (I like the ones of Rich Wareham, Andreas Aristodou and Pablo Colapinto a lot) and the book Geometric Algebra in Practice but generally we have no practical hackers guide to GA yet. To try and address the lack of available material I started working on adding example practical GA algorithm implementations to the Clifford python package as I have gone along in my PhD and these now almost all now sit in the clifford.tools submodule . Along with the Czech guys I have also been building some slide tutorials that people may find interesting ( https://slides.com/hugohadfield/cgapython ) and Eric Wieser and I are building some tutorials and starter packs for doing robot IK in CGA in python/cpp . Overall I think we are starting to get there with building tutorials and docs and the recent additions to the community of people who come from a professional software background has made an enormous difference to the tooling which in turn has made it much easier to get started with GA (see Steven De Keninck's Ganja.js, Utensil Song's work on Galgebra and Eric Wieser's improvement to Clifford). The problem of differing notation is still there and yet to be resolved, I have been trying to get people to come together and agree on something but lots of people have very strong opinions on how things should be done etc etc.. my opinion on all that is that it really doesn't matter what notation you use as long as it is self consistent and solves the problem you have at hand but this doesn't really help when it comes to introducing people to the field... overall I don't have a solution to the notation problem other than to try and encourage everyone I work with to use the same notation and to add caveats in different places on papers/tutorials saying where people in the field differ in notation. If anyone has suggestions (or additional tutorial pull requests :)) I'm all ears!
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5. aaaaaaaaaabOct 2018
   Here’s an appetizer from Eric Lengyel in the context of game development (or 3D graphics in general): https://m.youtube.com/watch?v=WZApQkDBr5o

   And here’s the in-depth stuff:

   Geometric Algebra for Computer Science: http://www.geometricalgebra.net

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6. c517402Sep 2017
   The Geometric Algebra version of Kramer's rule is one of coolest most insightful things I've seen. Good examples can be found in the opening chapters of "Geometric Algebra for Computer Science" by Dorst, Fontijne, & Mann.
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