Geometric Algebra for Computer Science
by Leo Dorst, Daniel Fontijne, Stephen Mann · first published 2007
67% recommend17% neutral17% critical
Why HN recommends it
Practical introduction to geometric algebra for graphics, vision, and modeling engineers. Its opening chapters and ray tracer example provide concrete, code-backed entry points.
Common criticism: Some readers find it hard to grasp the core ideas without prior linear algebra intuition.
Summarised by Claude from recommending comments
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…either of MacDonald’s books) If you’re interested in geometric modeling for robotics, computer graphics, computer vision, or similar, check out [these papers][invkinematics] and then look at the book [Geometric Algebra for Computer Science][gacs]. The “conformal geometric algebra” model proposed there is pretty neat. Also see [these papers][unifalg] about related topics. If you’re interested in crystallography, check out the papers [“Point…
on “Clifford Algebra: A visual introduction (2014)” ↗…historical and biographical details are fascinating. Also recommended is all of Hestenes’s work (e.g. A New Foundation for Classical Mechanics, his Oersted Medal lecture, various papers), as well as the book Geometric Algebra for Computer Science by Dorst, Fontijne, & Mann. The latter is a bit light on the mathematical formalities but gives a good introduction that could get someone started using geometric algebra in practice in e.g. robotics,…
on “A Unified Mathematical Language for Physics and Engineering (1996) [pdf]” ↗I found Geometric Algebra for Computer Science (Revised Edition): An Object-Oriented Approach to Geometry to be eye-opening. https://www.amazon.com/Geometric-Algebra-Computer-Science-Re...
on “TAPIR: Building Consistent Transactions with Inconsistent Replication (2015) [pdf]” ↗If you are interested in this stuff, I have heard that the book Geometric Algebra for Computer Science is good. You can find the first chapter as a pdf download here: http://geometricalgebra.org/downloads/ga4cs_chapter1.pdf. It contains some code examples, and the complete source code is here: http://geometricalgebra.org/sandbox.html
on “Walking Paths with Complex Numbers” ↗…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…
on “Projective Geometric Algebra Done Right” ↗…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…
on “Projective Geometric Algebra Done Right” ↗…http://arxiv.org/pdf/1205.5935v1.pdf (this one is a good place to go if you get stuck in another source). (Or books might be better sources for going in depth. Search for New Foundations for Classical Mechanics, Geometric Algebra for Computer Science, Geometric Algebra for Physicists) You’d also probably enjoy Hestenes’s work on modeling in physics teaching, e.g. http://modeling.asu.edu/R&E/ModelingThryPhysics.pdf http://worrydream.com/refs/Hestenes%20-%20Modeling%20games%2... http://modeling.asu.edu/R&E/Notes_on_Modeling_Theory.pdf http://modeling.asu.edu/R&E/Hestenes-ModelingTheory2007.pdf
on “Learn Difficult Concepts with the ADEPT Method” ↗I discovered geometric algebra about a year ago, and it's been eye-opening. Bought the book Geometric Algebra for Computer Science. The Versor library looks really useful, and the guy's PhD is a must-read: http://versor.mat.ucsb.edu/ArticulatingSpace.pdf From the site: GA combines many other maths (matrix, tensor, vector, and…
on “Versor Geometric Algebra Library” ↗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.
on “A Bigger Mathematical Picture for Computer Graphics [video]” ↗…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
on “Introduction to Clifford Algebra (2006)” ↗…spatial relationships and transformations than the alternatives for many if not most purposes. For anyone dealing with computer vision, graphics, or modeling type fields, I recommend the more recent book “Geometric Algebra for Computer Science”. http://www.geometricalgebra.net/
on “What are imaginary numbers?” ↗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
on “Understanding Quaternions” ↗>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.
on “Geometric Algebra (2012)” ↗My personal recommendation for a book on geometric algebra is the one by Hestenes, New Foundations for Classical Mechanics (https://www.amazon.com/dp/0792355148/). I was disappointed by Geometric Algebra for Computer Science and I recently got rid of my copy when I moved to a new apartment, but I have a mathematics background and tend to prefer denser books. I would say that "alternative" is a viable word here. Yes, you'll…
on “Less Weird Quaternions Using Geometric Algebra” ↗Hmm, that is interesting. Let me cite a book Geometric Algebra for Computer Science: To understand the structure of the book, you need a better feeling for what geometric algebra is, and how it relates to more classical techniques such as linear algebra. I followed first chapters of…
on “The Exterior Algebra and Central Notions in Mathematics (2015) [pdf]” ↗