I think that geometric algebra makes describing rotations quite easy - pick two vectors in the plane you want to rotate, at a suitable angle you desire to rotate through - but makes computing them more difficult. In dimensions higher than 2, its always better (in terms of number of multiplications and additions) to use the GA rotor to generate a matrix which applies the rotation. This is the same way that one would use quaternions to track the orientation of an object in a scene, but when the pedal hits the metal you want your graphics card to be doing matrix-vector multiplications to rotate, not quaternion conjugations.

GA also makes proving properties about reflections and rotations quite nice, but that’s not usually useful for actual computation (except in a learning environment).

There’s Leo Dorst’s Geometric Algebra for Computer Science but I haven’t really read it in any substantial way. Might be worth checking out still.

I have it and highly recommend it. It was my intro to GA.

Foundations of Game Engine Development, Volume 1: Mathematics by Eric Lengyel

Chapter 1-3 is usual stuff, Chapter 4 is GA

He posts to his blog about GA too:

http://terathon.com/blog/projective-geometric-algebra-done-r...

And, he has a website dedicated to PGA:

http://projectivegeometricalgebra.org

I tried reading this book. There are no practical examples of how to calculate anything useful with geometry algebra in Chapter 4. This seems rather odd because Chapters 1-3 are very practical, including both equations and code examples.

I'm currently working through Naive Lie Theory https://www.amazon.com/Naive-Theory-Undergraduate-Texts-Math... by Stillwell and there's a lot about quaternions in the first chapter, including their standard matrix representation. You'd need to be familiar with some group theory to fully understand the 3D rotations but the matrix operations are clear enough to start coding with, I think.

You want to pick an algebra that fits your problem.

Here's an example of a high performance GA lib targeting specific hardware. https://github.com/jeremyong/klein

Also you can use matrices to do calculations. Pauli or Dirac matrices can be used as the basis vectors for GA.

I’m curious - what are you working on that brings you to sensor fusion?

There are probably less than a hundred people today outside the defense industry who would want to build a sensor fusion system on an embedded platform. I suspect that half or more of this population lives in the Bay Area.

It’s always fun to run into one of you out here :)

That probably made it sound more sophisticated than it it is. I’m using Arduino and fooling around trying to make a musical instrument. I have accelerometer and gyroscope sensors and I’m trying to figure out the up vector and measure tilt while the player is moving it around.

Interesting.

This is probably overkill, but this is the most comprehensive treatment on the subject I've come across till date [1]. Note that the price on Amazon is ridiculous, the author has a very 90s looking website with a much more reasonable price. It has a very sketchy looking "enter credit card information here:" online store - I was nervous to buy from there, but I successfully got my copies, and the author emailed me to let me know he had personally dropped off the books at USPS :)

[1] https://www.amazon.com/Strapdown-Analytics-Part-Paul-Sav/dp/...

> There are probably less than a hundred people today outside the defense industry who would want to build a sensor fusion system on an embedded platform.

LOL, no. What a short-sighted thing to say.

Maybe more than you think ;)

There is a saying that “the amount of work is constant, you only move it from one place to another”.

In the end, space motion is space motion and the cmoutations are always the same, one way ir anothe.

The key? They are not commutative.