Versor Geometric Algebra Library
github.com
github.com
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 lie algebras). It is holistic. CGA uses a particular mapping (a conformal one) of 3D Euclidean space to a 4D sphere. Operations on that hypersphere are then projected back down to 3D. That how it works in a nutshell.
[...] basically, Geometric Algebra offers a particular richness of spatial expression. Imagine needing glasses and not knowing you needed glasses. Then, when you do get glasses, the world changes unexpectedly. GA is like glasses for the inside of your brain. Conformal Geometric Algebra, especially the 5D variety enlisted here, are like x-ray glasses.