JuliaCon 2023

SimpleGA. A lightweight Geometric Algebra library.
07-27, 15:30–16:00 (US/Eastern), 32-144

Geometric algebra (GA) is a powerful language for formulating and solving problems in geometry, physics, engineering and graphics. SimpleGA is designed as a straightforward implementation of the most useful geometric algebras, with the key focus on performance. In this talk we use the library to explain some key properties of GA, and explain the motivation behind the design and how it utilises Julia's unique features.


Geometric algebra is a powerful mathematical language that unites many disparate concepts including complex numbers, quaternions, exterior algebra, spinors and projective geometry. The goal with this talk is to use a simple implementation of the algebra to explain the main features. No prior knowledge of geometric (aka Clifford) algebra will be assumed and by the end the audience should have a basic understanding of the properties of the geometric product - the key basis for the algebra. A novel implementation of this product in terms of binary operations will also be discussed. All of the SimpleGA source code is available, and there are many excellent free resources on geometric algebra for those interested in diving deaeper.

Chris Doran spent the early part of his career researching applications of geometric algebra in quantum theory and gravitation, before switching to graphics. In 2005 he founded Geomerics, which provided real-time global illumination technology to the games industry. Geomerics' Enlighten was used in 100s of games including Dragon Age, Overwatch and Final Fantasy. Chris spent 4 years as a Director of Research at Arm, and now focuses on helping start-ups and university spin-outs. He is currently a Director of Monumo, who are actively using Julia in their research pipeline.