Projective geometric algebra is a four-dimensional mathematical model that naturally incorporates representations for Euclidean points, lines, and planes as well as operations for performing rotations, reflections, and translations in a single algebraic structure. It completely subsumes conventional models that include homogeneous coordinates, Plücker coordinates, quaternions, and screw theory.

I am Eric Lengyel, and this page is a central resource containing all of my work on the subject of geometric algebra. Geometric algebra is a specific type of Clifford algebra, and it includes the simpler Grassmann algebra.

A **C++ math library** that implements projective geometric algebra is coming soon. It will be available on this page.

The most recent developments in projective geometric algebra can be found in my blog:

• Projective Geometric Algebra Done Right

• Symmetries in Projective Geometric Algebra

The two 18×24 inch reference posters below contain a huge amount of information, including new research from 2020. They can be downloaded as a single PDF.

Foundations of Game Engine Development, Volume 1: Mathematics This book, written in 2016, contains an entire chapter about projective geometry in Grassmann algebra. It is a detailed introduction to the subject that is the perfect starting place for anyone who wants to learn details about the wedge and antiwedge products. |

Grassmann Algebra in Game Development These are the slides from the talks about Grassmann algebra that I gave at the Game Developers Conference in 2012 and 2014. |