Course notes Geometric Algebra for Computer Graphics, SIGGRAPH 2019

What is the best representation for doing euclidean geometry on computers? These notes from a SIGGRAPH 2019 short course entitled "Geometric algebra for computer graphics" introduce projective geometric algebra (PGA) as a modern framework for this task. After constructing a developer's wish-list for such a framework, the article provides the necessary historical and mathematical background before defining what a geometric algebra is. It then proceeds to the specific algebra for euclidean geometry (euclidean PGA) and demonstrates that it fulfils all the features of the desired wish-list. The article also compares PGA to the traditional approach VLAAG (vector and linear algebra and analytic geometry), both conceptually and practically.