Geometric algebra for quadrics—transformations and their efficient implementation

Abstract

This paper describes the geometric algebra for quadrics (GAQ) with a focus on elements representing Euclidean transformations, particularly translations and rotations. We provide general methods of deriving the generators of such transformations and verify their correctness on examples. We also show how to compute the versors numerically, yet their exact form is rather technical and extensive because of the high dimension of GAQ. Thus, we introduce a convenient C++ implementation.

This article is part of the theme issue ‘Modern applications of geometric algebra’.