Normalization, Square Roots, and the Exponential and Logarithmic Maps in Geometric Algebras of Less than 6D

Abstract

Geometric algebras of dimension $n<6$ are becoming increasingly popular for the modeling of 3D and 3+1D geometry. With this increased popularity comes the need for efficient algorithms for common operations such as normalization, square roots, and exponential and logarithmic maps. The current work presents a signature agnostic analysis of these common operations in all geometric algebras of dimension $n<6$, and gives efficient numerical implementations in the most popular algebras ${\mathbb{R}}_4$, ${\mathbb{R}}_{3,1}$, ${\mathbb{R}}_{3,0,1}$ and ${\mathbb{R}}_{4,1}$, in the hopes of lowering the threshold for adoption of geometric algebra solutions by code maintainers.

16 pages, 4 figures

References in corpus (1)

• Normalization, Square Roots, and the Exponential and Logarithmic Maps in Geometric Algebras of Less than 6D

Cited by in corpus (1)

• Normalization, Square Roots, and the Exponential and Logarithmic Maps in Geometric Algebras of Less than 6D