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arXiv · 2206.07496

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

Steven De Keninck·Martin Roelfs
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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.

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Steven De Keninck, Martin Roelfs. 2022-05-11. Normalization, Square Roots, and the Exponential and Logarithmic Maps in Geometric Algebras of Less than 6D. https://doi.org/10.1002/mma.8639

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