Normalization, Square Roots, and the Exponential and Logarithmic Maps in Geometric Algebras of Less than 6D
Autor: | De Keninck, Steven, Roelfs, Martin |
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Rok vydání: | 2022 |
Předmět: | |
Zdroj: | Math Meth Appl Sci. 2022; 1- 17 |
Druh dokumentu: | Working Paper |
DOI: | 10.1002/mma.8639 |
Popis: | 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. Comment: 16 pages, 4 figures |
Databáze: | arXiv |
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