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

05/11/2022

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by   Steven De Keninck, et al.

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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 ℝ_4, ℝ_3,1, ℝ_3,0,1 and ℝ_4,1, in the hopes of lowering the threshold for adoption of geometric algebra solutions by code maintainers.