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.
Categories: cs.CG cs.SC