论文标题
归一化，平方根以及小于6D的几何代数中的指数和对数图
Normalization, Square Roots, and the Exponential and Logarithmic Maps in Geometric Algebras of Less than 6D
论文作者
论文摘要
维度的几何代数$ n <6 $在3D和3+1D几何形状的建模中变得越来越流行。随着这种普及，需要有效的算法来进行常规操作，例如归一化，方形根以及指数和对数图。当前的工作在所有尺寸的几何代数$ n <6 $中对这些常见操作进行了签名不可知分析，并在最流行的代数$ \ Mathbb {r} _ {4} $，$ \ Mathbb {R} $，$ \ Mathb {r} _ {3,3,3,3,3,3,3,3,3,3,3,3，$ {3,3,3,3,3,3,00和$ \ mathbb {r} _ {4,1} $，希望通过代码维护者降低采用几何代数解决方案的阈值。
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.
