New applications of Clifford's geometric algebra
The authors provide a comprehensive literature review on the progress made on many different areas related to Clifford algebras in the last ten years. The authors review more than 190 references and cover the following topics: \begin{itemize} \item Kinematics and robotics; \item Computer graphics and animation; \item Neural networks and pattern recognition; \item Signal and image processing particularly using quaternions; \item Applications of vectors and orthogonal transformations including Cayley factorization; \item Spinor and matrices; \item Applied geometric calculus; \item Physics; \item Encryption; \item Geographical information science (GIS) data and classification. \end{itemize} One of the strong points of the paper is the review of programming implementations related to Clifford algebras' tools and their applications. The authors discuss various implementations in three categories of pre-compilers, library generators, and template meta-programming. Given the very wide scope of the review each subject is reviewed in less than two pages. It seems the authors only aim at pointing out the latest advancements in the various fields, often providing insightful comments. It should be mentioned that the authors have also written another review article on the same subject [\textit{E. Hitzer} et al., Math. Meth. Appl. Sci. 2022, 1-- 31 (2022; \url{doi:10.1002/mma.8316})], whose focus is to survey only papers published in the years 2019--2022. Some topics, such as neural networks and encryption, overlap in the two papers. However, the latter article presents applications in electrical engineering, including optical fibers and material science, that are not discussed here. Overall, the interested reader should consult both articles for a complete overview.
Clifford's geometric algebra, engineering applications, neural networks
scientific article; zbMATH DE number 7488231
scientific article