New applications of Clifford's geometric algebra
type: Item
instance of: scholarly article
title: New applications of Clifford's geometric algebra
zbMATH Open document ID: 1490.15036
author: Stéphane Breuils
author: Kanta Tachibana
author: Eckhard Hitzer
published in: Advances in Applied Clifford Algebras
publication date: 2022-03-11T00:00:00Z
review text: 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.
reviewed by: Morteza Shahpari
Mathematics Subject Classification ID: 15A67
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 68T01
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 11E88
Mathematics Subject Classification ID: 70E60
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 7488231
zbMATH Keywords: Clifford's geometric algebra, engineering applications, neural networks
zbMATH Keywords: signal processing
zbMATH Keywords: image processing
zbMATH Keywords: encryption
zbMATH Keywords: implementations
zbMATH Keywords: discrete mathematics
zbMATH Keywords: surface representation
describes a project that uses: glga
describes a project that uses: TbGAL
describes a project that uses: Numba
describes a project that uses: GfG
describes a project that uses: SchurFkt
describes a project that uses: Garamon
describes a project that uses: GAALOPWeb
describes a project that uses: CLIFFORD
describes a project that uses: Gaalop
describes a project that uses: Gaigen
describes a project that uses: Quaternion
describes a project that uses: Clifford Multivector Toolbox
describes a project that uses: GAPPCO
describes a project that uses: ganja.js
describes a project that uses: BIGEBRA
describes a project that uses: CLUCalc
describes a project that uses: GMac
describes a project that uses: Gajit
describes a project that uses: Octonion
describes a project that uses: SymGroupAlgebra
describes a project that uses: Cliplus
MaRDI profile type: Publication
full work available at URL: s00006-021-01196-7
OpenAlex ID: W4213378223
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New applications of Clifford's geometric algebra (DOI)
DOI: 10.1007/S00006-021-01196-7