Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like
type: Item
instance of: scholarly article
title: Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like
zbMATH Open document ID: 1187.15026
author: Kanta Tachibana
author: Sven Buchholz
author: Isseki Yu
author: Eckhard Hitzer
published in: Advances in Applied Clifford Algebras
publication date: 2009-08-11T00:00:00Z
review text: A general framework for processing and evaluating geometric object information is developed in terms of the conformal model of the three-dimensional Euclidean geometry. This is done using the conformal geometric algebra \(\mathcal{C}\ell_{4,1} \simeq \mathcal{C}\ell_{1,1}\otimes \mathcal{C}\ell_{3,0}\), where \(\mathcal{C}\ell_{p,q}\) is the Clifford algebra of the quadratic space \(\mathbb{R}^{p,q}\). The conformal model has two classes of geometric objects: (i) four spheres \(S\) of dimensions zero (points), one (point pairs), two (circles) and three (spheres), and (ii) four flat objects \(F\) of dimensions zero (finite-infinite point pair), one (line), two (plane) and three (the embedded three-dimensional euclidean space). The authors derive general expressions for the spheres \(S\) and the flat objects \(F\) that are distinguished only by the corresponding scalar, vector, bivector and trivector Euclidean carriers, and obtain formulas to compute these carriers and the positions and (for the spheres) the radius of all objects. There are several potential applications for this algebraic framework, and the authors discuss one application to computational biochemistry.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 68T40
Mathematics Subject Classification ID: 68T45
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 92C40
zbMATH DE Number: 5593791
zbMATH Keywords: geometric algebra
zbMATH Keywords: conformal geometric algebra
zbMATH Keywords: carrier
zbMATH Keywords: Euclidean objects
zbMATH Keywords: pose
zbMATH Keywords: molecular configuration
zbMATH Keywords: tracking
zbMATH Keywords: Clifford algebra
zbMATH Keywords: biochemistry
describes a project that uses: KamiWaAi
MaRDI profile type: Publication
full work available at URL: s00006-009-0160-9
OpenAlex ID: W1999678567
DOI: 10.1007/S00006-009-0160-9
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description: scientific article; zbMATH DE number 5593791