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Foundations of Conic Conformal Geometric Algebra and Compact Versors for Rotation, Translation and Scaling

Hitzer, Eckhard and Sangwine, Stephen (2019) 'Foundations of Conic Conformal Geometric Algebra and Compact Versors for Rotation, Translation and Scaling.' Advances in Applied Clifford Algebras. ISSN 0188-7009

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Abstract

This paper explains in algebraic detail how two-dimensional conics can be defined by the outer products of conformal geometric algebra (CGA) points in higher dimensions. These multivector expressions code all types of conics in arbitrary scale, location and orientation. Conformal geometric algebra of two-dimensional Euclidean geometry is fully embedded as an algebraic subset. With small model preserving modifications, it is possible to consistently define in conic CGA versors for rotation, translation and scaling, similar to [10], but simpler, especially for translations.

Item Type: Article
Uncontrolled Keywords: Clifford algebra, conformal geometric algebra, conics, versors
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Elements
Date Deposited: 02 Oct 2019 15:35
Last Modified: 04 Oct 2020 01:00
URI: http://repository.essex.ac.uk/id/eprint/25528

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