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, 29 (5). DOI https://doi.org/10.1007/s00006-019-1016-6
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, 29 (5). DOI https://doi.org/10.1007/s00006-019-1016-6
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, 29 (5). DOI https://doi.org/10.1007/s00006-019-1016-6
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 Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 02 Oct 2019 15:35 |
Last Modified: | 30 Oct 2024 16:32 |
URI: | http://repository.essex.ac.uk/id/eprint/25528 |
Available files
Filename: 1905.0030v2.pdf