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

Authors: Eckhard Hitzer, Stephen J. Sangwine

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 Hrdina et al. (Adv. Appl Cliff. Algs. Vol. 28:66, pp. 1–21,,2018), but simpler, especially for translations.

Comments: Adv. of App. Cliff. Algs., (2019) 29(5):96 (First Online: 04 October 2019), 16 pages, DOI: 10.1007/s00006-019-1016-6, 1 table, 1 figure.

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Submission history

[v1] 2019-05-02 22:25:09
[v2] 2019-09-13 02:27:49

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