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, https://doi.org/10.1007/s00006-018-0879-2,2018), 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.
Unique-IP document downloads: 107 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.