Abstract
A geometric algebra provides a single environment in which geometric entities can be represented and manipulated and in which transforms can be applied to these entities. A number of versions of geometric algebra have been proposed and the aim of the paper is to investigate one of these as it has a number of advantageous features. Points, lines and planes are presented naturally by element of grades 1, 2, and 3 respectively. The self-reverse elements in the algebra form a field. This allows an equivalence relation between elements of grade 2 to be defined so that, although not every grade 2 element corresponds to a line, each equivalence class does, and vice versa. Examples are given to illustrate the ease in which geometric objects are represented and manipulated.
Original language | English |
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Article number | 50 |
Journal | Advances in Applied Clifford Algebras |
Volume | 30 |
Issue number | 4 |
Early online date | 15 Jul 2020 |
DOIs | |
Publication status | Published - 1 Sept 2020 |
Keywords
- Geometric algebra
- Line
- Plane
- Point
- Self-reverse element