Self-Reverse Elements and Lines in an Algebra for 3D Space
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Colleges, School and Institutes
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.
|Journal||Advances in Applied Clifford Algebras|
|Early online date||15 Jul 2020|
|Publication status||Published - 1 Sep 2020|
- Geometric algebra, Point, Line, Plane, Self-reverse element