Publication detail

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

HRDINA, J. NÁVRAT, A. VAŠÍK, P. DORST, L.

English title

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

Type

journal article in Web of Science

Language

en

Original abstract

We show that if Projective Geometric Algebra (PGA), i.e. the geometric algebra with degenerate signature (n, 0, 1), is understood as a subalgebra of Conformal Geometric Algebra (CGA) in a mathematically correct sense, then flat primitives share the same representation in PGA and CGA. Particularly, we treat duality in PGA in the framework of CGA. This leads to unification of PGA and CGA primitives which is important especially for software implementation and symbolic calculations.

English abstract

We show that if Projective Geometric Algebra (PGA), i.e. the geometric algebra with degenerate signature (n, 0, 1), is understood as a subalgebra of Conformal Geometric Algebra (CGA) in a mathematically correct sense, then flat primitives share the same representation in PGA and CGA. Particularly, we treat duality in PGA in the framework of CGA. This leads to unification of PGA and CGA primitives which is important especially for software implementation and symbolic calculations.

Keywords in English

Conformal geometric algebra; Projective geometric algebra; Euclidean geometry

Released

22.02.2021

Publisher

Birkhauser Verlag AG

Location

Basel, Switzerland

ISSN

0188-7009

Volume

31

Number

18

Pages from–to

1–13

Pages count

14

BIBTEX


@article{BUT169707,
  author="Jaroslav {Hrdina} and Aleš {Návrat} and Petr {Vašík} and Leo {Dorst},
  title="Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra",
  year="2021",
  volume="31",
  number="18",
  month="February",
  pages="1--13",
  publisher="Birkhauser Verlag AG",
  address="Basel, Switzerland",
  issn="0188-7009"
}