Detail publikačního výsledku

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

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

Originální název

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

Anglický název

Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Conformal geometric algebra; Projective geometric algebra; Euclidean geometry

Klíčová slova v angličtině

Conformal geometric algebra; Projective geometric algebra; Euclidean geometry

Autoři

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

Rok RIV

2021

Vydáno

22.02.2021

Nakladatel

Birkhauser Verlag AG

Místo

Basel, Switzerland

ISSN

0188-7009

Periodikum

Advances in Applied Clifford Algebras

Svazek

31

Číslo

18

Stát

Švýcarská konfederace

Strany od

1

Strany do

13

Strany počet

14

URL

https://link.springer.com/article/10.1007/s00006-021-01118-7

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",
  journal="Advances in Applied Clifford Algebras",
  year="2021",
  volume="31",
  number="18",
  pages="1--13",
  doi="10.1007/s00006-021-01118-7",
  issn="0188-7009",
  url="https://link.springer.com/article/10.1007/s00006-021-01118-7"
}