Detail publikačního výsledku

Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics

LOUČKA, P.; VAŠÍK, P.

Originální název

Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics

Anglický název

Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics

Druh

Článek WoS

Originální abstrakt

As an addition to proper points of the real plane, we introduce a representation of improper points, i.e. points at infinity, in terms of Geometric Algebra for Conics (GAC) and offer possible use of both types of points. More precisely, we present two algorithms fitting a conic to a dataset with a certain number of points lying on the conic precisely, referred to as the waypoints. Furthermore, we consider inclusion of one or two improper waypoints, which leads to the asymptotic directions of the fitted conic. The number of used waypoints may be up to four and we classify all the cases.

Anglický abstrakt

As an addition to proper points of the real plane, we introduce a representation of improper points, i.e. points at infinity, in terms of Geometric Algebra for Conics (GAC) and offer possible use of both types of points. More precisely, we present two algorithms fitting a conic to a dataset with a certain number of points lying on the conic precisely, referred to as the waypoints. Furthermore, we consider inclusion of one or two improper waypoints, which leads to the asymptotic directions of the fitted conic. The number of used waypoints may be up to four and we classify all the cases.

Klíčová slova

Conic fitting; Geometric algebra; Clifford algebra; Waypoint; Proper point; Improper point; Point at infinity; Ideal point

Klíčová slova v angličtině

Conic fitting; Geometric algebra; Clifford algebra; Waypoint; Proper point; Improper point; Point at infinity; Ideal point

Autoři

LOUČKA, P.; VAŠÍK, P.

Rok RIV

2025

Vydáno

01.02.2024

Nakladatel

SPRINGER BASEL AG

Místo

BASEL

ISSN

1661-4909

Periodikum

Advances in Applied Clifford Algebras

Svazek

34

Číslo

1

Stát

Švýcarská konfederace

Strany od

1

Strany do

22

Strany počet

22

URL

https://link.springer.com/article/10.1007/s00006-023-01308-5

BibTex

@article{BUT187178,
  author="Pavel {Loučka} and Petr {Vašík}",
  title="Algorithms for Conic Fitting Through Given Proper and Improper Waypoints in Geometric Algebra for Conics",
  journal="Advances in Applied Clifford Algebras",
  year="2024",
  volume="34",
  number="1",
  pages="1--22",
  doi="10.1007/s00006-023-01308-5",
  issn="0188-7009",
  url="https://link.springer.com/article/10.1007/s00006-023-01308-5"
}