Publication result detail

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

LOUČKA, P.; VAŠÍK, P.

Original Title

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

English Title

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

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

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

Key words in English

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

Authors

LOUČKA, P.; VAŠÍK, P.

RIV year

2025

Released

01.02.2024

Publisher

SPRINGER BASEL AG

Location

BASEL

ISBN

1661-4909

Periodical

Advances in Applied Clifford Algebras

Volume

34

Number

1

State

Swiss Confederation

Pages from

1

Pages to

22

Pages count

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"
}