Publication result detail

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

LOUČKA, P.

Original Title

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

English Title

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

Type

Paper in proceedings (conference paper)

Original Abstract

We introduce a new conic fitting algorithm using Geometric Algebra for Conics (GAC) that not only minimises the overall distance to a data set, but also causes the fitted conic to pass through prescribed waypoints. Moreover, the expression for points at infinity (also called improper points) in terms of GAC is derived; hence, the use of the improper waypoints in the conic fitting problem is enabled. Finally, a MATLAB implementation of the fitting algorithm and experimental results based on custom data sets are included.

English abstract

We introduce a new conic fitting algorithm using Geometric Algebra for Conics (GAC) that not only minimises the overall distance to a data set, but also causes the fitted conic to pass through prescribed waypoints. Moreover, the expression for points at infinity (also called improper points) in terms of GAC is derived; hence, the use of the improper waypoints in the conic fitting problem is enabled. Finally, a MATLAB implementation of the fitting algorithm and experimental results based on custom data sets are included.

Keywords

Clifford algebra; conic fitting; geometric algebra; ideal point; improper point; point at infinity; proper point; waypoint

Key words in English

Clifford algebra; conic fitting; geometric algebra; ideal point; improper point; point at infinity; proper point; waypoint

Authors

LOUČKA, P.

RIV year

2024

Released

27.04.2023

Publisher

Springer, Cham

Location

Switzerland

ISBN

978-3-031-30922-9

Book

EmpoweringNovel GeometricAlgebrafor GraphicsandEngineering

Edition

Lecture Notes in Computer Science

Pages from

67

Pages to

79

Pages count

13

URL

https://link.springer.com/chapter/10.1007/978-3-031-30923-6_6

BibTex

@inproceedings{BUT187886,
  author="Pavel {Loučka}",
  title="On Proper and Improper Points in Geometric Algebra for Conics and Conic Fitting Through Given Waypoints",
  booktitle="EmpoweringNovel GeometricAlgebrafor GraphicsandEngineering",
  year="2023",
  series="Lecture Notes in Computer Science",
  number="13862",
  pages="67--79",
  publisher="Springer, Cham",
  address="Switzerland",
  doi="10.1007/978-3-031-30923-6\{_}6",
  isbn="978-3-031-30922-9",
  url="https://link.springer.com/chapter/10.1007/978-3-031-30923-6_6"
}