Publication detail

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

LOUČKA, P.

English title

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

Type

conference paper

Language

en

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 in English

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

Released

27.04.2023

Publisher

Springer, Cham

Location

Switzerland

ISBN

978-3-031-30922-9

Book

EmpoweringNovel GeometricAlgebrafor GraphicsandEngineering

Edition number

13862

Pages from–to

67–79

Pages count

13

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",
  month="April",
  pages="67--79",
  publisher="Springer, Cham",
  address="Switzerland",
  isbn="978-3-031-30922-9"
}