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
Paper in proceedings (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.
Keywords in English
Clifford algebra; conic fitting; geometric algebra; ideal point; improper point; point at infinity; proper point; waypoint
Released
2023-04-27
Publisher
Springer, Cham
Location
Switzerland
ISBN
978-3-031-30922-9
Book
EmpoweringNovel GeometricAlgebrafor GraphicsandEngineering
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",
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"
}