Publication detail

A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions

VENTURA GIL, J. MARTINEZ, F. MANZANO-AGUGLIARO, F. NÁVRAT, A. HRDINA, J. EID, A. MONTOYA, F.

Original Title

A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions

Type

journal article in Web of Science

Language

English

Original Abstract

This paper introduces a novel method for solving the resection problem in two and three dimensions based on conformal geometric algebra (CGA). Advantage is taken because of the characteristics of CGA, which enables the representation of points, lines, planes, and volumes in a unified mathematical framework and offers a more intuitive and geometric understanding of the problem, in contrast to existing purely algebraic methods. Several numerical examples are presented to demonstrate the efficacy of the proposed method and to compare its validity with established techniques in the field. Numerical simulations indicate that our vector geometric algebra implementation is faster than the best-known algorithms to date, suggesting that the proposed GA-based methods can provide a more efficient and comprehensible solution to the two- and three-dimensional resection problem, paving the way for further applications and advances in geodesy research. Furthermore, the method's emphasis on graphical and geometric representation makes it particularly suitable for educational purposes, allowing the reader to grasp the concepts and principles of resection more effectively. The proposed method has potential applications in a wide range of other fields, including surveying, robotics, computer vision, or navigation.

Keywords

Resection problem; Triangulation; Snellius-Pothenot; Conformal geometric algebra

Authors

VENTURA GIL, J.; MARTINEZ, F.; MANZANO-AGUGLIARO, F.; NÁVRAT, A.; HRDINA, J.; EID, A.; MONTOYA, F.

Released

2. 6. 2024

Publisher

SPRINGER

Location

NEW YORK

ISBN

0949-7714

Periodical

JOURNAL OF GEODESY

Year of study

98

Number

6

State

Federal Republic of Germany

Pages from

1

Pages to

21

Pages count

21

URL

https://link.springer.com/article/10.1007/s00190-024-01854-1

BibTex

@article{BUT188781,
  author="Jorge {Ventura Gil} and Fernando {Martinez} and Francisco {Manzano-Agugliaro} and Aleš {Návrat} and Jaroslav {Hrdina} and Ahmad H {Eid} and Francisco G. {Montoya}",
  title="A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions",
  journal="JOURNAL OF GEODESY",
  year="2024",
  volume="98",
  number="6",
  pages="1--21",
  doi="10.1007/s00190-024-01854-1",
  issn="0949-7714",
  url="https://link.springer.com/article/10.1007/s00190-024-01854-1"
}