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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F24%3APU151458" target="_blank" >RIV/00216305:26210/24:PU151458 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s00190-024-01854-1" target="_blank" >https://link.springer.com/article/10.1007/s00190-024-01854-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00190-024-01854-1" target="_blank" >10.1007/s00190-024-01854-1</a>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

JOURNAL OF GEODESY

ISSN

0949-7714

e-ISSN

1432-1394

Volume of the periodical

98

Issue of the periodical within the volume

6

Country of publishing house

DE - GERMANY

Number of pages

21

Pages from-to

1-21

UT code for WoS article

001232858200001

EID of the result in the Scopus database

2-s2.0-85194878758