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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF GEODESY

ISSN

0949-7714

e-ISSN

1432-1394

Svazek periodika

98

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

001232858200001

EID výsledku v databázi Scopus

2-s2.0-85194878758