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

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dc.contributor.authorVentura Gil, Jorgecs
dc.contributor.authorMartinez, Fernandocs
dc.contributor.authorManzano-Agugliaro, Franciscocs
dc.contributor.authorNávrat, Alešcs
dc.contributor.authorHrdina, Jaroslavcs
dc.contributor.authorEid, Ahmad Hcs
dc.contributor.authorMontoya, Francisco G.cs
dc.coverage.issue6cs
dc.coverage.volume98cs
dc.date.accessioned2024-10-14T09:03:58Z
dc.date.available2024-10-14T09:03:58Z
dc.date.issued2024-06-02cs
dc.description.abstractThis 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.en
dc.formattextcs
dc.format.extent1-21cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationJOURNAL OF GEODESY. 2024, vol. 98, issue 6, p. 1-21.en
dc.identifier.doi10.1007/s00190-024-01854-1cs
dc.identifier.issn0949-7714cs
dc.identifier.orcid0000-0002-8100-4032cs
dc.identifier.orcid0000-0003-2460-7571cs
dc.identifier.other188781cs
dc.identifier.researcheridK-7147-2019cs
dc.identifier.scopus14044864000cs
dc.identifier.urihttps://hdl.handle.net/11012/249518
dc.language.isoencs
dc.publisherSPRINGERcs
dc.relation.ispartofJOURNAL OF GEODESYcs
dc.relation.urihttps://link.springer.com/article/10.1007/s00190-024-01854-1cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0949-7714/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectResection problemen
dc.subjectTriangulationen
dc.subjectSnellius-Pothenoten
dc.subjectConformal geometric algebraen
dc.titleA novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensionsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-188781en
sync.item.dbtypeVAVen
sync.item.insts2024.10.14 11:03:58en
sync.item.modts2024.09.19 11:32:11en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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