On the Constrained Solution of RBF Surface Approximation

dc.contributor.authorPasioti, Anastasia
dc.date.accessioned2022-09-12T14:13:54Z
dc.date.available2022-09-12T14:13:54Z
dc.date.issued2022-07-25
dc.date.updated2022-08-19T11:24:40Z
dc.description.abstractIn this contribution, a scattered data approximation problem, chosen from the literature and using the Radial Basis Function (RBF) approach, is considered for the application of point cloud modelling. Three solutions are investigated for the approximation problem. First, a technique known from the literature is investigated using a linear combination of thin-plate splines and linear polynomials, with additional constraint equations. Then, using the same approximation function as before, a technique is developed for a rigorous consideration of the constraint equations. Finally, a technique is presented in which the approximation function consists only of a linear combination of thin-plate splines, without the introduction of linear polynomials and constraint equations. In addition, some interpolation problems with the RBF approach are discussed to present the differences between an interpolation with thin-plate splines only and an interpolation with thin-plate splines together with linear polynomials and constraint equations. Numerical examples are given to illustrate and discuss the solutions from the different techniques.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2022en
dc.identifier.eissn2227-7390
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/17431
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-16212
dc.language.isoenen
dc.rightsLicensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.ddc550 Geowissenschaften, Geologiede
dc.subject.otherRadial Basis Functionen
dc.subject.otherthin-plate splineen
dc.subject.othersurface approximationen
dc.subject.othersurface interpolationen
dc.subject.otherpoint clouden
dc.subject.other65D12en
dc.subject.otherRBFen
dc.titleOn the Constrained Solution of RBF Surface Approximationen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber2582en
dcterms.bibliographicCitation.doi10.3390/math10152582en
dcterms.bibliographicCitation.issue15en
dcterms.bibliographicCitation.journaltitleMathematicsen
dcterms.bibliographicCitation.originalpublishernameMDPIen
dcterms.bibliographicCitation.originalpublisherplaceBaselen
dcterms.bibliographicCitation.volume10en
tub.accessrights.dnbfreeen
tub.affiliationFak. 6 Planen Bauen Umwelt>Inst. Geodäsie und Geoinformationstechnik>FG Methodik der Geoinformationstechnikde
tub.affiliation.facultyFak. 6 Planen Bauen Umweltde
tub.affiliation.groupFG Methodik der Geoinformationstechnikde
tub.affiliation.instituteInst. Geodäsie und Geoinformationstechnikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
Files
Original bundle
Now showing 1 - 1 of 1
Loading…
Thumbnail Image
Name:
mathematics-10-02582-v2.pdf
Size:
10.34 MB
Format:
Adobe Portable Document Format
Description:
Collections