# On the Constrained Solution of RBF Surface Approximation

 dc.contributor.author Pasioti, Anastasia dc.date.accessioned 2022-09-12T14:13:54Z dc.date.available 2022-09-12T14:13:54Z dc.date.issued 2022-07-25 dc.date.updated 2022-08-19T11:24:40Z dc.description.abstract In 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.sponsorship TU Berlin, Open-Access-Mittel â€“ 2022 en dc.identifier.eissn 2227-7390 dc.identifier.uri https://depositonce.tu-berlin.de/handle/11303/17431 dc.identifier.uri http://dx.doi.org/10.14279/depositonce-16212 dc.language.iso en en dc.rights.uri https://creativecommons.org/licenses/by/4.0/ en dc.subject.ddc 510 Mathematik de dc.subject.ddc 550 Geowissenschaften, Geologie de dc.subject.other Radial Basis Function en dc.subject.other thin-plate spline en dc.subject.other surface approximation en dc.subject.other surface interpolation en dc.subject.other point cloud en dc.subject.other 65D12 en dc.subject.other RBF en dc.title On the Constrained Solution of RBF Surface Approximation en dc.type Article en dc.type.version publishedVersion en dcterms.bibliographicCitation.articlenumber 2582 en dcterms.bibliographicCitation.doi 10.3390/math10152582 en dcterms.bibliographicCitation.issue 15 en dcterms.bibliographicCitation.journaltitle Mathematics en dcterms.bibliographicCitation.originalpublishername MDPI en dcterms.bibliographicCitation.originalpublisherplace Basel en dcterms.bibliographicCitation.volume 10 en tub.accessrights.dnb free en tub.affiliation Fak. 6 Planen Bauen Umwelt::Inst. GeodÃ¤sie und Geoinformationstechnik::FG Methodik der Geoinformationstechnik de tub.affiliation.faculty Fak. 6 Planen Bauen Umwelt de tub.affiliation.group FG Methodik der Geoinformationstechnik de tub.affiliation.institute Inst. GeodÃ¤sie und Geoinformationstechnik de tub.publisher.universityorinstitution Technische UniversitÃ¤t Berlin en

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