On the Constrained Solution of RBF Surface Approximation

Anastasia Pasioti
Additional contact information
Anastasia Pasioti: Institute of Geodesy and Geoinformation Science, Technische Universität Berlin, Kaiserin–Augusta–Allee 104–106, 10553 Berlin, Germany

Mathematics, 2022, vol. 10, issue 15, 1-26

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.

Keywords: Radial Basis Function (RBF); thin-plate spline; surface approximation; surface interpolation; point cloud (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/15/2582/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/15/2582/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:15:p:2582-:d:871183

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().