Interpolating countour lines with radial basis functions

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dc.contributor.advisorWeideman, Andreen_ZA
dc.contributor.authorSchall, Philipen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)en_ZA
dc.date.accessioned2022-03-10T06:04:29Z
dc.date.accessioned2022-04-29T09:29:43Z
dc.date.available2022-03-10T06:04:29Z
dc.date.available2022-04-29T09:29:43Z
dc.date.issued2022-04
dc.descriptionThesis (MSc)--Stellenbosch University, 2022.en_ZA
dc.description.abstractENGLISH SUMMARY : With the growing demand for digital elevation models (DEMs) in science and visualisation, there exists a need to generate these models cheaply and efficiently. While current methods such as remote sensing are often prohibitively expensive, interpolating contour data offer an economical way of generating DEMs. In this thesis, we investigate the feasibility of using radial basis function (RBF) based interpolation methods to interpolate DEMs from contour data. We present the basic theory of RBF interpolation, and introduce a number of RBF based techniques which are able to deal with the complexities of contour data. These complexities are mainly related to the extremely large data set sizes, and the irregular or scattered nature of the data. Furthermore, we compare RBF based interpolation methods to other established interpolation methods, and investigate the accuracy and quality of the resulting DEMs. We find that, particularly in our application, RBF based interpolation methods offer a robust, easily implementable and effective solution.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING : Met die stygende vraag na digitale hoogtemodelle (DHMs) in die wetenskap en industrie, ontstaan die aanvraag aan ’n goedkoop en effektiewe wyse om hierdie modelle te genereer. Anders as kontemporêre metodes soos afstand- waarneming, bied die interpolasie van kontoerlyne ’n bekostigbare, eenvoudige metode om DHMs te produseer. In hierdie tesis ondersoek ons die lewensvatbaarheid van die gebruik van radiale basisfunksie (RBF) gebaseerde interpolasie om DHMs uit kontoerlyn- data te skep. Ons bied ’n inleiding tot RBF-teorie aan, asook ’n aantal RBF-gebaseerde metodes wat doeltreffend met die uitdagings in kontoerlyndata om- gaan. Hierdie uitdagings hou hoofsaaklik verband met die grootte van die datastelle en die onreëlmatige verspreiding van die datapunte. Verder word RBF-gebaseerde interpolasiemetodes se akkuraatheid met dié van ander gebruiklike interpolasiemetodes vergelyk, en die akkuraatheid en kwaliteit van die daaruitspruitende DHMs word ondersoek. Ons bevind dat RBF gebaseerde interpolasiemetodes ’n robuuste, maklik implementeerbare en effektiewe oplossing tot ons toepassing bied.af_ZA
dc.description.versionMastersen_ZA
dc.format.extentxii, 60 pages ; illustrationsen_ZA
dc.identifier.urihttp://hdl.handle.net/10019.1/124740
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subjectNumerical analysisen_ZA
dc.subjectInterpolationen_ZA
dc.subjectDigital elevation modelsen_ZA
dc.subjectAltitudes -- Measurementen_ZA
dc.subjectDigital mappingen_ZA
dc.subjectUCTD
dc.titleInterpolating countour lines with radial basis functionsen_ZA
dc.typeThesisen_ZA
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Masters Degrees (Applied Mathematics)