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Interpolating countour lines with radial basis functions
Thesis (MSc)--Stellenbosch University, 2022.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2022
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| _version_ | 1867613911540301824 |
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| access_status_str | Open Access |
| author | Schall, Philip |
| author2 | Weideman, Andre |
| author_browse | Schall, Philip Weideman, Andre |
| author_facet | Weideman, Andre Schall, Philip |
| author_sort | Schall, Philip |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2022. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/124740 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:43:40.048Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/124740 Interpolating countour lines with radial basis functions Schall, Philip Weideman, Andre Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics) Numerical analysis Interpolation Digital elevation models Altitudes -- Measurement Digital mapping UCTD Thesis (MSc)--Stellenbosch University, 2022. ENGLISH 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. AFRIKAANSE 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. Masters 2022-03-10T06:04:29Z 2022-04-29T09:29:43Z 2022-03-10T06:04:29Z 2022-04-29T09:29:43Z 2022-04 Thesis http://hdl.handle.net/10019.1/124740 en_ZA Stellenbosch University xii, 60 pages ; illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Numerical analysis Interpolation Digital elevation models Altitudes -- Measurement Digital mapping UCTD Schall, Philip Interpolating countour lines with radial basis functions |
| title | Interpolating countour lines with radial basis functions |
| title_full | Interpolating countour lines with radial basis functions |
| title_fullStr | Interpolating countour lines with radial basis functions |
| title_full_unstemmed | Interpolating countour lines with radial basis functions |
| title_short | Interpolating countour lines with radial basis functions |
| title_sort | interpolating countour lines with radial basis functions |
| topic | Numerical analysis Interpolation Digital elevation models Altitudes -- Measurement Digital mapping UCTD |
| url | http://hdl.handle.net/10019.1/124740 |
| work_keys_str_mv | AT schallphilip interpolatingcountourlineswithradialbasisfunctions |