Hole-filling techniques by using minimal energy surfaces
In the last few years, several techniques to fill holes of a given surface by means of minimal energy surfaces have been proposed. In all cases, the filling patches are obtained by minimizing an `energy functional' defined in a vector space of spline functions over the Powell-Sabin triangulatio...
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| Format: | Article |
| Language: | English |
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Universidad Simón Bolívar
2016-10-01
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| Series: | Bulletin of Computational Applied Mathematics |
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| Online Access: | http://drive.google.com/open?id=0B5GyVVQ6O030MTljVC1rbDNMWW8 |
| _version_ | 1819054243970023424 |
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| author | Miguel Angel Fortes E. |
| author_facet | Miguel Angel Fortes E. |
| author_sort | Miguel Angel Fortes E. |
| collection | DOAJ |
| description | In the last few years, several techniques to fill holes of a given surface by means of minimal energy surfaces have been proposed. In all cases, the filling patches are obtained by minimizing an `energy functional' defined in a vector space of spline functions over the Powell-Sabin triangulation associated to a $\Delta^1$-type triangulation of a given domain D. The energy functional and the space of spline functions are defined in order to the filling patch fulfills certain geometric features. In this work we present, for the first time, a general framework to include most of techniques above referred. Under this general new frame, we review the main filling-holes techniques developed until now, we give their main characteristics, the computation aspects as well as some graphical examples. |
| first_indexed | 2024-12-21T12:48:32Z |
| format | Article |
| id | doaj.art-6501914ccc92444c91a025558ef0234c |
| institution | Directory Open Access Journal |
| issn | 2244-8659 2244-8659 |
| language | English |
| last_indexed | 2024-12-21T12:48:32Z |
| publishDate | 2016-10-01 |
| publisher | Universidad Simón Bolívar |
| record_format | Article |
| series | Bulletin of Computational Applied Mathematics |
| spelling | doaj.art-6501914ccc92444c91a025558ef0234c2022-12-21T19:03:33ZengUniversidad Simón BolívarBulletin of Computational Applied Mathematics2244-86592244-86592016-10-0142133164Hole-filling techniques by using minimal energy surfacesMiguel Angel Fortes E.0Department of Applied Mathematics, University of Granada, Granada, EspañaIn the last few years, several techniques to fill holes of a given surface by means of minimal energy surfaces have been proposed. In all cases, the filling patches are obtained by minimizing an `energy functional' defined in a vector space of spline functions over the Powell-Sabin triangulation associated to a $\Delta^1$-type triangulation of a given domain D. The energy functional and the space of spline functions are defined in order to the filling patch fulfills certain geometric features. In this work we present, for the first time, a general framework to include most of techniques above referred. Under this general new frame, we review the main filling-holes techniques developed until now, we give their main characteristics, the computation aspects as well as some graphical examples.http://drive.google.com/open?id=0B5GyVVQ6O030MTljVC1rbDNMWW8Minimal energy surfacefilling-holePowell-Sabinfinite element |
| spellingShingle | Miguel Angel Fortes E. Hole-filling techniques by using minimal energy surfaces Bulletin of Computational Applied Mathematics Minimal energy surface filling-hole Powell-Sabin finite element |
| title | Hole-filling techniques by using minimal energy surfaces |
| title_full | Hole-filling techniques by using minimal energy surfaces |
| title_fullStr | Hole-filling techniques by using minimal energy surfaces |
| title_full_unstemmed | Hole-filling techniques by using minimal energy surfaces |
| title_short | Hole-filling techniques by using minimal energy surfaces |
| title_sort | hole filling techniques by using minimal energy surfaces |
| topic | Minimal energy surface filling-hole Powell-Sabin finite element |
| url | http://drive.google.com/open?id=0B5GyVVQ6O030MTljVC1rbDNMWW8 |
| work_keys_str_mv | AT miguelangelfortese holefillingtechniquesbyusingminimalenergysurfaces |