APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEM
Fitting a smooth surface on irregular data is a problem in many applications of data analysis. Spline polynomials in different orders have been used for interpolation and approximation in one or two-dimensional space in many researches. These polynomials can be made by different degrees and they hav...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2019-10-01
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| Series: | The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences |
| Online Access: | https://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLII-4-W18/343/2019/isprs-archives-XLII-4-W18-343-2019.pdf |
| _version_ | 1819106576225533952 |
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| author | F. Esmaeili A. Amiri-Simkooei V. Nafisi A. Alizadeh Naeini |
| author_facet | F. Esmaeili A. Amiri-Simkooei V. Nafisi A. Alizadeh Naeini |
| author_sort | F. Esmaeili |
| collection | DOAJ |
| description | Fitting a smooth surface on irregular data is a problem in many applications of data analysis. Spline polynomials in different orders have been used for interpolation and approximation in one or two-dimensional space in many researches. These polynomials can be made by different degrees and they have continuous derivative at the boundaries. The advantage of using B-spline basis functions for obtaining spline polynomials is that they impose the continuity constraints in an implicit form and, more importantly, their calculation is much simpler. In this study, we explain the theory of the least squares B-spline method in surface approximation. Furthermore, we present numerical examples to show the efficiency of the method in linear, quadratic and cubic forms and it’s capability in modeling changes in numerical values. This capability can be used in different applications to represent any natural phenomenon which can’t be experienced by humans directly. Lastly, the method’s accuracy and reliability in different orders will be discussed. |
| first_indexed | 2024-12-22T02:40:20Z |
| format | Article |
| id | doaj.art-9b1eff0a981f4f1ab5a7cae8aa01b2aa |
| institution | Directory Open Access Journal |
| issn | 1682-1750 2194-9034 |
| language | English |
| last_indexed | 2024-12-22T02:40:20Z |
| publishDate | 2019-10-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences |
| spelling | doaj.art-9b1eff0a981f4f1ab5a7cae8aa01b2aa2022-12-21T18:41:39ZengCopernicus PublicationsThe International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences1682-17502194-90342019-10-01XLII-4-W1834334810.5194/isprs-archives-XLII-4-W18-343-2019APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEMF. Esmaeili0A. Amiri-Simkooei1V. Nafisi2A. Alizadeh Naeini3Department of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan, IranDepartment of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan, IranDepartment of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan, IranDepartment of Geomatics Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan, IranFitting a smooth surface on irregular data is a problem in many applications of data analysis. Spline polynomials in different orders have been used for interpolation and approximation in one or two-dimensional space in many researches. These polynomials can be made by different degrees and they have continuous derivative at the boundaries. The advantage of using B-spline basis functions for obtaining spline polynomials is that they impose the continuity constraints in an implicit form and, more importantly, their calculation is much simpler. In this study, we explain the theory of the least squares B-spline method in surface approximation. Furthermore, we present numerical examples to show the efficiency of the method in linear, quadratic and cubic forms and it’s capability in modeling changes in numerical values. This capability can be used in different applications to represent any natural phenomenon which can’t be experienced by humans directly. Lastly, the method’s accuracy and reliability in different orders will be discussed.https://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLII-4-W18/343/2019/isprs-archives-XLII-4-W18-343-2019.pdf |
| spellingShingle | F. Esmaeili A. Amiri-Simkooei V. Nafisi A. Alizadeh Naeini APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEM The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences |
| title | APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEM |
| title_full | APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEM |
| title_fullStr | APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEM |
| title_full_unstemmed | APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEM |
| title_short | APPLICATION OF B-SPLINE METHOD IN SURFACE FITTING PROBLEM |
| title_sort | application of b spline method in surface fitting problem |
| url | https://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLII-4-W18/343/2019/isprs-archives-XLII-4-W18-343-2019.pdf |
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