A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface
Subdivision surface schemes are used to produce smooth shapes, which are applied for modelling in computer-aided geometric design. In this paper, a new and efficient numerical technique is presented to estimate the error bound and subdivision depth of the uniform Doo-Sabin subdivision scheme. In thi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2510204 |
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| _version_ | 1850167589408342016 |
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| author | Faheem Khan Bushra Shakoor Ghulam Mustafa Sidra Razaq |
| author_facet | Faheem Khan Bushra Shakoor Ghulam Mustafa Sidra Razaq |
| author_sort | Faheem Khan |
| collection | DOAJ |
| description | Subdivision surface schemes are used to produce smooth shapes, which are applied for modelling in computer-aided geometric design. In this paper, a new and efficient numerical technique is presented to estimate the error bound and subdivision depth of the uniform Doo-Sabin subdivision scheme. In this technique, first, a result for computing bounds between Pk (a polygon at kth level) and P∞ (limit surface) of the Doo-Sabin scheme is obtained. After this, subdivision depth (the number of iterations) is computed by using the user-defined error tolerance. In addition, the results of the proposed technique are verified by taking distinct valence numbers of the Doo-Sabin surface scheme. |
| format | Article |
| id | doaj-art-e78fcc6621ea4e52a3a4ba56b330f533 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-e78fcc6621ea4e52a3a4ba56b330f5332025-08-20T02:21:10ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2510204A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision SurfaceFaheem Khan0Bushra Shakoor1Ghulam Mustafa2Sidra Razaq3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsSubdivision surface schemes are used to produce smooth shapes, which are applied for modelling in computer-aided geometric design. In this paper, a new and efficient numerical technique is presented to estimate the error bound and subdivision depth of the uniform Doo-Sabin subdivision scheme. In this technique, first, a result for computing bounds between Pk (a polygon at kth level) and P∞ (limit surface) of the Doo-Sabin scheme is obtained. After this, subdivision depth (the number of iterations) is computed by using the user-defined error tolerance. In addition, the results of the proposed technique are verified by taking distinct valence numbers of the Doo-Sabin surface scheme.http://dx.doi.org/10.1155/2022/2510204 |
| spellingShingle | Faheem Khan Bushra Shakoor Ghulam Mustafa Sidra Razaq A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface Journal of Mathematics |
| title | A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface |
| title_full | A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface |
| title_fullStr | A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface |
| title_full_unstemmed | A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface |
| title_short | A Convolution-Based Computational Technique for Subdivision Depth of Doo-Sabin Subdivision Surface |
| title_sort | convolution based computational technique for subdivision depth of doo sabin subdivision surface |
| url | http://dx.doi.org/10.1155/2022/2510204 |
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