Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces
The techniques for parametrizing nonsingular cubic surfaces have shown to be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/349315 |
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| _version_ | 1832564922145308672 |
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| author | Minghao Guo Tieru Wu Shugong Zhang |
| author_facet | Minghao Guo Tieru Wu Shugong Zhang |
| author_sort | Minghao Guo |
| collection | DOAJ |
| description | The techniques for parametrizing nonsingular cubic surfaces have shown to
be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be 𝐹3, 𝐹4, or
𝐹5 surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by Berry and Patterson in 2001, we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper. |
| format | Article |
| id | doaj-art-e71efaeb6d9c4da3a94b3d364e311519 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e71efaeb6d9c4da3a94b3d364e3115192025-02-03T01:09:53ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/349315349315Geometric Information and Rational Parametrization of Nonsingular Cubic Blending SurfacesMinghao Guo0Tieru Wu1Shugong Zhang2Key Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), School of Mathematics, Jilin University, Changchun 130012, ChinaKey Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), School of Mathematics, Jilin University, Changchun 130012, ChinaKey Laboratory of Symbolic Computation and Knowledge Engineering (Ministry of Education), School of Mathematics, Jilin University, Changchun 130012, ChinaThe techniques for parametrizing nonsingular cubic surfaces have shown to be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be 𝐹3, 𝐹4, or 𝐹5 surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by Berry and Patterson in 2001, we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper.http://dx.doi.org/10.1155/2011/349315 |
| spellingShingle | Minghao Guo Tieru Wu Shugong Zhang Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces Journal of Applied Mathematics |
| title | Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces |
| title_full | Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces |
| title_fullStr | Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces |
| title_full_unstemmed | Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces |
| title_short | Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces |
| title_sort | geometric information and rational parametrization of nonsingular cubic blending surfaces |
| url | http://dx.doi.org/10.1155/2011/349315 |
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