Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method
Although the uniform theory of diffraction (UTD) could be theoretically applied to arbitrarilyshaped convex objects modeled by nonuniform rational B-splines (NURBS), one of the great challenges in calculation of the UTD surface diffracted fields is the difficulty in determining the geodesic paths al...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2015/604861 |
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| author | Song Fu Yun-Hua Zhang Si-Yuan He Xi Chen Guo-Qiang Zhu |
| author_facet | Song Fu Yun-Hua Zhang Si-Yuan He Xi Chen Guo-Qiang Zhu |
| author_sort | Song Fu |
| collection | DOAJ |
| description | Although the uniform theory of diffraction (UTD) could be theoretically applied to arbitrarilyshaped convex objects modeled by nonuniform rational B-splines (NURBS), one of the great challenges in calculation of the UTD surface diffracted fields is the difficulty in determining the geodesic paths along which the creeping waves propagate on arbitrarilyshaped NURBS surfaces. In differential geometry, geodesic paths satisfy geodesic differential equation (GDE). Hence, in this paper, a general and efficient adaptive variable step Euler method is introduced for solving the GDE on arbitrarilyshaped NURBS surfaces. In contrast with conventional Euler method, the proposed method employs a shape factor (SF) ξ to efficiently enhance the accuracy of tracing and extends the application of UTD for practical engineering. The validity and usefulness of the algorithm can be verified by the numerical results. |
| format | Article |
| id | doaj-art-d611e23c4d9540e3a4eb222104eed297 |
| institution | Kabale University |
| issn | 1687-5869 1687-5877 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-d611e23c4d9540e3a4eb222104eed2972025-02-03T01:09:04ZengWileyInternational Journal of Antennas and Propagation1687-58691687-58772015-01-01201510.1155/2015/604861604861Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler MethodSong Fu0Yun-Hua Zhang1Si-Yuan He2Xi Chen3Guo-Qiang Zhu4School of Electronic Information, Wuhan University, Wuhan 430072, ChinaSchool of Electronic Information, Wuhan University, Wuhan 430072, ChinaSchool of Electronic Information, Wuhan University, Wuhan 430072, ChinaNo. 29 Research Institute, China Electronics Technology Group Corporation, Chengdu 610000, ChinaSchool of Electronic Information, Wuhan University, Wuhan 430072, ChinaAlthough the uniform theory of diffraction (UTD) could be theoretically applied to arbitrarilyshaped convex objects modeled by nonuniform rational B-splines (NURBS), one of the great challenges in calculation of the UTD surface diffracted fields is the difficulty in determining the geodesic paths along which the creeping waves propagate on arbitrarilyshaped NURBS surfaces. In differential geometry, geodesic paths satisfy geodesic differential equation (GDE). Hence, in this paper, a general and efficient adaptive variable step Euler method is introduced for solving the GDE on arbitrarilyshaped NURBS surfaces. In contrast with conventional Euler method, the proposed method employs a shape factor (SF) ξ to efficiently enhance the accuracy of tracing and extends the application of UTD for practical engineering. The validity and usefulness of the algorithm can be verified by the numerical results.http://dx.doi.org/10.1155/2015/604861 |
| spellingShingle | Song Fu Yun-Hua Zhang Si-Yuan He Xi Chen Guo-Qiang Zhu Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method International Journal of Antennas and Propagation |
| title | Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method |
| title_full | Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method |
| title_fullStr | Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method |
| title_full_unstemmed | Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method |
| title_short | Creeping Ray Tracing Algorithm for Arbitrary NURBS Surfaces Based on Adaptive Variable Step Euler Method |
| title_sort | creeping ray tracing algorithm for arbitrary nurbs surfaces based on adaptive variable step euler method |
| url | http://dx.doi.org/10.1155/2015/604861 |
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