基于自适应变步长欧拉法的NURBS曲面爬行波寻迹算法
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摘要
虽然一致性几何绕射理论(UTD)理论上可以应用于由非均匀有理B样条(NURBS)建模的任意形状的曲面,但UTD表面衍射场的计算中有一个巨大挑战,即难以确定爬行波在任意形状的NURBS表面上传播的测地线路径。在微分几何中,测地路径满足测地微分方程(GDE)。因此,引入了一种通用且高效的自适应变量欧拉法来解决任意形状的NURBS曲面上的GDE。与传统的欧拉法相比,所提出的方法采用形状因子(SF)ξ来有效提高跟踪精度,并扩展了UTD在实际工程中的应用。算法的有效性和有用性可以通过数值计算结果进行验证。
Although the uniform theory of diffraction(UTD) could be theoretically applied to arbitrarily-shaped convex objects modeled by non-uniform 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 arbitrarily-shaped NURBS surfaces. In dif-ferential 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 arbitrarily-shaped 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.
Although the uniform theory of diffraction(UTD) could be theoretically applied to arbitrarily-shaped convex objects modeled by non-uniform 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 arbitrarily-shaped NURBS surfaces. In dif-ferential 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 arbitrarily-shaped 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.
引文
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[3]SURAZHSKY V,SURAZHSKY T,KIRSANOV D,et al.Fast exact and approximate geodesics on meshes[J].ACM Transactions on Graphics,2005,24(3):553-560.
[4]JHA R M,BOKHARI S A.A novel ray tracing on general paraboloids of revolution for UTD applications[J].IEEE Antennas and Propagation Magazine,1993,41(7):934-939.
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[7]李坤,刘涛,王永建,等.基于小波变换的电力线通信信号识别研究[J].电子技术应用,2016,42(6):113-120.
[8]BOCHM W.Generating the Bezier points of b-spline curves and surfaces[J].Computer Aided Design,1981,13(16):365-366.
[9]Fu Song,Zhang Yunhua,He Siyuan,et al.Creeping ray tracing algorithm for arbitrary NURBS surfaces based on adaptive variable step Euler method[J].International Journal of Antennas and Propagation,2015(5):1-12.
[10]付松.介质涂覆目标表面爬行波寻迹及其电磁绕射建模方法研究[D].武汉:武汉大学,2015.
[2]JHA R M,WIESBECK W.The geodesic constant method:a novel approach to analytical surface-ray tracing on convex conducting bodies[J].IEEE Antennas and Propagation Magazine,1995,37(5):28-38.
[3]SURAZHSKY V,SURAZHSKY T,KIRSANOV D,et al.Fast exact and approximate geodesics on meshes[J].ACM Transactions on Graphics,2005,24(3):553-560.
[4]JHA R M,BOKHARI S A.A novel ray tracing on general paraboloids of revolution for UTD applications[J].IEEE Antennas and Propagation Magazine,1993,41(7):934-939.
[5]P魪REZ J,C魣TEDRA M F.RCS of electrically large targets modeled with NURBS surfaces[J].Electronics Letters,1992,28(12):1119-1122.
[6]P魪REZ J,C魣TEDRA M F.Application of physical optics to the RCS computation of bodies modeled with NURBS surfaces[J].IEEE Transactions on Antennas and Propagation,1994,42(2):1404-1411.
[7]李坤,刘涛,王永建,等.基于小波变换的电力线通信信号识别研究[J].电子技术应用,2016,42(6):113-120.
[8]BOCHM W.Generating the Bezier points of b-spline curves and surfaces[J].Computer Aided Design,1981,13(16):365-366.
[9]Fu Song,Zhang Yunhua,He Siyuan,et al.Creeping ray tracing algorithm for arbitrary NURBS surfaces based on adaptive variable step Euler method[J].International Journal of Antennas and Propagation,2015(5):1-12.
[10]付松.介质涂覆目标表面爬行波寻迹及其电磁绕射建模方法研究[D].武汉:武汉大学,2015.