# 基于计算机代数系统的常用航线在不同投影下的可视化Visualization of Common Routes Based on Different Projections by Computer Algebra System

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The rhumb line, great circle route and large ellipse route are commonly used in the field of navi-gation and aviation, but it is difficult to analyze the different manifestations of them under the dif-ferent types of projection through the route equation. The computer algebra system not only has powerful symbolic operation function, but also has a strong image visualization function. It has the advantages in the application of drawing of map projection, calculation and analysis of projection deformation, and the transformation of projection. In this paper, by using the computer algebra system software Mathematica, the contour route, great circle route and large ellipse route are drawn under the different types of map projection based on the earth sphere model and ellipsoid model, respectively, which provide the strong support for research and teaching work on route planning in the field of aviation and navigation.

1. 引言

2. Mathematica简介

Mathematica软件是由美国Wolfram Research公司开发的一款计算机代数分析软件，是集成了数值计算、符号运算和可视化图形系统等多种功能的集成式、交互式符号运算系统。该软件凭借其强大的符号运算功能、二维和三维函数可视化功能以及多门学科的数据集，广泛应用于测绘、生物、金融等领域 [18] [19] 。

Table 1. Map editing command of Mathematica

Figure 1. Rhumb line on mercator projection and transverse mercator projection plane

3. 不同投影下的航线展绘

3.1. 不同投影下的国内航线展绘

Table 2. Parameters configuration of domestic route

(a) (b) (c) (d)

Figure 2. Rhumb line and great circle route on different projection planes (domestic). (a) Mercator projection; (b) Equidistance conical projection; (c) Polar stereographic projection; (d) Lambert isometric conical projection

3.2. 不同投影下的国际航线展绘

Table 3. Parameters configuration of international route

(a) (b) (c) (d)

Figure 3. Rhumb Line and Great Circle Route on Different Projection Planes (International). (a)Mercator Projection on Sphere; (b) Transverse Mercator Projectionon Sphere; (c)Equidistance Conical Projection on Sphere; (d) Lambert Isometric Conical Projection on Sphere

4. 结束语

(a) (b) (c) (d)

Figure 4. Rhumb line and large ellipse route on different projection planes (international). (a) Mercator projection on ellipsoid; (b) Transverse mercator projection on ellipsoid; (c) Equidistance conical projection on ellipsoid; (d) Lambert isometric conical projection on ellipsoid.

NOTES

*通讯作者。

 [1] 李宏利. 论等角航线的正反解[J]. 中国航海, 1989(1): 47-52. [2] Kaplan, G.H. (1995) Practical Sailing Formulas for Rhumb-Line Tracks on an Oblate Earth. Navigation, 42, 313-326. https://doi.org/10.1002/j.2161-4296.1995.tb01893.x [3] Bennett, G.G. (1996) Practical Rhumb Line Calculations on the Spheroid. Journal of Navigation, 49, 112-119. https://doi.org/10.1017/S0373463300013151 [4] 赵俊生, 刘雁春, 翟国君, 等. 恒向线与大地线长度差异的研究[J]. 海洋测绘, 2007, 27(4): 1-5. [5] 李厚朴, 边少锋. 等角航线正反解算的符号表达式[J]. 大连海事大学学报, 2008, 34(2): 15-18. [6] 张志衡, 彭认灿, 董箭, 等. 极地海区等距离正圆柱投影平面上等角航线的展绘方法[J]. 测绘科学技术学报, 2015, 32(5): 535-538. [7] Horton, J.O. (1968) Great Circle Route. Navigation, 15, 257-259. https://doi.org/10.1002/j.2161-4296.1968.tb01614.x [8] 付职忠. 大圆距离及大圆航向的计算[J]. 中国民航学院学报, 1990, 8(1): 1-10. [9] 洪德本. 解析法大圆航线的设计[J]. 大连海事大学学报, 1997, 23(4): 24-26. [10] 彭劲松, 秦永元. 大圆航线导航与控制律设计[J]. 火力与指挥控制, 2007, 32(6): 62-66. [11] Nastro, V. and Tancredi, U. (2010) Great Circle Navigation with Vectorial Methods. Journal of Navigation, 63, 557-563. https://doi.org/10.1017/S0373463310000044 [12] 丁佳波. 大圆航法与大椭圆航法的航程计算误差[J]. 天津航海, 1996(3): 3-4. [13] Williams, R. (1996) The Great Ellipse on the Surface of the Spheroid. Journal of Navigation, 49, 229-234. https://doi.org/10.1017/S0373463300013333 [14] 李厚朴, 王瑞. 大椭圆航法及其导航参数计算[J]. 海军工程大学学报, 2009, 21(4): 7-12. [15] Tseng, W.K. and Lee, H.S. (2010) Navigation on a Great Ellipse. Journal of Marine Science and Technology, 18, 369-375. [16] Sjöberg, L.E. (2012) Solutions to the Direct and Inverse Navigation Problems on the Great Ellipse. Journal of Geodetic Science, 2, 200-205. https://doi.org/10.2478/v10156-011-0040-9 [17] Tseng, W.K., Guo, J.L. and Liu, C.P. (2013) A Comparison of Great Circle, Great Ellipse, and Geodesic Sailing. Journal of Marine Science and Technology, 21, 287-299. [18] 陈基伟. 数值分析软件Mathematica在测绘中的应用[J]. 上海地质, 2007(1): 50-53. [19] 刘佳奇, 元建胜, 李厚朴. 基于计算机代数系统的地图投影可视化[J]. 黑龙江工程学院学报, 2017, 31(6): 1-5.