﻿ 基于椭球极投影的三维船舶航线高精度绘制 High Accuracy Rendering of 3D Ship Route Using Ellipsoidal Projection

Vol.06 No.01(2017), Article ID:19597,8 pages
10.12677/AAM.2017.61007

High Accuracy Rendering of 3D Ship Route Using Ellipsoidal Projection

Yuanming Song1, Lian Zhou1,2, Jun Chen3

1Department of Mathematics, Shanghai Maritime University, Shanghai

2School of Mathematical Science, University of Science and Technology of China, Hefei Anhui

3Faculty of Science, Ningbo University of Technology, Ningbo Zhejiang

Received: Jan. 2nd, 2017; accepted: Jan. 17th, 2017; published: Jan. 22nd, 2017

ABSTRACT

In order to solve the problem of 3D high accuracy rendering of ship route in electronic navigational chart, a method based on the ellipsoidal projection is presented. Firstly, the ellipsoidal projection is established, and the point on the ellipsoid is one-to-one corresponding to the point on the plane. Secondly, the port and ship position information is projected onto the plane, and a plane interpolation curve is constructed by using Hermite interpolation technique. Then using the inverse ellipsoidal projection, a curve on the earth surface is obtained. Based on the information of the ship heading, the algorithm of 3D route length optimization and multi-route intersection is presented. The automatic generation of 3D route and related calculation are realized. Finally, numerical experiments show that the method is more realistic and more accurate than the existing methods.

Keywords:Ellipsoidal Projection, Route Rendering, Electronic Navigational Chart, 3D Route

1上海海事大学数学系，上海

2中国科学技术大学数学学院，安徽 合肥

3宁波工程学院理学院，浙江 宁波

1. 引言

(a) (b)

Figure 1. Drawing of 3D route. (a) the existing method; (b) our method

2. 椭球极投影

2.1. 纸型

。 (1)

。 (2)

， (3)

Figure 2. Ellipsoidal projection

。(4)

3. 航线绘制

3.1. 三维投影至二维

3.2. 二维投影至三维

4. 航线长度的计算

5. 多组航线交点的求解

6. 数值实验

7. 总结和展望

Figure 3. Relation a between two line

Figure 4. Relation b between two line

Figure 5. Route drawn by data 1

Figure 6. Route drawn by data 2

Figure 7. Route intersection using data 1 and 2

Figure 8. Realistic rendering using data 1

High Accuracy Rendering of 3D Ship Route Using Ellipsoidal Projection[J]. 应用数学进展, 2017, 06(01): 54-61. http://dx.doi.org/10.12677/AAM.2017.61007

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