Journal of Zhejiang University SCIENCE A
(Monthly)

2006   Vol. 7   Suppl. II   p. 187-192

Numerical solution of geodesic through two given points on a simple surface

Wu Ming-Hua^†1, Mo Guo-Liang^†‡1, Yu Yi-Yue²

(¹School of Computational Science, Zhejiang University City College, Hangzhou 310015, China)
(²Department of Mathematics, Zhejiang University, Hangzhou 310027, China)
^‡ Corresponding Author
^†E-mail: wmhua@zju.edu.cn; mogl@zucc.edu.cn
Received Jan. 10, 2006 revision accepted Apr. 21, 2006

Abstract: The algorithm for the approximate solution of a geodesic connecting two given points on a simple surface is discussed in this paper. It arises from practical demands of the filament winding technique. Geodesic is the shortest path connecting two given points on a surface and it can also be regarded as the extremal curve of the arc length functional. The nonlinear equation system of the geodesic on some discrete points by means of the direct variation method is explored. By employing Newton’s iterative method, this nonlinear system is transformed into a linear one. And the approximate solution to the geodesic is obtained by solving the resultant linear system. This paper also proves that the iteration is convergent under certain circumstance. Moreover, the result is illustrated with three examples and an appropriate comparison between the analytical solution and the approximate solution to the geodesic is described on the cone surface.

Key words: Geodesic, Filament winding, Functional of arc length
doi:10.1631/jzus.2006.AS0187             CLC number: TP39

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