Journal of Zhejiang University-SCIENCE A

, Volume 7, Supplement 2, pp 187–192 | Cite as

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

  • Wu Ming-hua 
  • Mo Guo-liang Email author
  • Yu Yi-yue 


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 

CLC number



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Copyright information

© Zhejiang University 2006

Authors and Affiliations

  1. 1.School of Computational ScienceZhejiang University City CollegeHangzhouChina
  2. 2.Department of MathematicsZhejiang UniversityHangzhouChina

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