Numerical determination of the geodesic curves: the solution of a two-point boundary value problem

Document Type : Original Article


1 Department of Surveying Engineering, Arak University of Technology, Arak, Iran

2 Department of Geomatics Engineering, University of Calgary, Calgary, Alberta, Canada


In this paper, we suggest a simple iterative method to find the geodesic path on a surface parameterized by
orthogonal curvilinear system between two given points based on solving Boundary Value Problem. In this
supposed method, an iterative algorithm is used for finding the sufficient initial values as the destination
point agree with the boundary conditions. Geodesic determination between two given points is formulated
for a general surface, and specially tested for reference ellipsoid which has many applications in
geosciences and geodesy. Accuracy of the method is independent on the distant between two points on the
surface. Moreover, it can be used in aviation and sailings for finding the shortest path between start and
destination points.


Main Subjects

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