APPROXIMATION OF THE DISTANCE IN THE PLANE THROUGH THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEMS ASSOCIATED TO GEODESICS
DOI:
https://doi.org/10.17268/sel.mat.2015.02.08Keywords:
Euclidean distance, intrinsec distance, geodesic distance, geodesics, initial value problem, approximationAbstract
In this paper, we proposes an algorithm to approximate the Euclidean distance between points p and q of plane, by doing a search of geodesic that depart from the point p and arrive to a neighborhood of the point q . This search is done through the numerical solution of initial value problems associated with the system of ordinary differential equations of the geodesics; for this is choose a set of directions in the plane.References
Kaya, C. Y, y Noakes, J. L. The Leap-Frog Algorithm and Optimal Control: theoretical aspect. Proceedings of ICOTA 98, Perth, Australia.
Kaya, C. Y, y Noakes, J. L. Geodesic and an Optimal Control Algorithm, Proccedings of the 36 th IEEE CD6, San Diego, California, U.S.A, December 1997.
Noakes, J. L. A Global Algorithm for Geodesics, Journal of the Australian Mathematical Society, 1998.
Keller, H. B. Numerical Methods for Two-Point Boundary-Value Problems, Blaisdell Publishing Co, 1968.
Do Carmo, M. P. Differential Geometry of Curves and Surfaces. Prentice-Hall, Inc, Englewood Cliffs, New Jersey, 1976.
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