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Great circle stereographic trajectory representation. (English) Zbl 0656.65030

The problem of determining sufficiently accurate trajectory approximations to great circle routes is solved by obtaining expressions for the conformal latitude and conformal longitude in closed form as functions of time. This formulation allows the time of maximum deviation between a linear trajectory model and the true stereographic projection to be calculated in an efficient manner using Newton’s method. An algorithm for determining near-minimal trajectory representations for achieving a prescribed accuracy is described and numerical results for a typical great circle route are presented.

MSC:

65D15 Algorithms for approximation of functions
86A30 Geodesy, mapping problems
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References:

[1] Thomas, P. D., Conformal projections in geodesy and cartography, U.S. Department of Commerce, Coast and Geodetic Survey Special Publication No. 251 (1952)
[2] Saleh, N.; Smith, A.; Sokkappa, B., The stereographic projection in the national airspace system; principles, approximations and errors, The MITRE Corp., MTR-83W67 (May 1983)
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