Great circle stereographic trajectory representation (Q1110267)

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.