Direct Problem
Given an initial point (φ1, L1) and initial azimuth, α1, and a distance, s, along the geodesic the problem is to find the end point (φ2, L2) and azimuth, α2.
Start by calculating the following:
Then, using an initial value, iterate the following equations until there is no significant change in σ:
Once σ is obtained to sufficient accuracy evaluate:
If the initial point is at the North or South pole then the first equation is indeterminate. If the initial azimuth is due East or West then the second equation is indeterminate. If a double valued atan2 type function is used then these values are usually handled correctly.
Read more about this topic: Vincenty's Formulae
Famous quotes containing the words direct and/or problem:
“Pleasure is the rock which most young people split upon; they launch out with crowded sails in quest of it, but without a compass to direct their course, or reason sufficient to steer the vessel; for want of which, pain and shame, instead of pleasure, are the returns of their voyage.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.”
—Jean Giraudoux (1882–1944)