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:
“You will find that reason, which always ought to direct mankind, seldom does; but that passions and weaknesses commonly usurp its seat, and rule in its stead.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Will women find themselves in the same position they have always been? Or do we see liberation as solving the conditions of women in our society?... If we continue to shy away from this problem we will not be able to solve it after independence. But if we can say that our first priority is the emancipation of women, we will become free as members of an oppressed community.”
—Ruth Mompati (b. 1925)