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:
“I make this direct statement to the American people that there is far less chance of the United States getting into war, if we do all we can now to support the nations defending themselves against attack by the Axis than if we acquiesce in their defeat, submit tamely to an Axis victory, and wait our turn to be the object of attack in another war later on.”
—Franklin D. Roosevelt (1882–1945)
“If a problem is insoluble, it is Necessity. Leave it alone.”
—Mason Cooley (b. 1927)