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:
“However strongly they resist it, our kids have to learn that as adults we need the companionship and love of other adults. The more direct we are about our needs, the easier it may be for our children to accept those needs. Their jealousy may come from a fear that if we adults love each other we might not have any left for them. We have to let them know that it’s a different kind of love.”
—Ruth Davidson Bell. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 3 (1978)
“War is not a life: it is a situation,
One which may neither be ignored nor accepted,
A problem to be met with ambush and stratagem,
Enveloped or scattered.”
—T.S. (Thomas Stearns)