Closest point

[Aurélien Géron]

Hi,

I am developping a geography server (based on R-Trees) and I need to
calculate the minimum distance between a point M(latitude mt, longitude mg)
on the surface of the earth and a path P defined as follows:
P corresponds to a straight line between two points A(latitude at, longitude
ag) and B(latitude bt, longitude bg) on a cylindric projection (longitude on
the x axis, latitude on the y axis).

In other words, P is the set of points whose coordinates can be written like
this (0 <= x <= 1):
latitude(x) = (bt - at)*x + at
longitude(x) = (bg - ag)*x + ag

Note that I consider earth to be a perfect sphere and - in order to simplify
matters - I even assume that its radius is equal to one. I know that earth
is actually closer to an ellipsoid, and there are mountains, but I ignore
them for this version ! ;-)

Thanks for your help !
Aurélien Géron.