Re^2: Algorithm: point with N distance of a line between two other points

[LanX]

> Like Limbic~Region already said if the distance is small, an approximation is good enough, i.e. use a straight line instead of an arc.

IMHO one can choose a spherical projection around the point in question which keeps distances¹ fix, no matter how big the region is.

Shouldn't be too difficult to find corresponding techniques in spherical geometry.

1) maybe its even better to choose gnomonic projection, where "great circles are mapped to straight lines" as long as bigger distances have bigger projections.

UPDATE: ah indeed "Thus the shortest route between two locations in reality corresponds to that on the map.". Of course the real distance on the sphere still has to be calculated after back projecting the "nearest" point.