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Re^2: Algorithm: point with N distance of a line between two other pointsby LanX (Saint) 
on Nov 04, 2010 at 13:30 UTC ( [id://869464]=note: print w/replies, xml )  Need Help?? 
> 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.
Cheers Rolf 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.
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