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

I think that what you really want is the distance of a point to a segment, and not the distance to a line. Because a line is infinite, and the shortest distance of a point to a line might fall outside your segment.

In the case below, the distance of the point C to the line AB is CP. But P is outside of your segment, and what you really want is CA and not CP.

                 /
                x (B)
               /
              /
             /
 x (C)      x (A)
   `.      /
      `.  /
        `x
        / (P)
       /
      /
[download]

So, you must find the coordinate of P (the distance to the line) then check if P is outside of your segment. If it's outside, then you compute CA and CB and take the shortest.

Comment on Re: Algorithm: point with N distance of a line between two other points Download Code

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Re^2: Algorithm: point with N distance of a line between two other points by japhy (Canon) on Nov 03, 2010 at 20:08 UTC
Ooh, very good catch. Thank you for that! Jeff `japhy` Pinyan, P.L., P.M., P.O.D, X.S.: Perl, regex, and `perl` hacker Nos autem praedicamus Christum crucifixum (1 Cor. 1:23) - The Cross Reference (My Blog)	[reply]
Re^2: Algorithm: point with N distance of a line between two other points by DrHyde (Prior) on Nov 04, 2010 at 11:26 UTC
In fact, I believe that you want ... `(sort { $a <=> $b } (\|CA\|, \|CB\|, \|CP\|))[1]` [download] where \|...\| means "the distance between these points". Of course, because the OP is working with points on a curved surface, he may need to work with great circle distances (and even then he has to allow for the planet not being spherical if he wants to be really precise) whereas lots of the solutions you'll find online assume that you're working on a plane. The assumption that the surface is a plane really breaks down once you're talking about distances of more than a few hundred km.	[reply] [d/l]