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The euclidean steiner tree for 3 vertices (a,b,c) can be constructed by adding a steiner point (s) connecting 3 edges (as, bs, cs). One way to define the distance of edge (as, bs, cs) is by calculating the gromov product of 3 vertices, such that

d(a,s) = 0.5 * ( d(a,c) + d(a,b) - d(b,c) ) d(b,s) = 0.5 * ( d(b,c) + d(b,a) - d(a,c) ) d(c,s) = 0.5 * ( d(a,c) + d(b,c) - d(a,b) )

May I know is there other method to calculate the distance of steiner point from each set of vertices?

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Title asks for coordinates of Steiner point, body asks for distances from Steiner point to vertices. These are different, no? Please edit so title and body agree. –  Gerry Myerson Aug 17 '12 at 7:27
    
alright, calculating distance of steiner point from each vertices are what I am trying to look at.. –  twfx Aug 19 '12 at 9:05
    
The formulas you've given look amazingly simple. Why do you want another method? –  Gerry Myerson Aug 19 '12 at 9:47

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