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?