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I know that visibility graph is used to determine the shortest path between two points a mong a set of obstacles in the plane. So in the case that obstacles are triangles, is the maximal number of shortest paths between two points 3? Any hint to prove that?

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If you add a flat triangle perpendicular to a straight portion of the path, symmetrically, it doubles the number of shortest paths, so it looks like the maximal number of shortest paths is unbounded. –  galath Apr 25 '12 at 16:10
    
I meant "it increases the number of shortest paths". (doesn't have to be doubled) –  galath Apr 26 '12 at 1:28

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