Hello all I was hoping someone could help me with the following problem. I work on the railroads and my task is to improve the alignment of a curve. I have surveyed the existing geometry by going along the track and recording x, y, z co-ordinates at approx 1m intervals. I have plotted these points and then I have created a function that creates a smooth alignment. The problem is during the implementation. What I mean is this; on the railroads we have a machine called a Track Alignment Machine which is a rectangular locomotive which sits on the track and picks the track up and moves it left or right and puts it back down depending on the required design alignment. The Track Alignment Machine only moves the track at right angles to itself. So if the Track Alignment Machine was on a curve then every time the machine moves the track that movement whether it be left or right would be tangent to the curve. My problem it that how I implement my design alignment i.e f(x) if I can only move the track tangentially . I know need to know how much to move the track in both the x and y plane. Attached is a basic diagram of what I am referring to. Any help will b greatly appreciated.