Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help Re-Designing A Curve Using X Y Z Co-ordinates

  1. Mar 12, 2012 #1
    Hello all

    I work in railway transport.

    I am trying to re-design an existing railway curve; the existing curvature has several irregularities which result in the train being laterally displaced as it traverses the curve.

    What I have done is taken x,y and z co-ordinates along the railway curve and named each point A, B C … and so on.

    Using this data I want to re-design the curve so that the irregularities of the curve are removed, the only restriction I have is that I am only allowed to move the curve, at a particular point, tangent to the curve at that point.

    Attached is a basic diagram of I am referring to.
    • The red dots represent the points along the curve I have taken x y z co-ordinates.
    • The blue line represents the tangent line at that point.
    • The arrow which is 90 degrees to the tangent line represents the directions which the curve at that point can be moved to.

    Can anybody shed any light on how I can manipulate the co-ordinates such that I can smooth out the curve but making sure that any movement is tangential.

    Thank you or your help.

    Attached Files:

  2. jcsd
  3. Mar 12, 2012 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    I don't know about railroad tracks, but curves on roads are usually laid out by finding the circular arc that joins two tangents to the road. To lay out your track that way using the tangents at D and G, you would have to put additional points and tangents between D and G and use an "S" shaped figure with two curves going in opposite directions.

    It looks simpler to join the the tangents at C and G with a circular arc.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook