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Fitting points from a straight line segment onto a circular segment

  1. Mar 12, 2007 #1
    Hello, I have a problem I need to solve quickly... basically, I have a set of points in 3D space that make up a straight segment of a nanotube, and I want to "bend" the points along a circle (to simulate what happens if you bend a nanotube into a torus). I basically want to do to all of my nanotube segment points what I've indicated in the attached image of points along one straight line.

    The problem: I don't know what to do! Is this a relatively simple procedure, or would it be quite a task? Is there a simple operation I can apply to each point (that is say, some distance R from some fixed point and some distance K from some fixed line) that would result in this sort of "central bending" like in the picture?

    Any help anyone could provide would be GREATLY, GREATLY appreciated. Thank you!

    Attached Files:

  2. jcsd
  3. Mar 12, 2007 #2
    What are the forces involved in the bending?

    It seems that the points should be connected by hookes law springs. Then it is a matter of solving the diff eq according to the boundary conditions!

    I would be happy to help you, using mathematica, if you can better define the goal of the simulation.
  4. Mar 13, 2007 #3
    Sorry for not giving enough info. I have already written a simulation that connects the points by Hooke's law springs (sort of, there's a few more terms in there); now I just want to wrap the vertices of the nanotube around a circle and show the forces acting on certain atoms that result from this bending. I'm using C++ and OpenGL.

    I know what I'm doing is physics simulation faux pas, but I just want to see what will happen. (My simul is not animated, either, it just colors each carbon based on the total force acting on the carbon).
  5. Mar 13, 2007 #4
    Not a faux pas, just a constraint!

    If I understand correctly, you want to setup the position of the carbons to lie on a circle, and then calculate the net force on each carbon?

    But doesn't your hooke-like system of equations give you the force on each carbon as a function of its relative position with all others?
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