Fitting points from a straight line segment onto a circular segment

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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!
 

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  • #2
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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.
 
  • #3
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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).
 
  • #4
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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).

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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