Fitting points from a straight line segment onto a circular segment

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Discussion Overview

The discussion revolves around the problem of bending a set of points representing a straight segment of a nanotube into a circular segment, simulating the behavior of the nanotube when bent into a toroidal shape. Participants explore the mathematical and physical implications of this bending, including the forces involved and the computational methods for simulating the scenario.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning
  • Experimental/applied

Main Points Raised

  • One participant seeks guidance on how to apply a transformation to the points of a nanotube segment to simulate bending along a circular path.
  • Another participant suggests that the forces involved in the bending could be modeled using Hooke's law springs, proposing to solve differential equations based on boundary conditions.
  • A participant clarifies that they have already implemented a simulation that connects the points with a Hooke's law-like model and expresses a desire to visualize the forces acting on the atoms during the bending process.
  • There is a discussion about the appropriateness of the simulation approach, with one participant asserting that the method is not a faux pas but rather a constraint, while questioning how the forces are calculated based on the relative positions of the atoms.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the simulation method and the specifics of force calculations, indicating that multiple competing perspectives exist regarding the approach to modeling the bending of the nanotube.

Contextual Notes

The discussion includes assumptions about the physical model being used, such as the application of Hooke's law and the nature of the forces acting on the atoms, which may not be fully defined or agreed upon among participants.

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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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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.
 
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).
 
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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