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I am simulating polymers of fixed length and fixed ends. I would like to search the phase space of all possible conformations quickly. Is there anyway I can generate efficiently a lot of (rather) smooth curves of fixed ends and fixed length? An even better option would be to make continues smooth transformations, i.e. the consecutive curves will resemble each other.

Thanks

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  • $\begingroup$ A travelling wave would satisfy your conditions $\endgroup$
    – Piyush Grover
    Commented Nov 6, 2019 at 6:18

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I would consider spline curves, specifically cubic splines. They are smooth curves, can have fixed endpoints and can be deformed into each other relatively easily. Also there are many software libraries that implement them.

This paper includes an algorithm to fix the length of the Bezier Curve.

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  • $\begingroup$ what about the fixed length condition? $\endgroup$
    – Davood Norouzi
    Commented Nov 6, 2019 at 18:55
  • $\begingroup$ @DavoodNorouzi I've added a reference that should help. $\endgroup$
    – Ivan Meir
    Commented Nov 6, 2019 at 19:31
  • $\begingroup$ Thanks. Looks promising. Hope it is computationally cheaper than my current Monte Carlo approach. $\endgroup$
    – Davood Norouzi
    Commented Nov 6, 2019 at 20:04
  • $\begingroup$ It should be an order of magnitude faster in my experience! Best of luck :-) $\endgroup$
    – Ivan Meir
    Commented Nov 6, 2019 at 20:14

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