Minimal direction displacement with defined constraint

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Given:



  • $n$ angles $phi_0 lt ... lt phi_n-1$ ($0 leq phi_i lt
    2pi)$

  • $delta$ ($2ndelta leq 2pi$)

Find new angles $theta_0, ..., theta_n-1$ such that $ |theta_i - theta_j| geq delta$ for every pair $(i, j) in (0,1), (1,2), ..., (n-2,n-1), (n-1, 0)$
and that $sum_i=0^n-1(phi_i - theta_i)^2$ is minimal.



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geometry optimization




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    Given:



    • $n$ angles $phi_0 lt ... lt phi_n-1$ ($0 leq phi_i lt
      2pi)$

    • $delta$ ($2ndelta leq 2pi$)

    Find new angles $theta_0, ..., theta_n-1$ such that $ |theta_i - theta_j| geq delta$ for every pair $(i, j) in (0,1), (1,2), ..., (n-2,n-1), (n-1, 0)$
    and that $sum_i=0^n-1(phi_i - theta_i)^2$ is minimal.



    MSPaint sketch




    geometry optimization




    share|cite|improve this question























      up vote
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      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Given:



      • $n$ angles $phi_0 lt ... lt phi_n-1$ ($0 leq phi_i lt
        2pi)$

      • $delta$ ($2ndelta leq 2pi$)

      Find new angles $theta_0, ..., theta_n-1$ such that $ |theta_i - theta_j| geq delta$ for every pair $(i, j) in (0,1), (1,2), ..., (n-2,n-1), (n-1, 0)$
      and that $sum_i=0^n-1(phi_i - theta_i)^2$ is minimal.



      MSPaint sketch




      geometry optimization




      share|cite|improve this question













      Given:



      • $n$ angles $phi_0 lt ... lt phi_n-1$ ($0 leq phi_i lt
        2pi)$

      • $delta$ ($2ndelta leq 2pi$)

      Find new angles $theta_0, ..., theta_n-1$ such that $ |theta_i - theta_j| geq delta$ for every pair $(i, j) in (0,1), (1,2), ..., (n-2,n-1), (n-1, 0)$
      and that $sum_i=0^n-1(phi_i - theta_i)^2$ is minimal.



      MSPaint sketch





      geometry optimization





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 31 at 19:45
























      asked Jul 31 at 19:11









      lovenjak

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