spline loop

• Click on a circle, then release the mouse button to remove the circle.
• Click on the curve, move the mouse, then release the button to change the shape.

• note: this is adaptation of a program for splines
  
• The equations for a loop are, of course, similar to the equations for an open curve. However, they lead to an equation that involves a matrix that is non-diagonal (and not even band-diagonal), because there is an element in every corner.
  

    |   b0 c0 0  0  ...    .      .      .      a0    |
    |   a1 b1 c1 0  ...    .      .      .      0     |
    |   0  a2 b2 c2 ..     .      .      .      0     |
    |   .   . .  .  ...    .      .      .      .     | 
    |   .   . .  .  ...    .      .      .      .     |
    |   0   0 0  0  ... a[n-3] b[n-3] c[n-3]    0     |
    |   0   0 0  0  ...    0   a[n-2] b[n-2]  c[n-2]  |
    |c[n-1] 0 0  0  ...    0      0   a[n-1]  b[n-1]  |
  

  However, there are so many zeros in the matrix, that gaussian elimination can be reduced to a process of order n (in stead of n²).
  Read the theory for details.
  Or look at the source code for details.
  Or you may tinker with the development code to try alternative calculations.