Superquadric Fitting
Channel: CurvSurf
Date: 2012-08-20

Ellipsoid-Superellipsoid fitting to the 30 points of:

      [-4,3,13],[1,16,29],[4,-11,10],[20,-17,22],[-11,1,4],[-26,7,-8],
      [-3,-13,1],[-7,-26,-15],[6,19,9],[11,24,19],[22,-8,4],[30,-9,12],
      [-8,15,-9],[-6,15,-18],[8,-13,-15],[3,-18,-25],[15,9,21],[18,-3,22],
      [-21,3,-13],[-4,-14,-22],[-2,19,11],[-14,14,1],[20,-17,15],[4,-20,-18],
      [6,20,24],[26,-14,17],[-22,12,-13],[-2,-22,-20],[-3,-3,9],[7,1,-5].

The initial values of ellipsoid are taken from the mass center and
the central rms distance of the 30 points:

Initial ellipsoid: (a, b, c, Xo, Yo, Zo, Omega, Phi, Kappa,) =
                 (25.66, 25.66, 25.66, 1.93, -1.00, 2.07, 0.0, 0.0, 0.0).

Fitting results:

Ellipsoid: (a, b, c, Xo, Yo, Zo, Omega, Phi, Kappa,) =
       (9.4018, 25.3691, 53.5932, 0.8967, -2.5021, -0.9564, -0.3021, 0.6266, 0.6803).

Superellipsoid: (a, b, c, e1, e2, Xo, Yo, Zo, Omega, Phi, Kappa,) =
         (24.6719, 20.4927, 8.2460, 0.0946, 0.0374, 1.9096, -1.0234, 2.0191, -2.4454, 0.6952, -0.6960).

Mathematics used: Orthogonal Distance Fitting.

Reference: S.J. Ahn, "Least Squares Orthogonal Distance Fitting of Curves and Surfaces in Space", Springer-Verlag, 2005.