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      Given a 3-dimensional distribution of points, determines the best
      ellipsoidal shape using particles in an interatively-defined ellipsoid
      (or ellipsoidal shell) of the same shape.



Calling Sequence

      Result = SHAPE_ITERATIVE(Pos, Radius)


      Pos: An Nx3 array specifying the 3d positions of the N particles
                that make up the mass distribution.
      Radius: Radius at which to compute the shape. For a filled ellipsoid,
                this is the geometric mean radius of the principal axes that
                define the outer limits of the ellipsoid; for an ellipsoidal shell,
                this is the geometric mean radius at the center of the shell.

Keyword Parameters

      SHELL: Use an ellipsoidal shell rather than a filled ellipsoid. The
              value is the width of the shell.
      AXES: An output 3x3 array containing the principal axes.
              AXES[*,i] is the direction of the i-th principal axis.
      MASSES: An N-element vector of the mass of each point. If not
              specified, all masses are assumed to be unity.
      R2WEIGHT: If /R2WEIGHT is specified then particles are downweighted
                by a factor of 1/r^2 so that all particles have equal
                effect regardless of radius.
      FVAL: Iterate until the axis ratios and directions of the axes
                vary by less than FVAL. Default is 0.001.
      MAXIT: Maximum number of iterations to allow. Default is 20.
      VERBOSE: Print information about each iteration.


      The function returns a 3-element array containing the lengths of the
      principal axes of the ellipse.


      Set up a 1/r^2 ellipsoidal density distribution and find its shape.
      np = 100000
      r = 200 * randomu(seed, np)
      ph = 2. * !pi * randomu(seed, np)
      th = acos(randomu(seed, np))
      x = 2. * r * cos(ph) * sin(th)
      y = r * sin(ph) * sin(th)
      z = 3. * r * cos(th)
      print, shape_iterative([[x],[y],[z]], 100., axes=axes)
      print, axes

Modification History

      Written by: Jeremy Bailin
      22 July 2011 Initial release

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