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Required Reading


   CSPICE_SAELGV calculates the semi-axis vectors of an ellipse generated
   by two arbitrary three-dimensional vectors.



      vec2   the two vectors defining an ellipse (the generating vectors).

             [3,1]   = size(vec1); double = class(vec1)
             [3,1]   = size(vec2); double = class(vec2)

             The ellipse is the set of points

                center  +  cos(theta) vec1  +  sin(theta) vec2

             where theta ranges over the interval (-pi, pi] and
             center is an arbitrary point at which the ellipse
             is centered.  An ellipse's semi-axes are
             independent of its center, so the vector center
             shown above is not an input to this routine.

             'vec1' and 'vec2' need not be linearly independent;
             degenerate input ellipses are allowed.

   the call:

      [ smajor, sminor ] = cspice_saelgv( vec1, vec2 )


      smajor   the semi-major axis of the ellipse.

               [3,1]   = size(smajor); double = class(smajor)

      sminor   the semi-minor axis of the ellipse.

               [3,1]   = size(sminor); double = class(sminor)


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

      % Define two arbitrary, linearly independent, vectors.
      vec1 = [ 1;  1; 1 ];
      vec2 = [ 1; -1; 1 ];

      % Calculate the semi-major and semi-minor axes of an
      % ellipse generated by the two vectors.
      [ smajor, sminor] = cspice_saelgv( vec1, vec2 )

   MATLAB outputs:

      smajor =


      sminor =



   We note here that two linearly independent but not necessarily
   orthogonal vectors vec1 and vec2 can define an ellipse
   centered at the origin:  the ellipse is the set of points in

      center  +  cos(theta) vec1  +  sin(theta) vec2

   where theta is in the interval (-pi, pi] and center is an
   arbitrary point at which the ellipse is centered.

   This routine finds vectors that constitute semi-axes of an
   ellipse that is defined, except for the location of its center,
   by vec1 and vec2.  The semi-major axis is a vector of largest
   possible magnitude in the set

      cos(theta) vec1  +  sin(theta) vec2

   There are two such vectors; they are additive inverses of each
   other. The semi-minor axis is an analogous vector of smallest
   possible magnitude.  The semi-major and semi-minor axes are
   orthogonal to each other. If smajor and sminor are choices of
   semi-major and semi-minor axes, then the input ellipse can also
   be represented as the set of points

      center  +  cos(theta) smajor  +  sin(theta) sminor

   where theta is in the interval (-pi, pi].

   The capability of finding the axes of an ellipse is useful in
   finding the image of an ellipse under a linear transformation.
   Finding this image is useful for determining the orthogonal and
   gnomonic projections of an ellipse, and also for finding the limb
   and terminator of an ellipsoidal body.

Required Reading

   For important details concerning this module's function, please refer to
   the CSPICE routine saelgv_c.



   -Mice Version 1.0.1, 23-MAR-2015, EDW (JPL)

       Edited I/O section to conform to NAIF standard for Mice documentation.

   -Mice Version 1.0.0, 07-MAY-2008, EDW (JPL)


   semi-axes of ellipse from generating vectors

Wed Apr  5 18:00:34 2017