Abstract

   CSPICE_FRAME builds a right handed orthonormal frame (x,y,z) from a
   3-dimensional input vector, where the X-axis of the resulting
   frame is parallel to the original input vector.

I/O

   Given:

      x        the vector used to form the first vector of a right-handed
               orthonormal triple.

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

   the call:

      [x, y, z] = cspice_frame( x )

   returns:

      x,
      y,
      z        the vectors that form a right handed orthonormal frame, with
               output `x' parallel to the input `x'.

               [3,1] = size(x); double = class(x)
               [3,1] = size(y); double = class(y)
               [3,1] = size(z); double = class(z)

Parameters

   None.

Examples

   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.

   1) Given some arbitrary vector, create three right handed orthonormal
      frames, each of them with a different coordinate-axis parallel to
      that vector.

      Example code begins here.


      function frame_ex1()

         %
         % Given some arbitrary vector
         %
         vec = [ 23., -3., 18. ]';

         uvec = vec/norm(vec);
         disp( 'Unitary input vector' )
         fprintf( '   %16.8e   %16.8e   %16.8e\n\n', uvec )

         %
         % Create an orthonormal frame with the
         % x axis parallel to vec.
         %
         disp( 'Input vector parallel to output X vector' )

         [ x, y, z ] = cspice_frame( vec );
         fprintf( 'x  %16.8e   %16.8e   %16.8e\n', x )
         fprintf( 'y  %16.8e   %16.8e   %16.8e\n', y )
         fprintf( 'z  %16.8e   %16.8e   %16.8e\n\n', z )



         %
         % Alternative, make a frame with y parallel to
         % vec...
         %
         disp( 'Input vector parallel to output Y vector' )

         [ y, z, x ] = cspice_frame( vec );
         fprintf( 'x  %16.8e   %16.8e   %16.8e\n', x )
         fprintf( 'y  %16.8e   %16.8e   %16.8e\n', y )
         fprintf( 'z  %16.8e   %16.8e   %16.8e\n\n', z )



         %
         % ...or a frame with z parallel to vec.
         %
         disp( 'Input vector parallel to output Z vector' )

         [ z, x, y ] = cspice_frame( vec );
         fprintf( 'x  %16.8e   %16.8e   %16.8e\n', x )
         fprintf( 'y  %16.8e   %16.8e   %16.8e\n', y )
         fprintf( 'z  %16.8e   %16.8e   %16.8e\n\n', z )


      When this program was executed on a Mac/Intel/Octave6.x/64-bit
      platform, the output was:


      Unitary input vector
           7.83383109e-01    -1.02180405e-01     6.13082433e-01

      Input vector parallel to output X vector
      x    7.83383109e-01    -1.02180405e-01     6.13082433e-01
      y    6.16308262e-01     0.00000000e+00    -7.87505001e-01
      z    8.04675803e-02     9.94765884e-01     6.29746281e-02

      Input vector parallel to output Y vector
      x    8.04675803e-02     9.94765884e-01     6.29746281e-02
      y    7.83383109e-01    -1.02180405e-01     6.13082433e-01
      z    6.16308262e-01     0.00000000e+00    -7.87505001e-01

      Input vector parallel to output Z vector
      x    6.16308262e-01     0.00000000e+00    -7.87505001e-01
      y    8.04675803e-02     9.94765884e-01     6.29746281e-02
      z    7.83383109e-01    -1.02180405e-01     6.13082433e-01


      Note the positive nature of the permutation on x-y-z
      in the cspice_frame call.

Particulars

   Given an input vector x, this routine returns unit vectors x,
   y, and z such that xyz forms a right-handed orthonormal frame
   where the output x is parallel to the input x.

   This routine is intended primarily to provide a basis for
   the plane orthogonal to x. There are no special properties
   associated with y and z other than that the resulting xyz frame
   is right handed and orthonormal. There are an infinite
   collection of pairs (y,z) that could be used to this end.
   Even though for a given x, y and z are uniquely determined, users
   should regard the pair (y,z) as a random selection from this
   infinite collection.

Exceptions

   1)  If `x' on input is the zero vector the "standard" frame (ijk)
       is returned.

   2)  If the input argument `x' is undefined, an error is signaled
       by the Matlab error handling system.

   3)  If the input argument `x' is not of the expected type, or it
       does not have the expected dimensions and size, an error is
       signaled by the Mice interface.

Files

   None.

Restrictions

   None.

Required_Reading

   MICE.REQ
   FRAMES.REQ

Literature_References

   None.

Author_and_Institution

   J. Diaz del Rio     (ODC Space)
   S.C. Krening        (JPL)
   E.D. Wright         (JPL)

Version

   -Mice Version 1.1.0, 03-JUL-2021 (EDW) (JDR)

       Edited the header to comply with NAIF standard.
       Reformatted example's output and added problem statement.

       Added -Parameters, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections.

       Eliminated use of "lasterror" in rethrow.

       Removed reference to the function's corresponding CSPICE header from
       -Required_Reading section.

   -Mice Version 1.0.0, 12-MAR-2012 (EDW) (SCK)

Index_Entries

   build a right handed coordinate frame