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Required Reading


   CSPICE_PL2NVC returns a unit normal vector and constant defining
   a specified plane.



      plane   a structure describing a SPICE plane.

              [1,1] = size(plane); struct = class(plane)

              The structure has the fields:

                 normal:     [3,1] = size(normal); double = class(normal)
                 constant:   [1,1] = size(constant); double = class(constant)

   the call:

      [normal, constant] = cspice_pl2nvc( plane )


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

      constant   [1,1] = size(constant); double = class(constant)

                 are, respectively, a unit normal vector and
                 constant that define the geometric plane
                 represented by 'plane'.  Let the symbol < a, b >
                 indicate the inner product of vectors a and b; then
                 the geometric plane is the set of vectors x in
                 three-dimensional space that satisfy

                    < x,  normal >  =  constant.

                 'normal' is a unit vector. 'constant' is the distance
                 of the plane from the origin;

                    constant * normal

                 is the closest point in the plane to the origin.


   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.

      % A simple task, determine the distance of a plane
      % from the origin.
      % Define the plane with a vector normal to the plane
      % and a point in the plane.
      normal = [ -1.;  5.;    -3.5 ];
      point  = [  9.; -0.65;  -12. ];

      % create the SPICE plane from the normal and constant.
      plane = cspice_nvp2pl( normal, point );

      % Calculate the normal vector and constant defining
      % the plane. The constant value is the distance from
      % the origin to the plane.
      [normal, constant ] = cspice_pl2nvc( plane )

      % Confirm the results. Calculate a vector
      % from the origin to the plane.
      vec = constant * normal;

      % Now calculate a vector in the plane from the
      % location in the plane defined by 'vec'.
      plane_vec = vec - point;

      % These vectors should be orthogonal.
      dot( plane_vec, vec )

   MATLAB outputs:

      normal =


      constant =


   The dot product result to check orthogonality...

      ans =


   Zero, to double precision round-off, so orthogonal to that


   Mice geometry routines that deal with planes use the `plane'
   data type to represent input and output planes.  This data type
   makes the subroutine interfaces simpler and more uniform.

   The Mice routines that produce SPICE planes from data that
   define a plane are:

      cspice_nvc2pl ( Normal vector and constant to plane )
      cspice_nvp2pl ( Normal vector and point to plane    )
      cspice_psv2pl ( Point and spanning vectors to plane )

   The Mice routines that convert SPICE planes to data that
   define a plane are:

      cspice_pl2nvc ( Plane to normal vector and constant )
      cspice_pl2nvp ( Plane to normal vector and point    )
      cspice_pl2psv ( Plane to point and spanning vectors )

   Any of these last three routines may be used to convert this
   routine's output, 'plane', to another representation of a
   geometric plane.

Required Reading

   For important details concerning this module's function, please refer to
   the CSPICE routine pl2nvc_c.



   -Mice Version 1.0.0, 27-AUG-2012, EDW (JPL)


   plane to normal vector and constant

Wed Apr  5 18:00:34 2017