Make a CSPICE plane from a point and two spanning vectors. 

   PLANES 

   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   point, 
   span1, 
   span2      I   A point and two spanning vectors defining a plane. 
   plane      O   A CSPICE plane representing the plane. 

   point, 
   span1, 
   span2          are, respectively, a point and two spanning vectors 
                  that define a geometric plane in three-dimensional 
                  space. The plane is the set of vectors 

                     point   +   s * span1   +   t * span2 

                  where s and t are real numbers.  The spanning 
                  vectors span1 and span2 must be linearly 
                  independent, but they need not be orthogonal or 
                  unitized. 

   plane          is a CSPICE plane that represents the geometric 
                  plane defined by point, span1, and span2. 

   None. 

   CSPICE 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 CSPICE routines that produce CSPICE planes from data that 
   define a plane are: 

      nvc2pl_c ( Normal vector and constant to plane ) 
      nvp2pl_c ( Normal vector and point to plane    ) 
      psv2pl_c ( Point and spanning vectors to plane ) 

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

      pl2nvc_c ( Plane to normal vector and constant ) 
      pl2nvp_c ( Plane to normal vector and point    ) 
      pl2psv_c ( 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. 

   1)  Project a vector v orthogonally onto a plane defined by 
       point, span1, and span2.  proj is the projection we want; it 
       is the closest vector in the plane to v. 

          psv2pl_c ( point,  span1,   span2,  &plane ); 
          vprjp_c  ( v,      &plane,  proj           );


   2)  Find the plane determined by a spacecraft's position vector 
       relative to a central body and the spacecraft's velocity 
       vector.  We assume that all vectors are given in the same 
       coordinate system. 

          /.
          pos is the spacecraft's position, relative to 
          the central body.  vel is the spacecraft's velocity 
          vector.  pos is a point (vector, if you like) in 
          the orbit plane, and it is also one of the spanning 
          vectors of the plane. 
          ./
          psv2pl_c ( pos, pos, vel, &plane );

   None. 

   1)  If span1 and span2 are linearly dependent, then the vectors 
       point, span1, and span2 do not define a plane.  The error 
       SPICE(DEGENERATECASE) is signaled. 

   None. 

   N.J. Bachman   (JPL) 

   [1] `Calculus and Analytic Geometry', Thomas and Finney. 

   -CSPICE Version 1.0.0, 05-MAR-1999 (NJB)

   point and spanning vectors to plane