Make a CSPICE plane from a normal vector and a point. 

   PLANES 

   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   normal, 
   point      I   A normal vector and a point defining a plane. 
   plane      O   A CSPICE plane structure representing the plane. 

   normal, 
   point 
                  are, respectively, a normal vector and point that 
                  define a plane in three-dimensional space.  normal 
                  need not be a unit vector. 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 - point, normal >  =  0. 

   plane          is a CSPICE plane structure that represents the 
                  geometric plane defined by point and normal. 

   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 
       and normal.  proj is the projection we want; it is the 
       closest vector in the plane to v. 

          nvp2pl_c ( normal,  point,   &plane ); 
          vprjp_c  ( v,       &plane,  proj   );


   2)  Given a point in a plane and a normal vector, find the 
       distance of the plane from the origin.  We make a 
       `plane' from the point and normal, then convert the 
       plane to a unit normal and constant.  The output constant 
       is (according to the specification of pl2nvc_c) the distance of 
       the plane from the origin. 

          nvp2pl_c ( normal,  point,  &plane   ); 
          pl2nvc_c ( &plane,  normal, constant );

   None. 

   1)  If the input vector normal is the zero vector, the error 
       SPICE(ZEROVECTOR) is signaled. 

   None. 

   N.J. Bachman   (JPL) 

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

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

   normal vector and point to plane