Procedure

   nvp2pl_c ( Normal vector and point to plane ) 

   void nvp2pl_c ( ConstSpiceDouble    normal[3],
                   ConstSpiceDouble    point [3],
                   SpicePlane        * plane     )

Abstract

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

Required_Reading

   PLANES

Keywords

   GEOMETRY
   MATH
   PLANE

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   normal,
   point      I   A normal vector and a point defining a plane.
   plane      O   A SPICE plane structure representing the plane.

Detailed_Input

   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.

Detailed_Output

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

Parameters

   None.

Exceptions

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

Files

   None.

Particulars

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

   The CSPICE routines that produce SPICE 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 SPICE 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.

Examples

   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 );

Restrictions

   None.

Literature_References

   [1]  G. Thomas and R. Finney, "Calculus and Analytic Geometry,"
        7th Edition, Addison Wesley, 1988.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)

Version

   -CSPICE Version 1.0.1, 24-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard.

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

Index_Entries

   normal vector and point to plane