Procedure

   psv2pl_c ( Point and spanning vectors to plane ) 

   void psv2pl_c ( ConstSpiceDouble    point[3],
                   ConstSpiceDouble    span1[3],
                   ConstSpiceDouble    span2[3],
                   SpicePlane        * plane    )

Abstract

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

Required_Reading

   PLANES

Keywords

   GEOMETRY
   MATH
   PLANE

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   point,
   span1,
   span2      I   A point and two spanning vectors defining a plane.
   plane      O   A SPICE plane representing the plane.

Detailed_Input

   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.

Detailed_Output

   plane       is a SPICE plane that represents the geometric
               plane defined by `point', `span1', and `span2'.

Parameters

   None.

Exceptions

   1)  If `span1' and `span2' are linearly dependent, i.e. the vectors
       `point', `span1', and `span2' do not define a plane, the error
       SPICE(DEGENERATECASE) 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, 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 );

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

   point and spanning vectors to plane