Procedure

     PSV2PL ( Point and spanning vectors to plane )

     SUBROUTINE PSV2PL ( POINT, SPAN1, SPAN2, PLANE )

Abstract

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

Required_Reading

     PLANES

Keywords

     GEOMETRY
     MATH
     PLANE

Declarations

     IMPLICIT NONE

     INTEGER               UBPL
     PARAMETER           ( UBPL   =   4 )

     DOUBLE PRECISION      POINT (    3 )
     DOUBLE PRECISION      SPAN1 (    3 )
     DOUBLE PRECISION      SPAN2 (    3 )
     DOUBLE PRECISION      PLANE ( UBPL )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     POINT,
     SPAN1,
     SPAN2      I   A point and two spanning vectors defining a plane.
     PLANE      O   An array 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

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

        NVC2PL ( Normal vector and constant to plane )
        NVP2PL ( Normal vector and point to plane    )
        PSV2PL ( Point and spanning vectors to plane )

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

        PL2NVC ( Plane to normal vector and constant )
        PL2NVP ( Plane to normal vector and point    )
        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.

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.

            CALL PSV2PL ( POINT,   SPAN1,   SPAN2,   PLANE )
            CALL VPRJP  ( 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.

            C
            C     POS is the spacecraft's position, relative to
            C     the central body. VEL is the spacecraft's velocity
            C     vector. POS is a point (vector, if you like) in
            C     the orbit plane, and it is also one of the spanning
            C     vectors of the plane.
            C
                  CALL PSV2PL ( 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)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.2.0, 24-AUG-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.1.0, 31-AUG-2005 (NJB)

        Updated to remove non-standard use of duplicate arguments
        in VMINUS call.

    SPICELIB Version 1.0.1, 10-MAR-1992 (WLT)

        Comment section for permuted index source lines was added
        following the header.

    SPICELIB Version 1.0.0, 01-NOV-1990 (NJB)