Procedure

     PL2NVP ( Plane to normal vector and point )

     SUBROUTINE PL2NVP ( PLANE, NORMAL, POINT )

Abstract

     Return a unit normal vector and point that define a specified
     plane.

Required_Reading

     PLANES

Keywords

     GEOMETRY
     MATH
     PLANE

Declarations

     IMPLICIT NONE

     INTEGER               UBPL
     PARAMETER           ( UBPL   =    4 )

     DOUBLE PRECISION      PLANE  ( UBPL )
     DOUBLE PRECISION      NORMAL (    3 )
     DOUBLE PRECISION      POINT  (    3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     PLANE      I   A SPICE plane.
     NORMAL,
     POINT      O   A unit normal vector and point that define PLANE.

Detailed_Input

     PLANE    is a SPICE plane.

Detailed_Output

     NORMAL,
     POINT    are, respectively, a unit normal vector and point
              that define the geometric plane represented by
              PLANE. 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.

              POINT is always the closest point in the input
              plane to the origin. POINT is always a
              non-negative scalar multiple of NORMAL.

Parameters

     None.

Exceptions

     Error free.

     1)  The input plane MUST have been created by one of the SPICELIB
         routines

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

         Otherwise, the results of this routine are unpredictable.

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 )

Examples

     1)  Given a plane normal and constant, find a point in
         the plane. POINT is the point we seek.

            CALL NVC2PL ( NORMAL, CONST,  PLANE )
            CALL PL2NVP ( PLANE,  NORMAL, POINT )

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 1.1.0, 24-AUG-2021 (NJB) (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    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)