Procedure

     VPERP ( Perpendicular component of a 3-vector )

     SUBROUTINE VPERP ( A, B, P )

Abstract

     Find the component of a vector that is perpendicular to a second
     vector. All vectors are 3-dimensional.

Required_Reading

     None.

Keywords

     VECTOR

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   A ( 3 )
     DOUBLE PRECISION   B ( 3 )
     DOUBLE PRECISION   P ( 3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     A          I   The vector whose orthogonal component is sought.
     B          I   The vector used as the orthogonal reference.
     P          O   The component of A orthogonal to B.

Detailed_Input

     A        is a double precision, 3-dimensional vector. It the
              vector whose component orthogonal to B is sought. (There
              is a unique decomposition of A into a sum V + P, where V
              is parallel to B and P is orthogonal to B. We want the
              component P.)

     B        is a double precision, 3-dimensional vector. This
              vector is the vector used as a reference for the
              decomposition of A.

Detailed_Output

     P        is a double precision, 3-dimensional vector containing
              the component of A that is orthogonal to B.
              P may overwrite either A or B.

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     Given and non-zero vector B and a vector A, there is a unique
     decomposition of A as a sum V + P such that P is orthogonal
     to B and V is parallel to B. This routine finds the vector P.

     If B is a zero vector, P will be identical to A.

Examples

     The following table gives sample inputs and results from calling
     VPERP.

        A                  B                 P
        ------------------------------------------
        (6, 6, 6)      ( 2, 0, 0)        (0, 6, 6)
        (6, 6, 6)      (-3, 0, 0)        (0, 6, 6)
        (6, 6, 0)      ( 0, 7, 0)        (6, 0, 0)
        (6, 0, 0)      ( 0, 0, 9)        (6, 0, 0)

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)
     E.D. Wright        (JPL)

Version

    SPICELIB Version 1.2.0, 16-SEP-2020 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard.

    SPICELIB Version 1.1.1, 11-MAY-2010 (EDW)

        Minor edit to code comments eliminating typo.

        Reordered header sections to proper NAIF convention.
        Removed Revision section, it listed a duplication of a
        $Version section entry.

    SPICELIB Version 1.1.0, 09-SEP-2005 (NJB)

        Updated to remove non-standard use of duplicate arguments
        in VSCL 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, 31-JAN-1990 (WLT)