Procedure

     VPROJ ( Vector projection, 3 dimensions )

     SUBROUTINE VPROJ ( A, B, P )

Abstract

     Compute the projection of one 3-dimensional vector onto another
     3-dimensional vector.

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 to be projected.
     B          I   The vector onto which A is to be projected.
     P          O   The projection of A onto B.

Detailed_Input

     A        is a double precision, 3-dimensional vector. This
              vector is to be projected onto the vector B.

     B        is a double precision, 3-dimensional vector. This
              vector is the vector which receives the projection.

Detailed_Output

     P        is a double precision, 3-dimensional vector containing
              the projection of A onto B. (P is necessarily parallel
              to B.) If B is the zero vector then P will be returned
              as the zero vector.

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     Given any vectors A and B, there is a unique decomposition of
     A as a sum V + P such that V, the dot product of V and B, is zero,
     and the dot product of P with B is equal the product of the
     lengths of P and B. P is called the projection of A onto B. It
     can be expressed mathematically as

        DOT(A,B)
        -------- * B
        DOT(B,B)

     (This is not necessarily the prescription used to compute the
     projection. It is intended only for descriptive purposes.)

Examples

     The numerical results shown for this example may differ across
     platforms. The results depend on the SPICE kernels used as
     input, the compiler and supporting libraries, and the machine
     specific arithmetic implementation.

     1) Define two sets of vectors and compute the projection of
        each vector of the first set on the corresponding vector of
        the second set.

        Example code begins here.


              PROGRAM VPROJ_EX1
              IMPLICIT NONE

        C
        C     Local parameters.
        C
              INTEGER               NDIM
              PARAMETER           ( NDIM   = 3 )

              INTEGER               SETSIZ
              PARAMETER           ( SETSIZ = 4 )

        C
        C     Local variables.
        C
              DOUBLE PRECISION      SETA ( NDIM, SETSIZ )
              DOUBLE PRECISION      SETB ( NDIM, SETSIZ )
              DOUBLE PRECISION      PVEC ( NDIM )

              INTEGER               I
              INTEGER               J

        C
        C     Define the two vector sets.
        C
              DATA                  SETA / 6.D0,  6.D0,  6.D0,
             .                             6.D0,  6.D0,  6.D0,
             .                             6.D0,  6.D0,  0.D0,
             .                             6.D0,  0.D0,  0.D0  /

              DATA                  SETB / 2.D0,  0.D0,  0.D0,
             .                            -3.D0,  0.D0,  0.D0,
             .                             0.D0,  7.D0,  0.D0,
             .                             0.D0,  0.D0,  9.D0  /

        C
        C     Calculate the projection
        C
              DO I=1, SETSIZ

                 CALL VPROJ ( SETA(1,I), SETB(1,I), PVEC )

                 WRITE(*,'(A,3F5.1)') 'Vector A  : ',
             .                        ( SETA(J,I), J=1,3 )
                 WRITE(*,'(A,3F5.1)') 'Vector B  : ',
             .                        ( SETB(J,I), J=1,3 )
                 WRITE(*,'(A,3F5.1)') 'Projection: ', PVEC
                 WRITE(*,*) ' '

              END DO

              END


        When this program was executed on a Mac/Intel/gfortran/64-bit
        platform, the output was:


        Vector A  :   6.0  6.0  6.0
        Vector B  :   2.0  0.0  0.0
        Projection:   6.0  0.0  0.0

        Vector A  :   6.0  6.0  6.0
        Vector B  :  -3.0  0.0  0.0
        Projection:   6.0 -0.0 -0.0

        Vector A  :   6.0  6.0  0.0
        Vector B  :   0.0  7.0  0.0
        Projection:   0.0  6.0  0.0

        Vector A  :   6.0  0.0  0.0
        Vector B  :   0.0  0.0  9.0
        Projection:   0.0  0.0  0.0

Restrictions

     1)  An implicit assumption exists that A and B are specified in
         the same reference frame. If this is not the case, the
         numerical result has no meaning.

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, 26-OCT-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Added complete
        code example. Added entry in $Restrictions section.

    SPICELIB Version 1.0.2, 23-APR-2010 (NJB)

        Header correction: assertions that the output
        can overwrite the input have been removed.

    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)