Procedure

     VLCOM3 ( Vector linear combination, 3 dimensions )

     SUBROUTINE VLCOM3 ( A, V1, B, V2, C, V3, SUM )

Abstract

     Compute the vector linear combination of three double precision
     3-dimensional vectors.

Required_Reading

     None.

Keywords

     VECTOR

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION   A
     DOUBLE PRECISION   V1  ( 3 )
     DOUBLE PRECISION   B
     DOUBLE PRECISION   V2  ( 3 )
     DOUBLE PRECISION   C
     DOUBLE PRECISION   V3  ( 3 )
     DOUBLE PRECISION   SUM ( 3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     A          I   Coefficient of V1.
     V1         I   Vector in 3-space.
     B          I   Coefficient of V2.
     V2         I   Vector in 3-space.
     C          I   Coefficient of V3.
     V3         I   Vector in 3-space.
     SUM        O   Linear vector combination A*V1 + B*V2 + C*V3.

Detailed_Input

     A        is the double precision scalar variable that multiplies
              V1.

     V1       is an arbitrary, double precision 3-dimensional vector.

     B        is the double precision scalar variable that multiplies
              V2.

     V2       is an arbitrary, double precision 3-dimensional vector.

     C        is the double precision scalar variable that multiplies
              V3.

     V3       is a double precision 3-dimensional vector.

Detailed_Output

     SUM      is the double precision 3-dimensional vector which
              contains the linear combination

                 A * V1 + B * V2 + C * V3

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     The code reflects precisely the following mathematical expression

        For each value of the index I, from 1 to 3:

           SUM(I) = A * V1(I) + B * V2(I) + C * V3(I)

     No error checking is performed to guard against numeric overflow.

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) Suppose you have an instrument with an elliptical field
        of view described by its angular extent along the semi-minor
        and semi-major axes.

        The following code example demonstrates how to create
        16 vectors aiming at visualizing the field-of-view in
        three dimensional space.


        Example code begins here.


              PROGRAM VLCOM3_EX1
              IMPLICIT NONE

        C
        C     SPICELIB functions.
        C
              DOUBLE PRECISION      TWOPI

        C
        C     Local parameters.
        C
        C     Define the two angular extends, along the semi-major
        C     (U) and semi-minor (V) axes of the elliptical field
        C     of view, in radians.
        C
              DOUBLE PRECISION      MAXANG
              PARAMETER           ( MAXANG = 0.07D0 )

              DOUBLE PRECISION      MINANG
              PARAMETER           ( MINANG = 0.035D0 )

        C
        C     Local variables.
        C
              DOUBLE PRECISION      A
              DOUBLE PRECISION      B
              DOUBLE PRECISION      STEP
              DOUBLE PRECISION      THETA
              DOUBLE PRECISION      U      ( 3 )
              DOUBLE PRECISION      V      ( 3 )
              DOUBLE PRECISION      VECTOR ( 3 )
              DOUBLE PRECISION      Z      ( 3 )

              INTEGER               I

        C
        C     Let U and V be orthonormal 3-vectors spanning the
        C     focal plane of the instrument, and Z its
        C     boresight.
        C
              DATA                  U  /  1.D0,  0.D0,  0.D0 /
              DATA                  V  /  0.D0,  1.D0,  0.D0 /
              DATA                  Z  /  0.D0,  0.D0,  1.D0 /

        C
        C     Find the length of the ellipse's axes. Note that
        C     we are dealing with unitary vectors.
        C
              A = TAN ( MAXANG )
              B = TAN ( MINANG )

        C
        C     Compute the vectors of interest and display them
        C
              THETA = 0.D0
              STEP  = TWOPI() / 16

              DO I = 1, 16

                 CALL VLCOM3 ( 1.D0,           Z, A * COS(THETA), U,
             .                 B * SIN(THETA), V, VECTOR            )

                 WRITE(*,'(I2,A,3F10.6)') I, ':', VECTOR

                 THETA = THETA + STEP

              END DO

              END


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


         1:  0.070115  0.000000  1.000000
         2:  0.064777  0.013399  1.000000
         3:  0.049578  0.024759  1.000000
         4:  0.026832  0.032349  1.000000
         5:  0.000000  0.035014  1.000000
         6: -0.026832  0.032349  1.000000
         7: -0.049578  0.024759  1.000000
         8: -0.064777  0.013399  1.000000
         9: -0.070115  0.000000  1.000000
        10: -0.064777 -0.013399  1.000000
        11: -0.049578 -0.024759  1.000000
        12: -0.026832 -0.032349  1.000000
        13: -0.000000 -0.035014  1.000000
        14:  0.026832 -0.032349  1.000000
        15:  0.049578 -0.024759  1.000000
        16:  0.064777 -0.013399  1.000000

Restrictions

     1)  No error checking is performed to guard against numeric
         overflow or underflow. The user is responsible for insuring
         that the input values are reasonable.

Literature_References

     None.

Author_and_Institution

     J. Diaz del Rio    (ODC Space)
     W.L. Taber         (JPL)

Version

    SPICELIB Version 1.1.0, 06-JUL-2021 (JDR)

        Added IMPLICIT NONE statement.

        Edited the header to comply with NAIF standard. Added complete
        code example.

        Added restriction #1.

    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 (WLT)