Procedure

     PLTNRM ( DSK, compute outward normal of plate )

     SUBROUTINE PLTNRM ( V1, V2, V3, NORMAL )

Abstract

     Compute an outward normal vector of a triangular plate.
     The vector does not necessarily have unit length.

Required_Reading

     DSK

Keywords

     DSK
     FILES
     TOPOGRAPHY

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      V1     ( 3 )
     DOUBLE PRECISION      V2     ( 3 )
     DOUBLE PRECISION      V3     ( 3 )
     DOUBLE PRECISION      NORMAL ( 3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     V1,
     V2,
     V3         I   Vertices of a plate.
     NORMAL     O   Plate's outward normal vector.

Detailed_Input

     V1,
     V2,
     V3       are vertices of a triangular plate.

Detailed_Output

     NORMAL   is an outward normal vector of the plate defined by
              the input vertices. The order of the vertices is
              used to determine the choice of normal direction:
              the normal vector is

                 ( V2 - V1 ) x ( V3 - V2 )

Parameters

     None.

Exceptions

     1)  The input plate may be degenerate: it may be a line segment
         or a point. These are not considered to be erroneous inputs.

Files

     None.

Particulars

     This routine saves computation time by not scaling the output
     vector to unit length. The caller can scale the vector using
     the routine VHAT.

Examples

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

     1) Compute an upward normal of an equilateral triangle lying
        in the X-Y plane and centered at the origin.

        Example code begins here.


              PROGRAM PLTNRM_EX1
              IMPLICIT NONE

              DOUBLE PRECISION      NORMAL ( 3 )
              DOUBLE PRECISION      S
              DOUBLE PRECISION      V1     ( 3 )
              DOUBLE PRECISION      V2     ( 3 )
              DOUBLE PRECISION      V3     ( 3 )


              S = SQRT(3.D0)/2

              CALL VPACK (    S,  -0.5D0,  0.D0, V1 )
              CALL VPACK ( 0.D0,    1.D0,  0.D0, V2 )
              CALL VPACK (   -S,  -0.5D0,  0.D0, V3 )


              CALL PLTNRM ( V1, V2, V3, NORMAL )

              WRITE (*, '(A,3F18.14)' ) 'NORMAL = ', NORMAL

              END


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


        NORMAL =   0.00000000000000  0.00000000000000  2.59807621135332

Restrictions

     None.

Literature_References

     None.

Author_and_Institution

     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)

Version

    SPICELIB Version 1.0.1, 08-JUL-2020 (JDR)

        Edited the header to comply with NAIF standard..
        Changed code example output format for the solution to fit
        within the $Examples section without modifications.

    SPICELIB Version 1.0.0, 26-JAN-2016 (NJB)