Procedure

     PLTEXP ( Plate expander )

     SUBROUTINE PLTEXP ( IVERTS, DELTA, OVERTS )

Abstract

     Expand a triangular plate by a specified amount. The expanded
     plate is co-planar with, and has the same orientation as, the
     original. The centroids of the two plates coincide.

Required_Reading

     DSK

Keywords

     GEOMETRY
     MATH
     TOPOGRAPHY

Declarations

     IMPLICIT NONE

     DOUBLE PRECISION      IVERTS ( 3, 3 )
     DOUBLE PRECISION      DELTA
     DOUBLE PRECISION      OVERTS ( 3, 3 )

Brief_I/O

     VARIABLE  I/O  DESCRIPTION
     --------  ---  --------------------------------------------------
     IVERTS     I   Vertices of the plate to be expanded.
     DELTA      I   Fraction by which the plate is to be expanded.
     OVERTS     O   Vertices of the expanded plate.

Detailed_Input

     IVERTS   is an array containing three vertices of a triangular
              plate. Each vertex is a three-dimensional vector. The
              elements

                 IVERTS(J,I), J = 1, 3

              are, respectively, the X, Y, and Z components of the
              Ith vertex.


     DELTA    is a fraction by which the plate is to be scaled.
              Scaling is done so that the scaled plate has the
              following properties:

                 -  it is co-planar with the input plate

                 -  its centroid coincides with that of the input
                    plate

                 -  its sides remain parallel to the corresponding
                    sides of the input plate

                 -  the distance of each vertex from the centroid is
                    (1+DELTA) times the corresponding distance for
                    the input plate

Detailed_Output

     OVERTS   is an array containing three vertices of the triangular
              plate resulting from scaling the input plate.

              If CTROID is the centroid (the average of the vertices)
              of the input plate, then the Ith vertex of OVERTS

                 OVERTS(J,I), J = 1, 3

              is equal to

                 CTROID(J) + (1+DELTA)*( IVERTS(J,I) - CTROID(J) ),

                 J = 1, 3

Parameters

     None.

Exceptions

     Error free.

Files

     None.

Particulars

     This routine supports "greedy" ray-plate intercept algorithms.
     Such algorithms attempt to ensure that false negatives---in which
     an intersection is not found due to round-off error---do not
     occur. In such an algorithm, the plate of interest is expanded
     slightly before the intersection test is performed.

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) Expand an equilateral triangle that lies in the plane

           { (x,y,z) : z = 7 }

        Use an expansion fraction of 1.D0; this doubles the size of
        the plate.

        Example code begins here.


              PROGRAM PLTEXP_EX1
              IMPLICIT NONE

              DOUBLE PRECISION      DELTA
              DOUBLE PRECISION      IVERTS ( 3, 3 )
              DOUBLE PRECISION      OVERTS ( 3, 3 )
              DOUBLE PRECISION      S

              INTEGER               I

              S = SQRT(3.D0)/2

              CALL VPACK (    S,  -0.5D0,  7.D0, IVERTS(1,1) )
              CALL VPACK ( 0.D0,    1.D0,  7.D0, IVERTS(1,2) )
              CALL VPACK (   -S,  -0.5D0,  7.D0, IVERTS(1,3) )

              DELTA = 1.D0

              CALL PLTEXP ( IVERTS, DELTA, OVERTS )

              WRITE (*,*) ' '
              WRITE (*,*) 'Vertices of input plate: '

              WRITE (*, '(1X,A,3E18.10)' ) ' I1 = ',
             .          (IVERTS(I,1), I = 1, 3)
              WRITE (*, '(1X,A,3E18.10)' ) ' I2 = ',
             .          (IVERTS(I,2), I = 1, 3)
              WRITE (*, '(1X,A,3E18.10)' ) ' I3 = ',
             .          (IVERTS(I,3), I = 1, 3)

              WRITE (*,*) ' '
              WRITE (*,*) 'Vertices of output plate: '

              WRITE (*, '(1X,A,3E18.10)' ) ' O1 = ',
             .          (OVERTS(I,1), I = 1, 3)
              WRITE (*, '(1X,A,3E18.10)' ) ' O2 = ',
             .          (OVERTS(I,2), I = 1, 3)
              WRITE (*, '(1X,A,3E18.10)' ) ' O3 = ',
             .          (OVERTS(I,3), I = 1, 3)
              WRITE (*,*) ' '
              END


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


         Vertices of input plate:
          I1 =   0.8660254038E+00 -0.5000000000E+00  0.7000000000E+01
          I2 =   0.0000000000E+00  0.1000000000E+01  0.7000000000E+01
          I3 =  -0.8660254038E+00 -0.5000000000E+00  0.7000000000E+01

         Vertices of output plate:
          O1 =   0.1732050808E+01 -0.1000000000E+01  0.7000000000E+01
          O2 =   0.0000000000E+00  0.2000000000E+01  0.7000000000E+01
          O3 =  -0.1732050808E+01 -0.1000000000E+01  0.7000000000E+01


        Note that the height of the plate is unchanged, but the vectors
        from the centroid to the vertices have doubled in length.

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.

        Edits to code example output format for the solution to fit
        within the $Examples section without modifications.

    SPICELIB Version 1.0.0, 29-FEB-2016 (NJB)

        Based on original version 28-MAY-2014 (NJB)