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pltexp_c
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Procedure
Abstract
Required_Reading
Keywords
Brief_I/O
Detailed_Input
Detailed_Output
Parameters
Exceptions
Files
Particulars
Examples
Restrictions
Literature_References
Author_and_Institution
Version
Index_Entries

Procedure

   void pltexp_c ( ConstSpiceDouble   iverts[3][3],
                   SpiceDouble        delta,
                   SpiceDouble        overts[3][3] ) 

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

 
   MATH  
   GEOMETRY 
   TOPOGRAPHY 
 

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[i][j], j = 0 ... 2
 
              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[i][j], j = 0 ... 2
 
              is equal to  
 
                 ctroid[j] + (1+delta)*( iverts[i][j] - ctroid[j] ), 
 
                 j = 0 ... 2
 
 

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 these examples 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 1.0; this doubles the size of 
      the plate. 
 
      Example code begins here.  
 
         /.
         Example program pltexp_ex1
         ./
         #include <stdio.h>
         #include <math.h>
         #include "SpiceUsr.h"

         int main()
         {
            /.
            Local variables 
            ./ 
            SpiceDouble             delta;
            SpiceDouble             iverts[3][3];
            SpiceDouble             overts[3][3];
            SpiceDouble             s;

            s     = sqrt( 3.0 ) / 2.0;

            vpack_c (   s,  -0.5,  7.0, iverts[0] );
            vpack_c ( 0.0,   1.0,  7.0, iverts[1] );
            vpack_c (  -s,  -0.5,  7.0, iverts[2] );

            delta = 1.0;

            pltexp_c ( iverts, delta, overts );

            printf ( "\n"
                     "Vertices of input plate: \n"
                     " I1 = %20.12f %20.12f %20.12f\n"
                     " I2 = %20.12f %20.12f %20.12f\n"
                     " I3 = %20.12f %20.12f %20.12f\n",
                     iverts[0][0], iverts[0][1], iverts[0][2], 
                     iverts[1][0], iverts[1][1], iverts[1][2], 
                     iverts[2][0], iverts[2][1], iverts[2][2]  );

            printf ( "\n"
                     "Vertices of output plate: \n"
                     " O1 = %20.12f %20.12f %20.12f\n"
                     " O2 = %20.12f %20.12f %20.12f\n"
                     " O3 = %20.12f %20.12f %20.12f\n\n",
                     overts[0][0], overts[0][1], overts[0][2], 
                     overts[1][0], overts[1][1], overts[1][2], 
                     overts[2][0], overts[2][1], overts[2][2]  );

            return ( 0 );
         }
 
 
 
   When this program was executed on a PC/Linux/gcc/64-bit 
   platform, the output was: 
 

      Vertices of input plate:
       I1 =       0.866025403784      -0.500000000000       7.000000000000
       I2 =       0.000000000000       1.000000000000       7.000000000000
       I3 =      -0.866025403784      -0.500000000000       7.000000000000

      Vertices of output plate:
       O1 =       1.732050807569      -1.000000000000       7.000000000000
       O2 =       0.000000000000       2.000000000000       7.000000000000
       O3 =      -1.732050807569      -1.000000000000       7.000000000000

 
   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) 
 

Version

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

Index_Entries

 
   expand triangular plate 
 
Wed Apr  5 17:54:40 2017