Procedure

   pltnp_c ( Nearest point on triangular plate ) 

   void pltnp_c ( ConstSpiceDouble    point[3],
                  ConstSpiceDouble    v1   [3],
                  ConstSpiceDouble    v2   [3],
                  ConstSpiceDouble    v3   [3],
                  SpiceDouble         pnear[3],
                  SpiceDouble       * dist      )

Abstract

   Find the nearest point on a triangular plate to a given point.

Required_Reading

   DSK

Keywords

   GEOMETRY
   MATH

Brief_I/O

   VARIABLE  I/O  DESCRIPTION
   --------  ---  --------------------------------------------------
   point      I   A point in 3-dimensional space.
   v1,
   v2,
   v3         I   Vertices of a triangular plate.
   pnear      O   Nearest point on the plate to `point'.
   dist       O   Distance between `pnear' and `point'.

Detailed_Input

   point       is an arbitrary point in 3-dimensional space.

   v1,
   v2,
   v3          are 3-vectors constituting the vertices of
               a triangular plate.

               The plate is allowed to be degenerate: it may
               consist of a line segment or of a single point.

Detailed_Output

   pnear       is the closest point on the plate to `point'.
               `pnear' is unique, since the plate is convex.

   dist        is the distance between `point' and `pnear'.

Parameters

   None.

Exceptions

   1)  The input plate is allowed to be degenerate: it may be
       a line segment or a single point.

Files

   None.

Particulars

   None.

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) Find the nearest point to the point (2,2,2) on a plate having
      vertices at the unit basis vectors that lie along the positive
      X, Y, and Z coordinate axes.


      Example code begins here.


      /.
         Program pltnp_ex1
      ./

      #include <stdio.h>
      #include "SpiceUsr.h"

      int main()
      {
         /.
         Local variables
         ./
         SpiceDouble             dist;
         SpiceDouble             pnear[3];
         SpiceDouble             point[3] = {2.0, 2.0, 2.0};
         SpiceDouble             v1   [3] = {1.0, 0.0, 0.0};
         SpiceDouble             v2   [3] = {0.0, 1.0, 0.0};
         SpiceDouble             v3   [3] = {0.0, 0.0, 1.0};

         pltnp_c ( point, v1, v2, v3, pnear, &dist );

         printf ( "\n"
                  "Plate vertex 1 = %14.7e %14.7e %14.7e\n"
                  "Plate vertex 2 = %14.7e %14.7e %14.7e\n"
                  "Plate vertex 3 = %14.7e %14.7e %14.7e\n"
                  "Input point    = %14.7e %14.7e %14.7e\n"
                  "\n"
                  "Near point     = %14.7e %14.7e %14.7e\n"
                  "Distance       = %14.7e\n"
                  "\n",
                  v1[0],    v1[1],    v1[2],
                  v2[0],    v2[1],    v2[2],
                  v3[0],    v3[1],    v3[2],
                  point[0], point[1], point[2],
                  pnear[0], pnear[1], pnear[2],
                  dist                                    );

         return ( 0 );
      }


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


      Plate vertex 1 =  1.0000000e+00  0.0000000e+00  0.0000000e+00
      Plate vertex 2 =  0.0000000e+00  1.0000000e+00  0.0000000e+00
      Plate vertex 3 =  0.0000000e+00  0.0000000e+00  1.0000000e+00
      Input point    =  2.0000000e+00  2.0000000e+00  2.0000000e+00

      Near point     =  3.3333333e-01  3.3333333e-01  3.3333333e-01
      Distance       =  2.8867513e+00

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

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

Version

   -CSPICE Version 1.0.1, 04-MAR-2019 (JDR)

       Edited the header to comply with NAIF standard.

   -CSPICE Version 1.0.0, 01-FEB-2016 (NJB)

Index_Entries

   nearest point on triangular plate