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Index Page pltar_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

       pltar_c ( Compute area of plate set )

       SpiceDouble pltar_c ( SpiceInt           nv,
                             ConstSpiceDouble   vrtces [][3],
                             SpiceInt           np,
                             ConstSpiceInt      plates [][3]  )

#### Abstract

       Compute the total area of a collection of triangular plates.

#### Required_Reading

       DSK

#### Keywords

       DSK
       GEOMETRY
       MATH
       TOPOGRAPHY

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       nv         I   Number of vertices.
       vrtces     I   Array of vertices.
       np         I   Number of triangular plates.
       plates     I   Array of plates.

       The function returns the total area of the set of plates.

#### Detailed_Input

       nv          is the number of vertices comprising the plate
                   set.

       vrtces      is an array containing the plate model's vertices.
                   Elements

                      vrtces[i-1][0]
                      vrtces[i-1][1]
                      vrtces[i-1][2]

                   are, respectively, the X, Y, and Z components of
                   the ith vertex, where i ranges from 1 to `nv'.

                   This routine doesn't associate units with the
                   vertices.

       np          is the number of triangular plates comprising the
                   plate set.

       plates      is an array containing 3-tuples of integers
                   representing the set of plates. The elements of
                   `plates' are vertex indices. The vertex indices are
                   1-based: vertices have indices ranging from 1 to
                   `nv'. The elements

                      plates[i-1][0]
                      plates[i-1][1]
                      plates[i-1][2]

                   are, respectively, the indices of the vertices
                   comprising the ith plate.

                   Note that the order of the vertices of a plate is
                   significant: the vertices must be ordered in the
                   positive (counterclockwise) sense with respect to
                   the outward normal direction associated with the
                   plate. In other words, if V1, V2, V3 are the
                   vertices of a plate, then

                      ( V2 - V1 )  x  ( V3 - V2 )

                   points in the outward normal direction. Here
                   "x" denotes the vector cross product operator.

#### Detailed_Output

       The function returns the total area of the input set of plates.
       Each plate contributes the area of the triangle defined by the
       plate's vertices.

       If the components of the vertex array have length unit L, then the
       output area has units

           2
          L

#### Parameters

       None.

#### Exceptions

       1)  If the number of plates is less than 0, the error
           SPICE(BADPLATECOUNT) is signaled by a routine in the call tree
           of this routine.

       2)  If the number of plates is positive and the number of vertices
           is less than 3, the error SPICE(TOOFEWVERTICES) is signaled by
           a routine in the call tree of this routine.

       3)  If any plate contains a vertex index outside of the range

              [1, nv]

           the error SPICE(INDEXOUTOFRANGE) is signaled by a routine in
           the call tree of this routine.

#### Files

       None.

#### Particulars

       This routine computes the total area of a set of triangular
       plates. The plates need not define a closed surface.

       Examples of valid plate sets:

          Tetrahedron
          Box
          Tiled ellipsoid
          Tiled ellipsoid with one plate removed
          Two disjoint boxes
          Two boxes with intersection having positive volume
          Single plate
          Empty plate set

#### 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 the area of the pyramid defined by the four
          triangular plates whose vertices are the 3-element
          subsets of the set of vectors:

             ( 0, 0, 0 )
             ( 1, 0, 0 )
             ( 0, 1, 0 )
             ( 0, 0, 1 )

          Example code begins here.

          /.
             Program pltar_ex1

             Compute the area of a plate model representing the pyramid
             with one vertex at the origin and the other vertices
             coinciding with the standard basis vectors.
          ./

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

          int main()
          {
             /.
             Local constants
             ./
             #define NVERT           4
             #define NPLATE          4

             /.
             Local variables
             ./
             SpiceDouble             area;

             /.
             Let the notation

                < A, B >

             denote the dot product of vectors A and B.

             The plates defined below lie in the following planes,
             respectively:

                Plate 1:    { P :  < P, (-1,  0,  0) > = 0 }
                Plate 2:    { P :  < P, ( 0, -1,  0) > = 0 }
                Plate 3:    { P :  < P, ( 0,  0, -1) > = 0 }
                Plate 4:    { P :  < P, ( 1,  1,  1) > = 1 }

             ./
             SpiceDouble             vrtces[NVERT ][3] =

                                     { { 0.0, 0.0, 0.0 },
                                       { 1.0, 0.0, 0.0 },
                                       { 0.0, 1.0, 0.0 },
                                       { 0.0, 0.0, 1.0 }  };

             SpiceInt                plates[NPLATE][3] =

                                     { { 1, 4, 3 },
                                       { 1, 2, 4 },
                                       { 1, 3, 2 },
                                       { 2, 3, 4 }  };

             area = pltar_c( NVERT, vrtces, NPLATE, plates );

             printf ( "Expected area  =    (3 + sqrt(3)) / 2\n"
                      "               =    0.23660254037844384e+01\n" );
             printf ( "Computed area  =   %24.17e\n", area            );

             return ( 0 );
          }

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

          Expected area  =    (3 + sqrt(3)) / 2
                         =    0.23660254037844384e+01
          Computed area  =    2.36602540378443837e+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-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard.

       -CSPICE Version 1.0.0, 24-OCT-2016 (NJB)

#### Index_Entries

       compute plate model area

#### Link to routine pltar_c source file pltar_c.c

    Fri Dec 31 18:41:10 2021