Index Page pltar_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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

       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

       None.

#### Keywords

       DSK
       GEOMETRY
       MATH

#### 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.

       2) If the number of plates is positive and the number of vertices
          is less than 3, the error SPICE(TOOFEWVERTICES) is signaled.

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

             [1, nv]

          the error SPICE(INDEXOUTOFRANGE) will be signaled.

#### 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 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) 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 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 PC/Linux/gcc/64-bit platform,
       the output was:

          Expected area   =    (3 + SQRT(3)) / 2
                          =    0.23660254037844384E+01
          Computed area   =    2.3660254037844384

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman    (JPL)

#### Version

       -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

    Wed Apr  5 17:54:40 2017