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Index Page cgv2el_c

Table of contents

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

       cgv2el_c ( Center and generating vectors to ellipse )

       void cgv2el_c ( ConstSpiceDouble    center[3],
                       ConstSpiceDouble    vec1  [3],
                       ConstSpiceDouble    vec2  [3],
                       SpiceEllipse      * ellips    )

#### Abstract

       Form a SPICE ellipse from a center vector and two generating
       vectors.

#### Required_Reading

       ELLIPSES

#### Keywords

       ELLIPSE
       GEOMETRY

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       center,
       vec1,
       vec2       I   Center and two generating vectors for an ellipse.
       ellips     O   The SPICE ellipse defined by the input vectors.

#### Detailed_Input

       center,
       vec1,
       vec2        are a center and two generating vectors defining
                   an ellipse in three-dimensional space. The
                   ellipse is the set of points

                      center  +  cos(theta) * vec1  +  sin(theta) * vec2

                   where theta ranges over the interval (-pi, pi].
                   `vec1' and `vec2' need not be linearly independent.

#### Detailed_Output

       ellips      is the SPICE ellipse defined by the input
                   vectors.

#### Parameters

       None.

#### Exceptions

       1)  If `vec1' and `vec2' are linearly dependent, `ellips' will be
           degenerate. SPICE ellipses are allowed to represent
           degenerate geometric ellipses.

#### Files

       None.

#### Particulars

       SPICE ellipses serve to simplify calling sequences and reduce
       the chance for error in declaring and describing argument lists
       involving ellipses.

       The set of ellipse conversion routines is

          cgv2el_c ( Center and generating vectors to ellipse )
          el2cgv_c ( Ellipse to center and generating vectors )

#### Examples

       The numerical results shown for these examples may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       1) Create a SPICE ellipse given its center and two linearly
          independent generating vectors of the ellipse.

          Example code begins here.

          /.
             Program cgv2el_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables.
             ./
             SpiceDouble          ecentr [3];
             SpiceDouble          smajor [3];
             SpiceDouble          sminor [3];

             SpiceEllipse         ellips;

             /.
             Define the center and two linearly independent
             generating vectors of an ellipse (the vectors need not
             be linearly independent).
             ./
             SpiceDouble          center [3] = { -1.0,  1.0, -1.0 };
             SpiceDouble          vec1   [3] = {  1.0,  1.0,  1.0 };
             SpiceDouble          vec2   [3] = {  1.0, -1.0,  1.0 };

             /.
             Create the `ellips'.
             ./
             cgv2el_c ( center, vec1, vec2, &ellips );

             /.
             In a real application, please use CSPICE API el2cgv_c
             to retrieve the center and generating vectors from the
             ellipse structure (see next block).
             ./
             printf( "SPICE ellipse:\n" );
             printf( " Semi-minor axis: %9.6f %9.6f %9.6f\n",
                                         ellips.semiMinor[0],
                                         ellips.semiMinor[1],
                                         ellips.semiMinor[2] );
             printf( " Semi-major axis: %9.6f %9.6f %9.6f\n",
                                         ellips.semiMajor[0],
                                         ellips.semiMajor[1],
                                         ellips.semiMajor[2] );
             printf( " Center         : %9.6f %9.6f %9.6f\n",
                                            ellips.center[0],
                                            ellips.center[1],
                                            ellips.center[2] );
             printf( " \n" );

             /.
             Obtain the center and generating vectors from the
             `ellips'.
             ./
             el2cgv_c ( &ellips, ecentr, smajor, sminor );

             printf( "SPICE ellipse (using el2cgv_c):\n" );
             printf( " Semi-minor axis: %9.6f %9.6f %9.6f\n",
                              sminor[0], sminor[1], sminor[2] );
             printf( " Semi-major axis: %9.6f %9.6f %9.6f\n",
                              smajor[0], smajor[1], smajor[2] );
             printf( " Center         : %9.6f %9.6f %9.6f\n",
                              ecentr[0], ecentr[1], ecentr[2] );

             return ( 0 );
          }

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

          SPICE ellipse:
           Semi-minor axis:  0.000000  1.414214  0.000000
           Semi-major axis:  1.414214 -0.000000  1.414214
           Center         : -1.000000  1.000000 -1.000000

          SPICE ellipse (using el2cgv_c):
           Semi-minor axis:  0.000000  1.414214  0.000000
           Semi-major axis:  1.414214 -0.000000  1.414214
           Center         : -1.000000  1.000000 -1.000000

       2) Find the intersection of an ellipse with a plane.

          Example code begins here.

          /.
             Program cgv2el_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local variables.
             ./
             SpiceEllipse         ellips;
             SpicePlane           plane;
             SpiceDouble          xpts   [2][3];

             SpiceInt             i;
             SpiceInt             nxpts;

             /.
             The ellipse is defined by the vectors `center', `vec1', and
             `vec2'. The plane is defined by the normal vector `normal'
             and the `center'.
             ./
             SpiceDouble          center [3] = {  0.0,  0.0,  0.0 };
             SpiceDouble          vec1   [3] = {  1.0,  7.0,  2.0 };
             SpiceDouble          vec2   [3] = { -1.0,  1.0,  3.0 };

             SpiceDouble          normal [3] = {  0.0,  1.0,  0.0 };

             /.
             Make a SPICE ellipse and a plane.
             ./
             cgv2el_c ( center, vec1, vec2, &ellips );
             nvp2pl_c ( normal, center,     &plane  );

             /.
             Find the intersection of the ellipse and plane.
             `nxpts' is the number of intersection points; `xpts'
             are the points themselves.
             ./
             inelpl_c ( &ellips, &plane, &nxpts, xpts[0], xpts[1] );

             printf( "Number of intercept points: %2d\n", nxpts );

             for ( i = 0; i < nxpts; i++ )
             {
                printf( " Point %1d: %9.6f %9.6f %9.6f\n", i,
                                     xpts[i][0], xpts[i][1], xpts[i][2] );
             }

             return ( 0 );
          }

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

          Number of intercept points:  2
           Point 0:  1.131371  0.000000 -2.687006
           Point 1: -1.131371 -0.000000  2.687006

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.1.0, 24-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard.
           Added complete code examples.

           Changed the output argument name "ellipse" to "ellips" for
           consistency with other routines.

       -CSPICE Version 1.0.0, 05-MAR-1999 (NJB)

#### Index_Entries

       center and generating vectors to ellipse

#### Link to routine cgv2el_c source file cgv2el_c.c

    Fri Dec 31 18:41:02 2021