| el2cgv_c |
|
Table of contents
Procedure
el2cgv_c ( Ellipse to center and generating vectors )
void el2cgv_c ( ConstSpiceEllipse * ellips,
SpiceDouble center[3],
SpiceDouble smajor[3],
SpiceDouble sminor[3] )
AbstractConvert a SPICE ellipse to a center vector and two generating vectors. The selected generating vectors are semi-axes of the ellipse. Required_ReadingELLIPSES KeywordsELLIPSE GEOMETRY Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- ellips I A SPICE ellipse. center, smajor, sminor O Center and semi-axes of `ellips'. Detailed_Inputellips is a SPICE ellipse. Detailed_Output
center,
smajor,
sminor are, respectively, a center vector, a semi-major
axis vector, and a semi-minor axis vector that
generate the input ellipse. This ellipse is the
set of points
center + cos(theta) * smajor + sin(theta) * sminor
where theta ranges over the interval (-pi, pi].
ParametersNone. ExceptionsError free. FilesNone. 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 )
A word about the output of this routine: the semi-major axis of
an ellipse is a vector of largest possible magnitude in the set
cos(theta) * vec1 + sin(theta) * vec2,
where `theta' is in the interval (-pi, pi]. There are two such
vectors; they are additive inverses of each other. The semi-minor
axis is an analogous vector of smallest possible magnitude. The
semi-major and semi-minor axes are orthogonal to each other. If
smajor and sminor are choices of semi-major and semi-minor axes,
then the input ellipse can also be represented as the set of
points
center + cos(theta) * smajor + sin(theta) * sminor
where theta ranges over the interval (-pi, pi].
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) Given a SPICE ellipse structure, extract its components into
independent variables.
Example code begins here.
/.
Program el2cgv_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) Given an ellipsoid and a viewpoint exterior to it, calculate
the limb ellipse as seen from that viewpoint.
Example code begins here.
/.
Program el2cgv_ex2
./
#include <math.h>
#include <stdio.h>
#include "SpiceUsr.h"
int main( )
{
/.
Local constants.
./
#define UBEL 9
/.
Local variables.
./
SpiceDouble a;
SpiceDouble b;
SpiceDouble c;
SpiceDouble ecentr [3];
SpiceEllipse limb;
SpiceDouble smajor [3];
SpiceDouble sminor [3];
/.
Define a viewpoint exterior to the ellipsoid.
./
SpiceDouble viewpt [3] = { 2.0, 0.0, 0.0 };
/.
Define an ellipsoid.
./
a = sqrt( 2.0 );
b = 2.0 * sqrt( 2.0 );
c = sqrt( 2.0 );
/.
Calculate the limb ellipse as seen by from the
viewpoint.
./
edlimb_c ( a, b, c, viewpt, &limb );
/.
Output the structure components.
./
el2cgv_c ( &limb, ecentr, smajor, sminor );
printf( "Limb ellipse as seen from viewpoint:\n" );
printf( " Semi-minor axis: %10.6f %10.6f %10.6f\n",
sminor[0], sminor[1], sminor[2] );
printf( " Semi-major axis: %10.6f %10.6f %10.6f\n",
smajor[0], smajor[1], smajor[2] );
printf( " Center : %10.6f %10.6f %10.6f\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:
Limb ellipse as seen from viewpoint:
Semi-minor axis: 0.000000 0.000000 -1.000000
Semi-major axis: 0.000000 2.000000 -0.000000
Center : 1.000000 0.000000 0.000000
RestrictionsNone. Literature_ReferencesNone. Author_and_InstitutionN.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, 12-JUN-1999 (NJB)
Index_Entriesellipse to center and generating vectors |
Fri Dec 31 18:41:06 2021