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sphlat_c

 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

sphlat_c ( Spherical to latitudinal coordinates )

void sphlat_c ( SpiceDouble     r,
SpiceDouble     colat,
SpiceDouble     slon,
SpiceDouble   * lon,
SpiceDouble   * lat )

Abstract

Convert from spherical coordinates to latitudinal coordinates.

None.

CONVERSION
COORDINATES

Brief_I/O

VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
r          I   Distance of the point from the origin.
colat      I   Angle of the point from positive z axis (radians).
slon       I   Angle of the point from the XZ plane (radians).
radius     O   Distance of a point from the origin
lon        O   Angle of the point from the XZ plane in radians
lat        O   Angle of the point from the XY plane in radians

Detailed_Input

r           is the distance of the point from the origin.

colat       is the angle between the vector from the origin to the
point and the positive Z-axis in radians.

slon        is the angle of the point from the XZ plane (radians).

Detailed_Output

radius      is the distance of a point from the origin.

lon         is the angle of the point from the XZ plane in
radians. `lon' is set equal to `slon'.

lat         is the angle of the point from the XY plane in
radians. `lat' is computed as pi/2 - colat.

None.

Error free.

None.

Particulars

This routine returns the latitudinal coordinates of a point
whose position is input in spherical coordinates.

Latitudinal coordinates are defined by a distance from a central
reference point, an angle from a reference meridian, and an angle
above the equator of a sphere centered at the central reference
point.

Spherical coordinates are defined by a distance from a central
reference point, an angle from a reference meridian, and an angle
from the z-axis.

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) Latitude is obtained by subtracting co-latitude from halfpi_c
Radius and longitude mean the same thing in both latitudinal
and spherical coordinates. The table below lists `lat' and
corresponding `colat' in terms of degrees.

lat     colat
-----    -----
0        90
20        70
45        45
-30       120
90         0
-45       135

2) Compute the spherical coordinates of the position of the Moon
as seen from the Earth, and convert them to latitudinal and
rectangular coordinates.

Use the meta-kernel shown below to load the required SPICE
kernels.

KPL/MK

File name: sphlat_ex2.tm

This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.

In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.

The names and contents of the kernels referenced
by this meta-kernel are as follows:

File name                     Contents
---------                     --------
de421.bsp                     Planetary ephemeris
naif0012.tls                  Leapseconds

\begindata

'naif0012.tls'  )

\begintext

End of meta-kernel

Example code begins here.

/.
Program sphlat_ex2
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local variables
./
SpiceDouble          colat;
SpiceDouble          et;
SpiceDouble          lt;
SpiceDouble          lat;
SpiceDouble          lon;
SpiceDouble          pos    ;
SpiceDouble          r;
SpiceDouble          rectan ;
SpiceDouble          slon;

/.
Load SPK and LSK kernels, use a meta kernel for
convenience.
./
furnsh_c ( "sphlat_ex2.tm" );

/.
Look up the geometric state of the Moon as seen from
the Earth at 2017 Mar 20, relative to the J2000
reference frame.
./
str2et_c ( "2017 Mar 20", &et );

spkpos_c ( "Moon", et, "J2000", "NONE", "Earth", pos, &lt );

/.
Convert the position vector `pos' to spherical
coordinates.
./
recsph_c ( pos, &r, &colat, &slon );

/.
Convert the spherical coordinates to latitudinal.
./
sphlat_c ( r, colat, slon, &radius, &lon, &lat );

/.
Convert the latitudinal coordinates to rectangular.
./
latrec_c ( radius, lon, lat, rectan );

printf( " \n" );
printf( "Original rectangular coordinates:\n" );
printf( " \n" );
printf( " X           (km):  %19.8f\n", pos );
printf( " Y           (km):  %19.8f\n", pos );
printf( " Z           (km):  %19.8f\n", pos );
printf( " \n" );
printf( "Spherical coordinates:\n" );
printf( " \n" );
printf( " Radius      (km):  %19.8f\n", r );
printf( " Colatitude (deg):  %19.8f\n", colat*dpr_c ( ) );
printf( " Longitude  (deg):  %19.8f\n", slon*dpr_c ( ) );
printf( " \n" );
printf( "Latitudinal coordinates:\n" );
printf( " \n" );
printf( " Longitude  (deg):  %19.8f\n", lon*dpr_c ( ) );
printf( " Latitude   (deg):  %19.8f\n", lat*dpr_c ( ) );
printf( " \n" );
printf( "Rectangular coordinates from latrec_c:\n" );
printf( " \n" );
printf( " X           (km):  %19.8f\n", rectan );
printf( " Y           (km):  %19.8f\n", rectan );
printf( " Z           (km):  %19.8f\n", rectan );
printf( " \n" );

return ( 0 );
}

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

Original rectangular coordinates:

X           (km):      -55658.44323296
Y           (km):     -379226.32931475
Z           (km):     -126505.93063865

Spherical coordinates:

Colatitude (deg):         108.26566077
Longitude  (deg):         -98.34959789

Latitudinal coordinates:

Longitude  (deg):         -98.34959789
Latitude   (deg):         -18.26566077

Rectangular coordinates from latrec_c:

X           (km):      -55658.44323296
Y           (km):     -379226.32931475
Z           (km):     -126505.93063865

3) Create a table showing a variety of spherical coordinates
and the corresponding cylindrical coordinates.

Corresponding spherical and cylindrical coordinates are
listed to three decimal places. Input and output angles
are in degrees.

Example code begins here.

/.
Program sphlat_ex3
./
#include <stdio.h>
#include "SpiceUsr.h"

int main( )
{

/.
Local parameters.
./
#define NREC         11

/.
Local variables.
./
SpiceDouble          lat;
SpiceDouble          lon;
SpiceDouble          rcolat;
SpiceDouble          rslon;

SpiceInt             i;

/.
Define the input spherical coordinates. Angles in degrees.
./
SpiceDouble          r      [NREC] = {  0.0,  1.0,     1.0,
1.0,  1.4142,  1.0,
1.0,  1.0,     1.4142,
1.0,  0.0             };

SpiceDouble          colat  [NREC] = {  0.0,  90.0,  90.0,
0.0,  45.0,  90.0,
180.0,  90.0, 135.0,
0.0,  90.0        };

SpiceDouble          slon   [NREC] = {  0.0,   0.0,  90.0,
0.0, 180.0, -90.0,
0.0,  45.0, 180.0,
180.0,  33.0        };

/.
Print the banner.
./
printf( "    r      colat     slon    radius    lon      lat\n"   );
printf( " -------  -------  -------  -------  -------  -------\n" );

/.
Do the conversion. Output angles in degrees.
./
for ( i = 0; i < NREC; i++ )
{

rcolat = colat[i] * rpd_c ( );
rslon  = slon[i]  * rpd_c ( );

sphlat_c ( r[i], rcolat, rslon, &radius, &lon, &lat );

printf( "%8.3f %8.3f %8.3f ", r[i], colat[i], slon[i] );
printf( "%8.3f %8.3f %8.3f\n", radius, lon * dpr_c ( ),
lat * dpr_c ( ) );

}

return ( 0 );
}

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

r      colat     slon    radius    lon      lat
-------  -------  -------  -------  -------  -------
0.000    0.000    0.000    0.000    0.000   90.000
1.000   90.000    0.000    1.000    0.000    0.000
1.000   90.000   90.000    1.000   90.000    0.000
1.000    0.000    0.000    1.000    0.000   90.000
1.414   45.000  180.000    1.414  180.000   45.000
1.000   90.000  -90.000    1.000  -90.000    0.000
1.000  180.000    0.000    1.000    0.000  -90.000
1.000   90.000   45.000    1.000   45.000    0.000
1.414  135.000  180.000    1.414  180.000  -45.000
1.000    0.000  180.000    1.000  180.000   90.000
0.000   90.000   33.000    0.000   33.000    0.000

None.

None.

Author_and_Institution

J. Diaz del Rio     (ODC Space)
B.V. Semenov        (JPL)
W.L. Taber          (JPL)
E.D. Wright         (JPL)

Version

-CSPICE Version 1.1.0, 05-JUL-2021 (JDR)

Changed the output argument name "lons" to "slon" for
consistency with other routines.

Edited the header to comply with NAIF standard.