Table of contents
CSPICE_LATREC converts latitudinal coordinates to rectangular
(Cartesian) coordinates.
Given:
radius the value(s) describing the distance of the position
from the origin.
[1,n] = size(radius); double = class(radius)
lon the value(s) describing the angle of the position from
the XZ plane measured in radians.
[1,n] = size(lon); double = class(lon)
lat the value(s) describing the angle of the position from the
XY plane measured in radians.
[1,n] = size(lat); double = class(lat)
the call:
[rectan] = cspice_latrec( radius, lon, lat )
returns:
rectan the array(s) containing the rectangular coordinates of the
position or set of positions
[3,n] = size(rectan); double = class(rectan)
`rectan' returns with the same units associated with `radius'.
`rectan' returns with the vectorization measure, N, as
`radius', `lon', and `lat'.
None.
Any numerical results shown for these examples may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
1) Compute the latitudinal coordinates of the position of the Moon
as seen from the Earth, and convert them to rectangular
coordinates.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: latrec_ex1.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
KERNELS_TO_LOAD = ( 'de421.bsp',
'naif0012.tls' )
\begintext
End of meta-kernel
Example code begins here.
function latrec_ex1()
%
% Load an SPK and leapseconds kernels.
%
cspice_furnsh( 'latrec_ex1.tm' )
%
% Convert the time to ET.
%
et = cspice_str2et( '2017 Mar 20' );
%
% Retrieve the position of the moon seen from earth at 'et'
% in the J2000 frame without aberration correction.
%
[pos, et] = cspice_spkpos( 'MOON', et, 'J2000', 'NONE', 'EARTH' );
fprintf( 'Original rectangular coordinates:\n' )
fprintf( ' X (km): %20.8f\n', pos(1) )
fprintf( ' Y (km): %20.8f\n', pos(2) )
fprintf( ' Z (km): %20.8f\n', pos(3) )
%
% Convert the position vector 'pos' to latitudinal
% coordinates.
%
[radius, lon, lat] = cspice_reclat(pos);
fprintf( '\n' )
fprintf( 'Latitudinal coordinates:\n' )
fprintf( ' Radius (km): %20.8f\n', radius )
fprintf( ' Longitude (deg): %20.8f\n', lon * cspice_dpr )
fprintf( ' Latitude (deg): %20.8f\n', lat * cspice_dpr )
%
% Convert the latitudinal to rectangular.
%
[rectan] = cspice_latrec( radius, lon, lat);
fprintf( '\n' )
fprintf( 'Rectangular coordinates from cspice_latrec:\n' )
fprintf( ' X (km): %20.8f\n', rectan(1) )
fprintf( ' Y (km): %20.8f\n', rectan(2) )
fprintf( ' Z (km): %20.8f\n', rectan(3) )
%
% It's always good form to unload kernels after use,
% particularly in MATLAB due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Original rectangular coordinates:
X (km): -55658.44323296
Y (km): -379226.32931475
Z (km): -126505.93063865
Latitudinal coordinates:
Radius (km): 403626.33912495
Longitude (deg): -98.34959789
Latitude (deg): -18.26566077
Rectangular coordinates from cspice_latrec:
X (km): -55658.44323296
Y (km): -379226.32931475
Z (km): -126505.93063865
2) Create a table showing a variety of latitudinal coordinates
and the corresponding rectangular coordinates.
Corresponding latitudinal and rectangular coordinates are
listed to four decimal places. Input angles are in degrees.
Example code begins here.
function latrec_ex2()
%
% Define eleven sets of latitudinal coordinates.
%
r = [ 0., 1., 1., 1., 1., 1., 1., ...
sqrt(2), sqrt(2), sqrt(2), sqrt(3) ];
longitude = [ 0., 0., 90., 0. 180., -90., ...
0., 45., 0., 90., 45. ];
latitude = [ 0., 0., 0., 90., 0., 0., ...
-90., 0., 45., 45., 35.2643 ];
%
% ...convert the latitudinal coordinates to rectangular coordinates
%
longitude = longitude * cspice_rpd;
latitude = latitude * cspice_rpd;
rectan = cspice_latrec(r, longitude, latitude);
%
% Loop over each set of coordinates for output, convert `longitude'
% and `latitude' to degrees...
%
longitude = longitude * cspice_dpr;
latitude = latitude * cspice_dpr;
%
% Create an array of values for output.
%
output = [ r; longitude; latitude; rectan ];
%
% Output banner.
%
disp(' r lon lat rect(1) rect(2) rect(3)')
disp(' ------- -------- -------- ------- ------- -------')
txt = sprintf( '%9.3f %9.3f %9.3f %9.3f %9.3f %9.3f\n', output );
disp( txt )
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
r lon lat rect(1) rect(2) rect(3)
------- -------- -------- ------- ------- -------
0.000 0.000 0.000 0.000 0.000 0.000
1.000 0.000 0.000 1.000 0.000 0.000
1.000 90.000 0.000 0.000 1.000 0.000
1.000 0.000 90.000 0.000 0.000 1.000
1.000 180.000 0.000 -1.000 0.000 0.000
1.000 -90.000 0.000 0.000 -1.000 0.000
1.000 0.000 -90.000 0.000 0.000 -1.000
1.414 45.000 0.000 1.000 1.000 0.000
1.414 0.000 45.000 1.000 0.000 1.000
1.414 90.000 45.000 0.000 1.000 1.000
1.732 45.000 35.264 1.000 1.000 1.000
This routine returns the rectangular coordinates of a point
whose position is input in latitudinal 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.
1) If any of the input arguments, `radius', `lon' or `lat', is
undefined, an error is signaled by the Matlab error handling
system.
2) If any of the input arguments, `radius', `lon' or `lat', is
not of the expected type, or it does not have the expected
dimensions and size, an error is signaled by the Mice
interface.
3) If the input vectorizable arguments `radius', `lon' and `lat'
do not have the same measure of vectorization (N), an error is
signaled by the Mice interface.
None.
None.
MICE.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Mice Version 1.1.0, 24-AUG-2021 (EDW) (JDR)
Changed input argument names "longitude" and "latitude" to "lon" and
"lat".
Edited the header to comply with NAIF standard. Added
meta-kernel to example #1. Updated code example #1 to produce
formatted output and added a call to cspice_kclear. Added the
problem statement to both examples.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections, and
completed -Particulars section.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.1, 01-DEC-2014 (EDW)
Edited -I/O section to conform to NAIF standard for Mice
documentation.
-Mice Version 1.0.0, 22-NOV-2005 (EDW)
latitudinal to rectangular coordinates
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