Table of contents
CSPICE_SPHLAT converts spherical coordinates to latitudinal
coordinates.
Given:
r the value(s) describing the distance of the position
from the origin.
[1,n] = size(r); double = class(r)
colat the value(s) describing the angle between the point and the
positive z-axis, measured in radians (also referred to
as the polar angle).
[1,n] = size(colat); double = class(colat)
slon the value(s) describing the angle of the projection of the
point to the XY plane from the positive X-axis, measured
in radians, with range:
-pi < slon <= pi
The positive Y-axis is at longitude PI/2 radians.
[1,n] = size(slon); double = class(slon)
the call:
[radius, lon, lat] = cspice_sphlat(r, colat, slon)
returns:
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 argument `radius' returns in the same units associated
with `r'.
`radius', `lon', and `lat' return with the same
vectorization measure (N) as the `r', `colat',
and `slon'.
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) Latitude is obtained by subtracting co-latitude from cspice_halfpi
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
KERNELS_TO_LOAD = ( 'de421.bsp',
'naif0012.tls' )
\begintext
End of meta-kernel
Example code begins here.
function sphlat_ex2()
%
% Load an SPK and leapseconds kernels.
%
cspice_furnsh( 'sphlat_ex2.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 spherical
% coordinates.
%
[radius, colat, slon] = cspice_recsph(pos);
fprintf( '\n' )
fprintf( 'Spherical coordinates:\n' )
fprintf( ' Radius (km): %20.8f\n', radius )
fprintf( ' Polar Angle (deg): %20.8f\n', colat * cspice_dpr )
fprintf( ' Longitude (deg): %20.8f\n', slon * cspice_dpr )
%
% Convert the spherical coords to latitudinal.
%
[r, lon, lat] = cspice_sphlat(radius, colat, slon);
fprintf( '\n' )
fprintf( 'Latitudinal coordinates:\n' )
fprintf( ' Radius (km): %20.8f\n', r )
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(r, 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
Spherical coordinates:
Radius (km): 403626.33912495
Polar Angle (deg): 108.26566077
Longitude (deg): -98.34959789
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
3) Create a table showing a variety of spherical coordinates
and the corresponding latitudinal coordinates.
Corresponding spherical and latitudinal coordinates are
listed to three decimal places. Input and output angles
are in degrees.
Example code begins here.
function sphlat_ex3()
%
% Define six sets of spherical coordinates, `slon' and `colat'
% expressed in degrees - converted to radians by use of cspice_rpd.
%
r = [ 1., 1., 1.4142, 1.4142, 1. , 0. ];
colat = [ 90., 90., 45. , 135. , 0. , 0. ] * cspice_rpd;
slon = [ 0., 90., 180. , 180. , 180., 33.] * cspice_rpd;
%
% ...convert the spherical coordinates to latitudinal coordinates
%
[rad, lon, lat] = cspice_sphlat(r, colat, slon);
%
% ...convert angular measure to degrees.
%
colat = colat * cspice_dpr;
lon = lon * cspice_dpr;
slon = slon * cspice_dpr;
lat = lat * cspice_dpr;
%
% Output banner.
%
disp(' r colat slon radius lon lat' )
disp(' ------- ------- ------- ------- ------- -------')
%
% Create an array of values for output.
%
output = [ r; colat; slon; rad; lon; lat];
txt = sprintf( '%8.3f %8.3f %8.3f %8.3f %8.3f %8.3f\n', output );
disp( txt )
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
r colat slon radius lon lat
------- ------- ------- ------- ------- -------
1.000 90.000 0.000 1.000 0.000 0.000
1.000 90.000 90.000 1.000 90.000 0.000
1.414 45.000 180.000 1.414 180.000 45.000
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 0.000 33.000 0.000 33.000 90.000
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.
1) If any of the input arguments, `r', `colat' or `slon', is
undefined, an error is signaled by the Matlab error handling
system.
2) If any of the input arguments, `r', `colat' or `slon', 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 `r', `colat' and `slon' 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, 10-AUG-2021 (EDW) (JDR)
Changed input argument name "lons" to "slon".
Edited the -Examples section to comply with NAIF standard. Added
meta-kernel to example #2. Updated code example #2 to produce
formatted output and added a call to cspice_kclear. Added the
example #1 and the problem statement to all 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, 12-DEC-2005 (EDW)
spherical to latitudinal coordinates
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