Table of contents
CSPICE_RECSPH converts rectangular (Cartesian) coordinates to
spherical coordinates. All coordinates are expressed as
double precision values.
Given:
rectan the array(s) containing the rectangular coordinates of the
position or set of positions.
[3,n] = size(rectan); double = class(rectan)
the call:
[r, colat, slon] = cspice_recsph( rectan )
returns:
r the value(s) describing the distance of the position
from the origin.
[1,n] = size(radius); double = class(radius)
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 argument `r' returns with the same units associated
with `rectan'.
`r', `colat', and `slon' return with the same vectorization
measure (N) as `rectan'.
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 spherical 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: recsph_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 recsph_ex1()
%
% Load an SPK and leapseconds kernels.
%
cspice_furnsh( 'recsph_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 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 to rectangular.
%
[rectan] = cspice_sphrec(radius, colat, slon);
fprintf( '\n' )
fprintf( 'Rectangular coordinates from cspice_sphrec:\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
Rectangular coordinates from cspice_sphrec:
X (km): -55658.44323296
Y (km): -379226.32931475
Z (km): -126505.93063865
2) Create a table showing a variety of rectangular coordinates
and the corresponding spherical coordinates.
Corresponding rectangular and spherical coordinates are
listed to three decimal places. Output angles are in degrees.
Example code begins here.
function recsph_ex2()
%
% Define eleven sets of rectangular coordinates.
%
rec = [ [ 0., 1., 0., 0., -1., 0., 0., 1., 1., 0., 1. ]; ...
[ 0., 0., 1., 0., 0., -1., 0., 1., 0., 1., 1. ]; ...
[ 0., 0., 0., 1., 0., 0., -1., 0., 1., 1., 1. ] ];
%
% ...convert the rectangular coordinates to spherical coordinates
%
[r, colat, slon] = cspice_recsph(rec);
%
% Convert 'colat' and 'slon to degrees...
%
colat = colat * cspice_dpr;
slon = slon * cspice_dpr;
%
% Output banner.
%
disp(' r colat slon rect(1) rect(2) rect(3)')
disp(' ------- ------- ------- ------- ------- -------')
%
% Create an array of values for output.
%
output = [ r; colat; slon; rec(1,:); rec(2,:); rec(3,:) ];
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 rect(1) rect(2) rect(3)
------- ------- ------- ------- ------- -------
0.000 0.000 0.000 0.000 0.000 0.000
1.000 90.000 0.000 1.000 0.000 0.000
1.000 90.000 90.000 0.000 1.000 0.000
1.000 0.000 0.000 0.000 0.000 1.000
1.000 90.000 180.000 -1.000 0.000 0.000
1.000 90.000 -90.000 0.000 -1.000 0.000
1.000 180.000 0.000 0.000 0.000 -1.000
1.414 90.000 45.000 1.000 1.000 0.000
1.414 45.000 0.000 1.000 0.000 1.000
1.414 45.000 90.000 0.000 1.000 1.000
1.732 54.736 45.000 1.000 1.000 1.000
This routine returns the spherical coordinates of a point
whose position is input in rectangular coordinates.
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 the input argument `rectan' is undefined, an error is
signaled by the Matlab error handling system.
2) If the input argument `rectan' is not of the expected type, or
it does not have the expected dimensions and size, 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, 23-AUG-2021 (EDW) (JDR)
Changed the input argument name "lon" to "slon" for consistency
with other routines.
Edited the -Examples section 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)
rectangular to spherical coordinates
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