Table of contents
CSPICE_CYLSPH converts cylindrical coordinates to spherical
coordinates.
Given:
r the value(s) describing the distance of the point of
interest from z axis.
[1,n] = size(r); double = class(r)
clon the value(s) describing the cylindrical angle of the point of
interest from the XZ plane measured in radians.
[1,n] = size(clon); double = class(clon)
z the value(s) describing the height of the point above
the XY plane.
[1,n] = size(z); double = class(z)
the call:
[radius, colat, slon] = cspice_cylsph( r, clon, z)
returns:
radius 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 `radius' returns in the same units associated
with `r' and `z'.
`radius', `colat', and `slon' return with the vectorization
measure (N) as `r', `clon', and `z'.
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 cylindrical coordinates of the position of the Moon
as seen from the Earth, and convert them to spherical and
rectangular coordinates.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: cylsph_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 cylsph_ex1()
%
% Load an SPK and leapseconds kernels.
%
cspice_furnsh( 'cylsph_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 cylindrical
% coordinates.
%
[r, clon, z] = cspice_reccyl(pos);
fprintf( '\n' )
fprintf( 'Cylindrical coordinates:\n' )
fprintf( ' Radius (km): %20.8f\n', r )
fprintf( ' Longitude (deg): %20.8f\n', clon * cspice_dpr )
fprintf( ' Z (km): %20.8f\n', z )
%
% Convert the cylindrical coords to spherical.
%
[radius, colat, slon] = cspice_cylsph(r, clon, z);
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
Cylindrical coordinates:
Radius (km): 383289.01777726
Longitude (deg): 261.65040211
Z (km): -126505.93063865
Spherical coordinates:
Radius (km): 403626.33912495
Polar Angle (deg): 108.26566077
Longitude (deg): 261.65040211
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 cylindrical coordinates
and the corresponding spherical coordinates.
Corresponding cylindrical and spherical coordinates are
listed to three decimal places. All input and output angles
are in degrees.
Example code begins here.
function cylsph_ex2()
%
% Define six sets of cylindrical coordinates, `clon' expressed
% in degrees - converted to radians by use of cspice_rpd.
%
r = [ 1., 1., 1., 1., 0., 0. ];
clon = [ 0., 90., 180., 180., 180., 33. ] * cspice_rpd;
z = [ 0., 0., 1., -1., 1., 0. ];
%
% ...convert the cylindrical coordinates to spherical coordinates
%
[radius, colat, slon] = cspice_cylsph(r, clon, z);
%
% ...convert angular measure to degrees.
%
colat = colat * cspice_dpr;
slon = slon * cspice_dpr;
clon = clon * cspice_dpr;
%
% Output banner.
%
disp(' r clon z radius slon colat ')
disp(' ------- -------- -------- ------- -------- --------')
%
% Create an array of values for output.
%
output = [ r; clon; z; radius; slon; colat ];
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 clon z radius slon colat
------- -------- -------- ------- -------- --------
1.000 0.000 0.000 1.000 0.000 90.000
1.000 90.000 0.000 1.000 90.000 90.000
1.000 180.000 1.000 1.414 180.000 45.000
1.000 180.000 -1.000 1.414 180.000 135.000
0.000 180.000 1.000 1.000 180.000 0.000
0.000 33.000 0.000 0.000 33.000 0.000
This returns the spherical coordinates of a point whose position
is input through cylindrical coordinates.
1) If any of the input arguments, `r', `clon' or `z', is
undefined, an error is signaled by the Matlab error handling
system.
2) If any of the input arguments, `r', `clon' or `z', 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', `clon' and `z' 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 the argument names "lonc" and "lon" to "clon" and "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.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.1, 30-OCT-2014 (EDW)
Edited -I/O section to conform to NAIF standard for Mice
documentation.
-Mice Version 1.0.0, 01-DEC-2005 (EDW)
cylindrical to spherical
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