Table of contents
CSPICE_SPHCYL converts spherical coordinates to cylindrical
coordinates.
Given:
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 call:
[r, clon, z] = cspice_sphcyl( radius, colat, slon )
returns:
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 arguments `r' and `z' return in the same units associated
with `radius'.
`r', `clon', and `z' return with the same vectorization
measure, N, as `radius', `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) Compute the spherical coordinates of the position of the Moon
as seen from the Earth, and convert them to cylindrical and
rectangular coordinates.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: sphcyl_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 sphcyl_ex1()
%
% Load an SPK and leapseconds kernels.
%
cspice_furnsh( 'sphcyl_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 coords to cylindrical.
%
[r, lon, z] = cspice_sphcyl(radius, colat, slon);
fprintf( '\n' )
fprintf( 'Cylindrical coordinates:\n' )
fprintf( ' Radius (km): %20.8f\n', r )
fprintf( ' Longitude (deg): %20.8f\n', lon * cspice_dpr )
fprintf( ' Z (km): %20.8f\n', z )
%
% Convert the cylindrical to rectangular.
%
[rectan] = cspice_cylrec(r, lon, z);
fprintf( '\n' )
fprintf( 'Rectangular coordinates from cspice_cylrec:\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
Cylindrical coordinates:
Radius (km): 383289.01777726
Longitude (deg): -98.34959789
Z (km): -126505.93063865
Rectangular coordinates from cspice_cylrec:
X (km): -55658.44323296
Y (km): -379226.32931475
Z (km): -126505.93063865
2) 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.
function sphcyl_ex2()
%
% Define six sets of spherical coordinates, `slon' and `colat'
% expressed in degrees - converted to radians by use of cspice_rpd.
%
radius = [ 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 cylindrical coordinates
%
[r, clon, z] = cspice_sphcyl(radius, colat, slon);
%
% ...convert angular measure to degrees.
%
colat = colat * cspice_dpr;
clon = clon * cspice_dpr;
slon = slon * 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( '%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 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
3) Other than the obvious conversion between coordinate systems
this routine could be used to obtain the axial projection
from a sphere to a cylinder about the z-axis that contains
the equator of the sphere.
Such a projection is valuable because it preserves the
areas between regions on the sphere and their projections to
the cylinder.
Example code begins here.
function sphcyl_ex3()
%
% Define the point whose projection is to be
% computed.
%
radius = 100.0;
slon = 45.0 * cspice_rpd;
colat = 102.5 * cspice_rpd;
%
% Convert the spherical coordinates to cylindrical.
%
[r, clon, z] = cspice_sphcyl( radius, colat, slon );
fprintf( 'Coordinates of the projected point on cylinder:\n' )
fprintf( ' \n' )
fprintf( ' Radius (km): %22.11f\n', r )
fprintf( ' Longitude (deg): %22.11f\n', clon*cspice_dpr )
fprintf( ' Z (km): %22.11f\n', z )
When this program was executed on a Mac/Intel/Octave6.x/64-bit
platform, the output was:
Coordinates of the projected point on cylinder:
Radius (km): 97.62960071199
Longitude (deg): 45.00000000000
Z (km): -21.64396139381
This returns the cylindrical coordinates of a point whose
position is input through spherical coordinates.
1) If any of the input arguments, `radius', `colat' or `slon', is
undefined, an error is signaled by the Matlab error handling
system.
2) If any of the input arguments, `radius', `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 `radius', `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, 24-AUG-2021 (EDW) (JDR)
Changed the output argument name "lonc" to "clon".
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 and a third example.
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 cylindrical coordinates
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