Table of contents
CSPICE_SPHREC converts spherical coordinates to rectangular
(Cartesian) coordinates.
Given:
r a double precision scalar or N-vector describing the distance of
the point from the origin.
help, r
DOUBLE = Scalar or DOUBLE = Array[N]
colat a double precision scalar or N-vector describing the angle
between the point and the positive Z-axis measured in radians.
help, colat
DOUBLE = Scalar or DOUBLE = Array[N]
slon a double precision scalar or N-vector describing the angle of
the projection of the point to the XY plane from the positive
X-axis measured in radians.
help, slon
DOUBLE = Scalar or DOUBLE = Array[N]
The positive Y-axis is at longitude PI/2 radians.
the call:
cspice_sphrec, r, colat, slon, rectan
returns:
rectan a double precision 3-vector or 3xN array containing the
rectangular coordinates of the position or set of positions.
help, rectan
DOUBLE = Array[3] or DOUBLE = Array[3,N]
`rectan' returns with the same measure of vectorization (N)
as `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) 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: sphrec_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.
PRO sphrec_ex1
;;
;; Load SPK and LSK kernels, use a meta kernel for
;; convenience.
;;
cspice_furnsh, 'sphrec_ex1.tm'
;;
;; Look up the geometric state of the Moon as seen from
;; the Earth at 2017 Mar 20, relative to the J2000
;; reference frame.
;;
cspice_str2et, '2017 Mar 20', et
cspice_spkpos, 'Moon', et, 'J2000', 'NONE', 'Earth', pos, ltime
;;
;; Convert the position vector `pos' to spherical
;; coordinates.
;;
cspice_recsph, pos, radius, colat, slon
;;
;; Convert the spherical coordinates to rectangular.
;;
cspice_sphrec, radius, colat, slon, rectan
print, ' '
print, 'Original rectangular coordinates:'
print, ' '
print, format='(A,F20.8)', ' X (km): ', pos[0]
print, format='(A,F20.8)', ' Y (km): ', pos[1]
print, format='(A,F20.8)', ' Z (km): ', pos[2]
print, ' '
print, 'Spherical coordinates:'
print, ' '
print, format='(A,F20.8)', ' Radius (km): ', radius
print, format='(A,F20.8)', ' Colatitude (deg): ', $
colat*cspice_dpr( )
print, format='(A,F20.8)', ' Longitude (deg): ', $
slon*cspice_dpr( )
print, ' '
print, 'Rectangular coordinates from cspice_sphrec:'
print, ' '
print, format='(A,F20.8)', ' X (km): ', rectan[0]
print, format='(A,F20.8)', ' Y (km): ', rectan[1]
print, format='(A,F20.8)', ' Z (km): ', rectan[2]
print, ' '
END
When this program was executed on a Mac/Intel/IDL8.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
Colatitude (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 spherical coordinates
and the corresponding rectangular coordinates.
Corresponding spherical and rectangular coordinates are
listed to three decimal places. Input angles are in degrees.
Example code begins here.
PRO sphrec_ex2
;;
;; Local parameters.
;;
NREC = 11
;;
;; Define the input spherical coordinates. Angles are in degrees.
;;
radius = [ 0.0d, 1.0d, 1.0d, 1.0d, 1.0d, 1.0d, $
1.0d, 1.4142d, 1.4142d, 1.4142d, 1.7320d ]
colat = [ 0.0d, 90.0d, 90.0d, 0.0d, 90.0d, 90.0d, $
180.0d, 90.0d, 45.0d, 45.0d, 54.7356d ]
slon = [ 0.0d, 0.0d, 90.0d, 0.0d, 180.0d, -90.0d, $
0.0d, 45.0d, 0.0d, 90.0d, 45.0d ]
;;
;; Print the banner.
;;
print, ' radius colat slon rect[0] rect[1] rect[2]'
print, ' ------- ------- ------- ------- ------- -------'
;;
;; Do the conversion.
;;
for i=0, NREC - 1L do begin
rcolat = colat[i] * cspice_rpd( )
rslon = slon[i] * cspice_rpd( )
cspice_sphrec, radius[i], rcolat, rslon, rectan
print, format='(3F9.3,$)', radius[i], colat[i], slon[i]
print, format='(3F9.3)', rectan[0], rectan[1], rectan[2]
endfor
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
radius colat slon rect[0] rect[1] rect[2]
------- ------- ------- ------- ------- -------
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 rectangular coordinates of a point
whose position is input in spherical 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. The co-latitude of the positive Z-axis is
zero. The longitude of the positive Y-axis is PI/2 radians.
1) If any of the input arguments, `r', `colat' or `slon', is
undefined, an error is signaled by the IDL 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 Icy
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 Icy interface.
4) If the output argument `rectan' is not a named variable, an
error is signaled by the Icy interface.
None.
None.
ICY.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.1.0, 13-AUG-2021 (JDR)
Edited the -Examples section to comply with NAIF standard.
Added complete code examples.
Changed the input argument name "lon" to "slon" for consistency
with other routines.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections, and
completed -Particulars section.
Removed reference to the routine's corresponding CSPICE header from
-Abstract section.
Added arguments' type and size information in the -I/O section.
-Icy Version 1.0.2, 05-FEB-2008 (EDW)
Edited -I/O section, replaced comment
"returns with the same order"
with
"returns with the same measure of vectorization"
-Icy Version 1.0.1, 09-DEC-2005 (EDW)
Added -Examples section.
-Icy Version 1.0.0, 16-JUN-2003 (EDW)
spherical to rectangular coordinates
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