Table of contents
CSPICE_PGRREC converts planetographic coordinates to
rectangular coordinates.
Given:
body the name of the body with which the planetographic coordinate
system is associated.
help, body
STRING = Scalar
`body' is used by this routine to look up from the
kernel pool the prime meridian rate coefficient giving
the body's spin sense. See the -Files and -Particulars
header sections below for details.
lon the planetographic longitude of the input point, or an N-vector
of longitudes.
help, lon
DOUBLE = Scalar or DOUBLE = Array[N]
This is the angle between the prime meridian and the meridian
containing the input point. For bodies having prograde (aka
direct) rotation, the direction of increasing longitude is
positive west: from the +X axis of the rectangular coordinate
system toward the -Y axis. For bodies having retrograde
rotation, the direction of increasing longitude is positive
east: from the +X axis toward the +Y axis.
The earth, moon, and sun are exceptions:
planetographic longitude is measured positive east for
these bodies.
The default interpretation of longitude by this
and the other planetographic coordinate conversion
routines can be overridden; see the discussion in
-Particulars below for details.
`lon' is measured in radians. On input, the range
of longitude is unrestricted.
lat the planetographic latitude of the input point, or an N-vector
of latitudes.
help, lat
DOUBLE = Scalar or DOUBLE = Array[N]
For a point P on the reference spheroid, this is the angle
between the XY plane and the outward normal vector at P. For a
point P not on the reference spheroid, the planetographic
latitude is that of the closest point to P on the spheroid.
`lat' is measured in radians. On input, the
range of latitude is unrestricted.
alt the altitude of point above the reference spheroid, or an
N-vector of altitudes.
help, alt
DOUBLE = Scalar or DOUBLE = Array[N]
Units of `alt' must match those of `re'.
re the equatorial radius of a reference spheroid.
help, re
DOUBLE = Scalar
This spheroid is a volume of revolution: its horizontal cross
sections are circular. The shape of the spheroid is defined by
an equatorial radius `re' and a polar radius `rp'. Units of `re'
must match those of `alt'.
f the flattening coefficient of the body, a
dimensionless value defined as:
(re - rp) / re
where `rp' is the polar radius of the spheroid, and the
units of `rp' match those of `re'.
help, f
DOUBLE = Scalar
the call:
cspice_pgrrec, body, lon, lat, alt, re, f, rectan
returns:
rectan the rectangular coordinates of the input point, or an
N-vector of coordinates.
help, rectan
DOUBLE = Array[3] or DOUBLE = Array[3,N]
See the discussion below in the -Particulars header section for
details.
The units associated with `rectan' are those associated
with the inputs `alt' and `re'.
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) Find the rectangular coordinates of the point having Mars
planetographic coordinates:
longitude = 90 degrees west
latitude = 45 degrees north
altitude = 300 km
Use the PCK kernel below to load the required triaxial
ellipsoidal shape model and orientation data for Mars.
pck00008.tpc
Example code begins here.
PRO pgrrec_ex1
;;
;; Load a PCK file containing a triaxial
;; ellipsoidal shape model and orientation
;; data for Mars.
;;
cspice_furnsh, 'pck00008.tpc'
;;
;; Example 1: convert a single set of planetographic
;; coordinates to rectangular bodyfixed
;; coordinates.
;;
;; Look up the radii for Mars. Although we
;; omit it here, we could check the kernel pool
;; to make sure the variable BODY499_RADII
;; has three elements and numeric data type.
;; If the variable is not present in the kernel
;; pool, cspice_bodvrd will signal an error.
;;
body = 'MARS'
cspice_bodvrd, body, 'RADII', 3, radii
;;
;;
;; Calculate the flatness coefficient.
;;
re = radii[0]
rp = radii[2]
flat = ( re - rp ) / re
;; Set a longitude, latitude, altitude position.
;; Note that we must provide longitude and
;; latitude in radians.
;;
lon = 90.d * cspice_rpd()
lat = 45.d * cspice_rpd()
alt = 3.d2
;;
;; Do the conversion.
;;
cspice_pgrrec, body, lon, lat, alt, re, flat, x
;;
;; Output.
;;
print, 'Rectangular coordinates in km (x, y, z)'
print, FORMAT='( F9.3,3x, F9.3,3x, F9.3)', x
print
print, 'Planetographic coordinates in degs and km (lon, lat, alt)'
print, FORMAT='( F9.3,3x, F9.3,3x, F9.3)', lon *cspice_dpr() $
, lat *cspice_dpr() $
, alt
;;
;; It's always good form to unload kernels after use,
;; particularly in IDL due to data persistence.
;;
cspice_kclear
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
Rectangular coordinates in km (x, y, z)
0.000 -2620.679 2592.409
Planetographic coordinates in degs and km (lon, lat, alt)
90.000 45.000 300.000
2) Create a table showing a variety of rectangular coordinates
and the corresponding Mars planetographic coordinates. The
values are computed using the reference spheroid having radii
Equatorial radius: 3396.190
Polar radius: 3376.200
Note: the values shown above may not be current or suitable
for your application.
Corresponding rectangular and planetographic coordinates are
listed to three decimal places.
Use the PCK file from example 1 above.
Example code begins here.
;;
;; Example 2: convert a vectorized set of planetographic coordinates
;; to rectangular bodyfixed coordinates.
PRO pgrrec_ex2
;;
;; Load a PCK file containing a triaxial
;; ellipsoidal shape model and orientation
;; data for Mars.
;;
cspice_furnsh, 'pck00008.tpc'
;;
;; Look up the radii for Mars. Although we
;; omit it here, we could check the kernel pool
;; to make sure the variable BODY499_RADII
;; has three elements and numeric data type.
;; If the variable is not present in the kernel
;; pool, cspice_bodvrd will signal an error.
;;
body = 'MARS'
cspice_bodvrd, body, 'RADII', 3, radii
;;
;;
;; Calculate the flatness coefficient.
;;
re = radii[0]
rp = radii[2]
flat = ( re - rp ) / re
;;
;; Define vectors of longitudes, latitudes, and altitudes.
;;
lon = [ 0.d, $
180.d, $
180.d, $
180.d, $
90.d, $
270.d, $
0.d, $
0.d, $
0.d ]
lat = [ 0.d, $
0.d, $
0.d, $
0.d, $
0.d, $
0.d, $
90.d, $
-90.d, $
90.d ]
alt = [ 0.d, $
0.d, $
10.d, $
-10.d, $
0.d, $
0.d, $
0.d, $
0.d, $
-3376.200d ]
;;
;; Convert angular measures to radians.
;;
lon = lon*cspice_rpd()
lat = lat*cspice_rpd()
;;
;; Using the same Mars parameters, convert the lon, lat, alt
;; vectors to bodyfixed rectangular coordinates.
;;
cspice_pgrrec, body, lon, lat, alt, re, flat, x
;;
;; Load the data for easy output.
;;
output = dblarr(6,9)
;;
;; Pack the bodyfixed coordinates (x,y,z) into the first three
;; columns of the output array.
;;
output(0,*) = x[0,*]
output(1,*) = x[1,*]
output(2,*) = x[2,*]
;;
;; Pack the planetographic coordinates(lon,lat,alt) into
;; the final three columns of the output array.
;; Convert angular values to degrees.
;;
output(3,*) = lon * cspice_dpr()
output(4,*) = lat * cspice_dpr()
output(5,*) = alt
;;
;; Output the `output' array. Display a banner for clarity.
;;
print, FORMAT='( A9, 2x, A9, 2x, A9, 2x, A8, 2x, A8, 2x, A9)', $
'rectan[0]', 'rectan[1]', 'rectan[2]', 'lon', 'lat', 'alt'
print, '----------------------------------' +$
'----------------------------'
print, FORMAT='(F9.3,2x,F9.3,2x,F9.3,2x,F8.3,2x,F8.3,2x,F9.3)', $
output
;;
;; It's always good form to unload kernels after use,
;; particularly in IDL due to data persistence.
;;
cspice_kclear
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
rectan[0] rectan[1] rectan[2] lon lat alt
--------------------------------------------------------------
3396.190 -0.000 0.000 0.000 0.000 0.000
-3396.190 -0.000 0.000 180.000 0.000 0.000
-3406.190 -0.000 0.000 180.000 0.000 10.000
-3386.190 -0.000 0.000 180.000 0.000 -10.000
0.000 -3396.190 0.000 90.000 0.000 0.000
-0.000 3396.190 0.000 270.000 0.000 0.000
0.000 -0.000 3376.200 0.000 90.000 0.000
0.000 -0.000 -3376.200 0.000 -90.000 0.000
0.000 0.000 0.000 0.000 90.000 -3376.200
3) Below we show the analogous relationships for the earth,
using the reference ellipsoid radii
Equatorial radius: 6378.140
Polar radius: 6356.750
Note the change in longitudes for points on the +/- Y axis
for the earth vs the Mars values.
rectan[0] rectan[1] rectan[2] lon lat alt
--------------------------------------------------------------
6378.140 0.000 0.000 0.000 0.000 0.000
-6378.140 0.000 0.000 180.000 0.000 0.000
-6388.140 0.000 0.000 180.000 0.000 10.000
-6368.140 0.000 0.000 180.000 0.000 -10.000
0.000 -6378.140 0.000 270.000 0.000 0.000
0.000 6378.140 0.000 90.000 0.000 0.000
0.000 0.000 6356.750 0.000 90.000 0.000
0.000 0.000 -6356.750 0.000 -90.000 0.000
0.000 0.000 0.000 0.000 90.000 -6356.750
Given the planetographic coordinates of a point, this routine
returns the body-fixed rectangular coordinates of the point. The
body-fixed rectangular frame is that having the X-axis pass
through the 0 degree latitude 0 degree longitude direction, the
Z-axis pass through the 90 degree latitude direction, and the
Y-axis equal to the cross product of the unit Z-axis and X-axis
vectors.
The planetographic definition of latitude is identical to the
planetodetic (also called "geodetic" in SPICE documentation)
definition. In the planetographic coordinate system, latitude is
defined using a reference spheroid. The spheroid is
characterized by an equatorial radius and a polar radius. For a
point P on the spheroid, latitude is defined as the angle between
the X-Y plane and the outward surface normal at P. For a point P
off the spheroid, latitude is defined as the latitude of the
nearest point to P on the spheroid. Note if P is an interior
point, for example, if P is at the center of the spheroid, there
may not be a unique nearest point to P.
In the planetographic coordinate system, longitude is defined
using the spin sense of the body. Longitude is positive to the
west if the spin is prograde and positive to the east if the spin
is retrograde. The spin sense is given by the sign of the first
degree term of the time-dependent polynomial for the body's prime
meridian Euler angle "W": the spin is retrograde if this term is
negative and prograde otherwise. For the sun, planets, most
natural satellites, and selected asteroids, the polynomial
expression for W may be found in a SPICE PCK kernel.
The earth, moon, and sun are exceptions: planetographic longitude
is measured positive east for these bodies.
If you wish to override the default sense of positive longitude
for a particular body, you can do so by defining the kernel
variable
BODY<body ID>_PGR_POSITIVE_LON
where <body ID> represents the NAIF ID code of the body. This
variable may be assigned either of the values
'WEST'
'EAST'
For example, you can have this routine treat the longitude
of the earth as increasing to the west using the kernel
variable assignment
BODY399_PGR_POSITIVE_LON = 'WEST'
Normally such assignments are made by placing them in a text
kernel and loading that kernel via cspice_furnsh.
The definition of this kernel variable controls the behavior of
the Icy planetographic routines
cspice_pgrrec
cspice_recpgr
cspice_dpgrdr
cspice_drdpgr
It does not affect the other Icy coordinate conversion
routines.
1) If the body name `body' cannot be mapped to a NAIF ID code, and
if `body' is not a string representation of an integer, the
error SPICE(IDCODENOTFOUND) is signaled by a routine in the
call tree of this routine.
2) If the kernel variable
BODY<ID code>_PGR_POSITIVE_LON
is present in the kernel pool but has a value other
than one of
'EAST'
'WEST'
the error SPICE(INVALIDOPTION) is signaled by a routine in the
call tree of this routine. Case and blanks are ignored when
these values are interpreted.
3) If polynomial coefficients for the prime meridian of `body' are
not available in the kernel pool, and if the kernel variable
BODY<ID code>_PGR_POSITIVE_LON is not present in the kernel
pool, the error SPICE(MISSINGDATA) is signaled by a routine in
the call tree of this routine.
4) If the equatorial radius is non-positive, the error
SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call
tree of this routine.
5) If the flattening coefficient is greater than or equal to one,
the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in
the call tree of this routine.
6) If any of the input arguments, `body', `lon', `lat', `alt',
`re' or `f', is undefined, an error is signaled by the IDL
error handling system.
7) If any of the input arguments, `body', `lon', `lat', `alt',
`re' or `f', is not of the expected type, or it does not have
the expected dimensions and size, an error is signaled by the
Icy interface.
8) If the input vectorizable arguments `lon', `lat' and `alt' do
not have the same measure of vectorization (N), an error is
signaled by the Icy interface.
9) If the output argument `rectan' is not a named variable, an
error is signaled by the Icy interface.
This routine expects a kernel variable giving BODY's prime
meridian angle as a function of time to be available in the
kernel pool. Normally this item is provided by loading a PCK
file. The required kernel variable is named
BODY<body ID>_PM
where <body ID> represents a string containing the NAIF integer
ID code for `body'. For example, if `body' is 'JUPITER', then
the name of the kernel variable containing the prime meridian
angle coefficients is
BODY599_PM
See the PCK Required Reading for details concerning the prime
meridian kernel variable.
The optional kernel variable
BODY<body ID>_PGR_POSITIVE_LON
also is normally defined via loading a text kernel. When this
variable is present in the kernel pool, the prime meridian
coefficients for `body' are not required by this routine. See the
-Particulars section below for details.
None.
ICY.REQ
KERNEL.REQ
NAIF_IDS.REQ
PCK.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.0.3, 13-AUG-2021 (JDR)
Edited the header to comply with NAIF standard. Corrected typos in
header.
Split the existing code example into two separate examples and
added example 3. Added reference to cspice_dpgrdr and
cspice_drdpgr routines in -Particulars section.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
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-JAN-2011 (EDW)
Corrected header typo, furnsh_c replaced with cspice_furnsh.
-Icy Version 1.0.1, 22-JAN-2008 (EDW)
Extended header documentation to parallel the CSPICE
and Mice versions.
Replaced the comment fragment in the -I/O section
"return with the same order"
with
"return with the same measure of
vectorization"
-Icy Version 1.0.0, 29-DEC-2004 (EDW)
convert planetographic to rectangular coordinates
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