Table of contents
pgrrec_c ( Planetographic to rectangular )
void pgrrec_c ( ConstSpiceChar * body,
SpiceDouble rectan )
Convert planetographic coordinates to rectangular coordinates.
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
body I Body with which coordinate system is associated.
lon I Planetographic longitude of a point (radians).
lat I Planetographic latitude of a point (radians).
alt I Altitude of a point above reference spheroid.
re I Equatorial radius of the reference spheroid.
f I Flattening coefficient.
rectan O Rectangular coordinates of the point.
body is the name of the body with which the planetographic
coordinate system is associated.
`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 is the planetographic longitude of the input point.
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
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 is the planetographic latitude of the input point.
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 is the altitude of point above the reference spheroid.
Units of `alt' must match those of `re'.
re is the equatorial radius of a reference spheroid.
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
f is 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'.
rectan are the rectangular coordinates of the input point.
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'.
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
is present in the kernel pool but has a value other
than one of
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 the `body' input string pointer is null, the error
SPICE(NULLPOINTER) is signaled.
7) If the `body' input string has zero length, the error
SPICE(EMPTYSTRING) is signaled.
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
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
See the PCK Required Reading for details concerning the prime
meridian kernel variable.
The optional kernel variable
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.
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
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
where <body ID> represents the NAIF ID code of the body. This
variable may be assigned either of the values
For example, you can have this routine treat the longitude
of the earth as increasing to the west using the kernel
BODY399_PGR_POSITIVE_LON = 'WEST'
Normally such assignments are made by placing them in a text
kernel and loading that kernel via furnsh_c.
The definition of this kernel variable controls the behavior of
the CSPICE planetographic routines
It does not affect the other CSPICE coordinate conversion
The numerical results shown for these examples may differ across
platforms. The results depend on the SPICE kernels used as
input, the compiler and supporting libraries, and the machine
specific arithmetic implementation.
1) Find the rectangular coordinates of the point having Mars
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.
Example code begins here.
SpiceDouble radii ;
SpiceDouble rectan ;
Load a PCK file containing a triaxial
ellipsoidal shape model and orientation
data for Mars.
furnsh_c ( "pck00008.tpc" );
Look up the radii for Mars. Although we
omit it here, we could first call badkpv_c
to make sure the variable BODY499_RADII
has three elements and numeric data type.
If the variable is not present in the kernel
pool, bodvrd_c will signal an error.
bodvrd_c ( "MARS", "RADII", 3, &n, radii );
Compute flattening coefficient.
re = radii;
rp = radii;
f = ( re - rp ) / re;
Do the conversion. Note that we must provide
longitude and latitude in radians.
lon = 90.0 * rpd_c();
lat = 45.0 * rpd_c();
alt = 3.e2;
pgrrec_c ( "mars", lon, lat, alt, re, f, rectan );
printf ( "\n"
" Longitude (deg) = %18.9e\n"
" Latitude (deg) = %18.9e\n"
" Altitude (km) = %18.9e\n"
"Ellipsoid shape parameters:\n"
" Equatorial radius (km) = %18.9e\n"
" Polar radius (km) = %18.9e\n"
" Flattening coefficient = %18.9e\n"
" X (km) = %18.9e\n"
" Y (km) = %18.9e\n"
" Z (km) = %18.9e\n"
lon / rpd_c(),
lat / rpd_c(),
return ( 0 );
When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:
Longitude (deg) = 9.000000000e+01
Latitude (deg) = 4.500000000e+01
Altitude (km) = 3.000000000e+02
Ellipsoid shape parameters:
Equatorial radius (km) = 3.396190000e+03
Polar radius (km) = 3.376200000e+03
Flattening coefficient = 5.886007556e-03
X (km) = 1.604703022e-13
Y (km) = -2.620678915e+03
Z (km) = 2.592408909e+03
2) Below is 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.
rectan rectan rectan 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 rectan rectan 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
C.H. Acton (JPL)
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
H.A. Neilan (JPL)
B.V. Semenov (JPL)
W.L. Taber (JPL)
-CSPICE Version 1.0.1, 10-AUG-2021 (JDR)
Edited the header to comply with NAIF standard.
-CSPICE Version 1.0.0, 26-DEC-2004 (CHA) (NJB) (HAN) (BVS) (WLT)
convert planetographic to rectangular coordinates