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.
[1,c1] = size(body); char = class(body)
or
[1,1] = size(body); cell = class(body)
`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(s) of the input point(s).
[1,n] = size(lon); double = class(lon)
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(s) of the input point(s).
[1,n] = size(lat); double = class(lat)
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(s) of point(s) above the reference spheroid.
[1,n] = size(alt); double = class(alt)
Units of `alt' must match those of `re'.
re the equatorial radius of a reference spheroid.
[1,1] = size(re); double = class(re)
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'.
[1,1] = size(f); double = class(f)
the call:
[rectan] = cspice_pgrrec( body, lon, lat, alt, re, f )
returns:
rectan the rectangular coordinates of the input point(s).
[3,n] = size(rectan); double = class(rectan)
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'.
`rectan' returns with the same vectorization measure, N,
as `lon', `lat' and `alt'.
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.
function 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';
radii = cspice_bodvrd( body, 'RADII', 3 );
%
%
% Calculate the flatness coefficient. Set a bodyfixed
% position vector, `x'.
%
re = radii(1);
rp = radii(3);
flat = ( re - rp ) / re;
% Set a longitude, latitude, altitude position.
% Note that we must provide longitude and
% latitude in radians.
%
lon = 90. * cspice_rpd;
lat = 45. * cspice_rpd;
alt = 3.d2;
%
% Do the conversion.
%
x = cspice_pgrrec( body, lon, lat, alt, re, flat );
%
% Output.
%
disp( 'Rectangular coordinates in km (x, y, z)' )
fprintf( '%9.3f %9.3f %9.3f\n', x' )
disp( 'Planetographic coordinates in degs and km (lon, lat, alt)' )
fprintf( '%9.3f %9.3f %9.3f\n', lon *cspice_dpr() ...
, lat *cspice_dpr() ...
, alt )
%
% 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:
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.
%
function 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';
radii = cspice_bodvrd( body, 'RADII', 3 );
%
%
% Calculate the flatness coefficient. Set a bodyfixed
% position vector, `x'.
%
re = radii(1);
rp = radii(3);
flat = ( re - rp ) / re;
%
% Define 1xN arrays of longitudes, latitudes, and altitudes.
%
lon = [ 0., ...
180., ...
180., ...
180., ...
90., ...
270., ...
0., ...
0., ...
0. ];
lat = [ 0., ...
0., ...
0., ...
0., ...
0., ...
0., ...
90., ...
-90., ...
90. ];
alt = [ 0., ...
0., ...
10., ...
10., ...
0., ...
0., ...
0., ...
0., ...
-3376.200 ];
%
% 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.
%
x = cspice_pgrrec( body, lon, lat, alt, re, flat);
disp( ['rectan(1) rectan(2) rectan(3)' ...
' lon lat alt'] )
disp( ['---------------------------------' ...
'------------------------------------'] )
%
% Create an array of values for output.
%
output = [ x(1,:); x(2,:); x(3,:); ...
lon*cspice_dpr; lat*cspice_dpr; alt ];
txt = sprintf( '%9.3f %9.3f %9.3f %9.3f %9.3f %9.3f\n', ...
output);
disp( txt )
%
% 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:
rectan(1) rectan(2) rectan(3) 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
-3406.190 -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(1) rectan(2) rectan(3) 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 Mice planetographic routines
cspice_pgrrec
cspice_recpgr
cspice_dpgrdr
cspice_drdpgr
It does not affect the other Mice 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 Matlab
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
Mice 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 Mice 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.
KERNEL.REQ
MICE.REQ
NAIF_IDS.REQ
PCK.REQ
None.
J. Diaz del Rio (ODC Space)
S.C. Krening (JPL)
E.D. Wright (JPL)
-Mice Version 1.1.0, 24-AUG-2021 (EDW) (JDR)
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections. Fixed
typos in header. Completed list of Mice planetographic routines in
-Particulars section. Extended Required Reading document list.
Edited the header to comply with NAIF standard.
Split the existing code example into two separate examples and
added example 3.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.1, 12-MAR-2012 (EDW) (SCK)
Corrected misspellings.
-Mice Version 1.0.0, 22-JAN-2008 (EDW)
convert planetographic to rectangular coordinates
|