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recpgr_c

 Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input Detailed_Output Parameters Exceptions Files Particulars Examples Restrictions Literature_References Author_and_Institution Version Index_Entries

Procedure

recpgr_c ( Rectangular to planetographic )

void recpgr_c ( ConstSpiceChar   * body,
SpiceDouble        rectan,
SpiceDouble        re,
SpiceDouble        f,
SpiceDouble      * lon,
SpiceDouble      * lat,
SpiceDouble      * alt       )

Abstract

Convert rectangular coordinates to planetographic coordinates.

KERNEL
NAIF_IDS
PCK

CONVERSION
COORDINATES
GEOMETRY
MATH

Brief_I/O

VARIABLE  I/O  DESCRIPTION
--------  ---  --------------------------------------------------
body       I   Body with which coordinate system is associated.
rectan     I   Rectangular coordinates of a point.
re         I   Equatorial radius of the reference spheroid.
f          I   Flattening coefficient.
lon        O   Planetographic longitude of the point (radians).
lat        O   Planetographic latitude of the point (radians).
alt        O   Altitude of the point above reference spheroid.

Detailed_Input

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

rectan      are the rectangular coordinates of a point. Units
are arbitrary, except that the input `re' must be
expressed in the same units.

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
`rectan'.

f           is the flattening coefficient =

(re-rp) / re

where `rp' is the polar radius of the spheroid, and the
units of `rp' match those of `re'.

Detailed_Output

lon         is the planetographic longitude of the input point.
This is the angle between the prime meridian and the
meridian containing `rectan'. 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 output in radians. The nominal range of `lon' is
given by:

0  <  lon  <  2*pi
-

However, round-off error could cause `lon' to equal 2*pi.

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 output in radians. The range of `lat' is given
by:

-pi/2  <  lat  <  pi/2
-       -

alt         is the altitude of point above the reference spheroid.

The units associated with `alt' are those associated
with the input `rectan' and `re'.

None.

Exceptions

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)  For points inside the reference ellipsoid, the nearest point
on the ellipsoid to `rectan' may not be unique, so latitude may
not be well-defined.

7)  If the `body' input string pointer is null, the error
SPICE(NULLPOINTER) is signaled.

8)  If the `body' input string has zero length, the error
SPICE(EMPTYSTRING) is signaled.

Files

This routine expects a kernel variable giving body's prime
meridian angle as a function of time to be available in the
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

The optional kernel variable

BODY<body ID>_PGR_POSITIVE_LON

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.

Particulars

Given the body-fixed rectangular coordinates of a point, this
routine returns the planetographic 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
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

The definition of this kernel variable controls the behavior of
the CSPICE planetographic routines

pgrrec_c
recpgr_c
dpgrdr_c
drdpgr_c

It does not affect the other CSPICE coordinate conversion
routines.

Examples

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 planetographic coordinates of the point having Mars
rectangular coordinates:

X (km) =      0.0
Y (km) =  -2620.678914818178
Z (km) =   2592.408908856967

(These input values have been chosen to create "simple" output
values.)

Use the PCK kernel below to load the required triaxial
ellipsoidal shape model and orientation data for Mars.

pck00008.tpc

Example code begins here.

/.
Program recpgr_ex1
./

#include <stdio.h>
#include "SpiceUsr.h"

int main()
{
/.
Local variables
./
SpiceDouble             alt;
SpiceDouble             f;
SpiceDouble             lat;
SpiceDouble             lon;
SpiceDouble             re;
SpiceDouble             rectan ;
SpiceDouble             rp;

SpiceInt                n;

/.
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.
./

/.
Compute flattening coefficient.
./
f   =  ( re - rp ) / re;

/.
Do the conversion.
./
rectan =      0.0;
rectan =  -2620.678914818178;
rectan =   2592.408908856967;

recpgr_c ( "mars", rectan, re, f, &lon, &lat, &alt );

printf ( "\n"
"Rectangular coordinates:\n"
"\n"
"  X (km)                 = %18.9e\n"
"  Y (km)                 = %18.9e\n"
"  Z (km)                 = %18.9e\n"
"\n"
"Ellipsoid shape parameters:\n"
"\n"
"  Equatorial radius (km) = %18.9e\n"
"  Polar radius      (km) = %18.9e\n"
"  Flattening coefficient = %18.9e\n"
"\n"
"Planetographic coordinates:\n"
"\n"
"  Longitude (deg)        = %18.9e\n"
"  Latitude  (deg)        = %18.9e\n"
"  Altitude  (km)         = %18.9e\n"
"\n",
rectan,
rectan,
rectan,
re,
rp,
f,
lon / rpd_c(),
lat / rpd_c(),
alt                   );

return ( 0 );
}

When this program was executed on a Mac/Intel/cc/64-bit
platform, the output was:

Rectangular coordinates:

X (km)                 =    0.000000000e+00
Y (km)                 =   -2.620678915e+03
Z (km)                 =    2.592408909e+03

Ellipsoid shape parameters:

Flattening coefficient =    5.886007556e-03

Planetographic coordinates:

Longitude (deg)        =    9.000000000e+01
Latitude  (deg)        =    4.500000000e+01
Altitude  (km)         =    3.000000000e+02

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

Note:  the values shown above may not be current or suitable

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,

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

None.

None.

Author_and_Institution

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)
E.D. Wright         (JPL)

Version

-CSPICE Version 1.0.2, 10-AUG-2021 (JDR)

Edited header to comply with NAIF standard.

-CSPICE Version 1.0.1, 23-JAN-2008 (EDW)

Corrected typo in LAT range description, from:

-pi/2  <  LAT  <  pi
-       -

to:

-pi/2  <  LAT  <  pi/2
-       -

-CSPICE Version 1.0.0, 26-DEC-2004 (CHA) (NJB) (HAN) (BVS) (WLT)

Index_Entries

convert rectangular to planetographic coordinates
Fri Dec 31 18:41:11 2021