| recpgr |
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Table of contents
Procedure
RECPGR ( Rectangular to planetographic )
SUBROUTINE RECPGR ( BODY, RECTAN, RE, F, LON, LAT, ALT )
Abstract
Convert rectangular coordinates to planetographic coordinates.
Required_Reading
KERNEL
NAIF_IDS
PCK
Keywords
CONVERSION
COORDINATES
GEOMETRY
MATH
Declarations
IMPLICIT NONE
INCLUDE 'zzctr.inc'
CHARACTER*(*) BODY
DOUBLE PRECISION RECTAN ( 3 )
DOUBLE PRECISION RE
DOUBLE PRECISION F
DOUBLE PRECISION LON
DOUBLE PRECISION LAT
DOUBLE PRECISION ALT
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 header
sections below for details.
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.
Parameters
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.
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. 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.
4) If the equatorial radius is non-positive, the error
SPICE(VALUEOUTOFRANGE) is signaled.
5) If the flattening coefficient is greater than or equal to one,
the error SPICE(VALUEOUTOFRANGE) is signaled.
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.
Files
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
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 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
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 FURNSH.
The definition of this kernel variable controls the behavior of
the SPICELIB planetographic routines
PGRREC
RECPGR
DPGRDR
DRDPGR
It does not affect the other SPICELIB 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
IMPLICIT NONE
C
C SPICELIB functions
C
DOUBLE PRECISION RPD
C
C Local variables
C
DOUBLE PRECISION ALT
DOUBLE PRECISION F
DOUBLE PRECISION LAT
DOUBLE PRECISION LON
DOUBLE PRECISION RADII ( 3 )
DOUBLE PRECISION RE
DOUBLE PRECISION RECTAN ( 3 )
DOUBLE PRECISION RP
INTEGER N
C
C Load a PCK file containing a triaxial
C ellipsoidal shape model and orientation
C data for Mars.
C
CALL FURNSH ( 'pck00008.tpc' )
C
C Look up the radii for Mars. Although we
C omit it here, we could first call BADKPV
C to make sure the variable BODY499_RADII
C has three elements and numeric data type.
C If the variable is not present in the kernel
C pool, BODVRD will signal an error.
C
CALL BODVRD ( 'MARS', 'RADII', 3, N, RADII )
C
C Compute flattening coefficient.
C
RE = RADII(1)
RP = RADII(3)
F = ( RE - RP ) / RE
C
C Do the conversion.
C
RECTAN(1) = 0.D0
RECTAN(2) = -2620.678914818178D0
RECTAN(3) = 2592.408908856967D0
CALL RECPGR ( 'MARS', RECTAN, RE, F, LON, LAT, ALT )
WRITE (*,*) ' '
WRITE (*,*) 'Rectangular coordinates:'
WRITE (*,*) ' '
WRITE (*,*) ' X (km) = ', RECTAN(1)
WRITE (*,*) ' Y (km) = ', RECTAN(2)
WRITE (*,*) ' Z (km) = ', RECTAN(3)
WRITE (*,*) ' '
WRITE (*,*) 'Ellipsoid shape parameters: '
WRITE (*,*) ' '
WRITE (*,*) ' Equatorial radius (km) = ', RE
WRITE (*,*) ' Polar radius (km) = ', RP
WRITE (*,*) ' Flattening coefficient = ', F
WRITE (*,*) ' '
WRITE (*,*) 'Planetographic coordinates:'
WRITE (*,*) ' '
WRITE (*,*) ' Longitude (deg) = ', LON / RPD()
WRITE (*,*) ' Latitude (deg) = ', LAT / RPD()
WRITE (*,*) ' Altitude (km) = ', ALT
WRITE (*,*) ' '
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
Rectangular coordinates:
X (km) = 0.0000000000000000
Y (km) = -2620.6789148181779
Z (km) = 2592.4089088569672
Ellipsoid shape parameters:
Equatorial radius (km) = 3396.1900000000001
Polar radius (km) = 3376.1999999999998
Flattening coefficient = 5.8860075555255261E-003
Planetographic coordinates:
Longitude (deg) = 90.000000000000000
Latitude (deg) = 45.000000000000014
Altitude (km) = 300.00000000000057
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(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
-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(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
Restrictions
None.
Literature_References
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
SPICELIB Version 1.1.1, 06-JUL-2021 (JDR)
Edited the header to comply with NAIF standard.
SPICELIB Version 1.1.0, 21-SEP-2013 (BVS)
Updated to save the input body name and ZZBODTRN state
counter and to do name-ID conversion only if the counter
has changed.
Updated to call LJUCRS instead of CMPRSS/UCASE.
SPICELIB 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
- -
SPICELIB Version 1.0.0, 26-DEC-2004 (CHA) (NJB) (HAN) (BVS) (WLT)
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Fri Dec 31 18:36:42 2021