void gfposc_c ( ConstSpiceChar * target,
ConstSpiceChar * frame,
ConstSpiceChar * abcorr,
ConstSpiceChar * obsrvr,
ConstSpiceChar * crdsys,
ConstSpiceChar * coord,
ConstSpiceChar * relate,
SpiceDouble refval,
SpiceDouble adjust,
SpiceDouble step,
SpiceInt nintvls,
SpiceCell * cnfine,
SpiceCell * result )
Determine time intervals for which a coordinate of an
observer-target position vector satisfies a numerical constraint.
GF
NAIF_IDS
SPK
TIME
WINDOWS
SEPARATION
GEOMETRY
SEARCH
EVENT
Variable I/O Description
-------- --- --------------------------------------------------
SPICE_GF_CNVTOL
P Convergence tolerance.
target I Name of the target body
frame I Name of the reference frame for coordinate calculations
abcorr I Aberration correction flag
obsrvr I Name of the observing body
crdsys I Name of the coordinate system containing COORD
coord I Name of the coordinate of interest
relate I Operator that either looks for an extreme value
(max, min, local, absolute) or compares the
coordinate value and refval
refval I Reference value
adjust I Adjustment value for absolute extrema searches
step I Step size used for locating extrema and roots
nintvls I Workspace window interval count
cnfine I-O SPICE window to which the search is restricted
result O SPICE window containing results
target the string name of a target body. Optionally, you may
supply the integer ID code for the object as an
integer string. For example both "MOON" and "301"
are legitimate strings that indicate the moon is the
target body.
The target and observer define a position vector
that points from the observer to the target.
frame the string name of the reference frame in which to perform
state look-ups and coordinate calculations.
The SPICE frame subsystem must recognize the 'frame' name.
abcorr the string description of the aberration corrections to apply
to the state evaluations to account for one-way light time
and stellar aberration.
This routine accepts the same aberration corrections as does
the SPICE routine SPKEZR. See the header of SPKEZR for a
detailed description of the aberration correction options.
For convenience, the options are listed below:
"NONE" Apply no correction.
"LT" "Reception" case: correct for
one-way light time using a Newtonian
formulation.
"LT+S" "Reception" case: correct for
one-way light time and stellar
aberration using a Newtonian
formulation.
"CN" "Reception" case: converged
Newtonian light time correction.
"CN+S" "Reception" case: converged
Newtonian light time and stellar
aberration corrections.
"XLT" "Transmission" case: correct for
one-way light time using a Newtonian
formulation.
"XLT+S" "Transmission" case: correct for
one-way light time and stellar
aberration using a Newtonian
formulation.
"XCN" "Transmission" case: converged
Newtonian light time correction.
"XCN+S" "Transmission" case: converged
Newtonian light time and stellar
aberration corrections.
The abcorr string lacks sensitivity to case, and to embedded,
leading and trailing blanks.
obsrvr the string naming the observing body. Optionally, you
may supply the ID code of the object as an integer
string. For example, both "EARTH" and "399" are
legitimate strings to supply to indicate the
observer is Earth.
crdsys the string name of the coordinate system for which the
coordinate of interest is a member.
coord the string name of the coordinate of interest in crdsys.
The supported coordinate systems and coordinate names are:
Coordinate System (CRDSYS) Coordinates (COORD) Range
"RECTANGULAR" "X"
"Y"
"Z"
"LATITUDINAL" "RADIUS"
"LONGITUDE" (-Pi,Pi]
"LATITUDE" [-Pi/2,Pi/2]
"RA/DEC" "RANGE"
"RIGHT ASCENSION" [0,2Pi)
"DECLINATION" [-Pi/2,Pi/2]
"SPHERICAL" "RADIUS"
"COLATITUDE" [0,Pi]
"LONGITUDE" (-Pi,Pi]
"CYLINDRICAL" "RADIUS"
"LONGITUDE" [0,2Pi)
"Z"
"GEODETIC" "LONGITUDE" (-Pi,Pi]
"LATITUDE" [-Pi/2,Pi/2]
"ALTITUDE"
"PLANETOGRAPHIC" "LONGITUDE" [0,2Pi)
"LATITUDE" [-Pi/2,Pi/2]
"ALTITUDE"
Limit searches for coordinate events in the GEODETIC and
PLANETOGRAPHIC coordinate systems to TARGET bodies with
axial symmetry in the equatorial plane, i.e. equality
of the body X and Y radii (oblate or prolate spheroids).
relate the string or character describing the relational operator
used to define a constraint on the selected coordinate of the
observer-target vector. The result window found by this routine
indicates the time intervals where the constraint is satisfied.
Supported values of relate and corresponding meanings are
shown below:
">" Separation is greater than the reference
value refval.
"=" Separation is equal to the reference
value refval.
"<" Separation is less than the reference
value refval.
"ABSMAX" Separation is at an absolute maximum.
"ABSMIN" Separation is at an absolute minimum.
"LOCMAX" Separation is at a local maximum.
"LOCMIN" Separation is at a local minimum.
The caller may indicate that the region of interest
is the set of time intervals where the quantity is
within a specified measure of an absolute extremum.
The argument ADJUST (described below) is used to
specify this measure.
Local extrema are considered to exist only in the
interiors of the intervals comprising the confinement
window: a local extremum cannot exist at a boundary
point of the confinement window.
The relate string lacks sensitivity to case, leading
and trailing blanks.
refval the double precision reference value used together with
relate argument to define an equality or inequality to
satisfy by the selected coordinate of the observer-target
vector. See the discussion of relate above for
further information.
The units of refval correspond to the type as defined
by coord, radians for angular measures, kilometers for
distance measures.
adjust a double precision value used to modify searches for
absolute extrema: when relate is set to ABSMAX or ABSMIN and
adjust is set to a positive value, gfposc_c finds times when the
observer-target vector coordinate is within adjust
radians/kilometers of the specified extreme value.
For relate set to ABSMAX, the result window contains
time intervals when the observer-target vector coordinate has
values between ABSMAX - adjust and ABSMAX.
For relate set to ABSMIN, the result window contains
time intervals when the observer-target vector coordinate has
values between ABSMIN and ABSMIN + adjust.
adjust is not used for searches for local extrema,
equality or inequality conditions.
step the double precision time step size to use in the search.
step must be short enough for a search using this step
size to locate the time intervals where coordinate function
of the observer-target vector is monotone increasing or
decreasing. However, step must not be *too* short, or
the search will take an unreasonable amount of time.
The choice of step affects the completeness but not
the precision of solutions found by this routine; the
precision is controlled by the convergence tolerance.
step has units of seconds.
nintvls an integer value specifying the number of intervals in the
the internal workspace array used by this routine. 'nintvls'
should be at least as large as the number of intervals
within the search region on which the specified observer-target
vector coordinate function is monotone increasing or decreasing.
It does no harm to pick a value of 'nintvls' larger than the
minimum required to execute the specified search, but if chosen
too small, the search will fail.
cnfine a double precision SPICE window that confines the time
period over which the specified search is conducted.
cnfine may consist of a single interval or a collection
of intervals.
In some cases the confinement window can be used to
greatly reduce the time period that must be searched
for the desired solution. See the Particulars section
below for further discussion.
See the Examples section below for a code example
that shows how to create a confinement window.
cnfine is the input confinement window, updated if necessary
so the control area of its data array indicates the
window's size and cardinality. The window data are
unchanged.
result the SPICE window of intervals, contained within the
confinement window cnfine, on which the specified
constraint is satisfied.
If result is non-empty on input, its contents
will be discarded before gfposc_c conducts its
search.
result must be declared and initialized with sufficient
size to capture the full set of time intervals
within the search region on which the specified constraint
is satisfied.
If the search is for local extrema, or for absolute
extrema with adjust set to zero, then normally each
interval of result will be a singleton: the left and
right endpoints of each interval will be identical.
If no times within the confinement window satisfy the
constraint, result will be returned with a
cardinality of zero.
SPICE_GF_CNVTOL
is the convergence tolerance used for finding endpoints
of the intervals comprising the result window.
SPICE_GF_CNVTOL is used to determine when binary searches
for roots should terminate: when a root is bracketed
within an interval of length SPICE_GF_CNVTOL; the root is
considered to have been found.
The accuracy, as opposed to precision, of roots found by
this routine depends on the accuracy of the input data.
In most cases, the accuracy of solutions will be inferior
to their precision.
SPICE_GF_CNVTOL has the value 1.0e-6. Units are TDB
seconds.
1) In order for this routine to produce correct results,
the step size must be appropriate for the problem at hand.
Step sizes that are too large may cause this routine to miss
roots; step sizes that are too small may cause this routine
to run unacceptably slowly and in some cases, find spurious
roots.
This routine does not diagnose invalid step sizes, except
that if the step size is non-positive, an error is signaled
by a routine in the call tree of this routine.
2) Due to numerical errors, in particular,
- Truncation error in time values
- Finite tolerance value
- Errors in computed geometric quantities
it is *normal* for the condition of interest to not always be
satisfied near the endpoints of the intervals comprising the
result window.
The result window may need to be contracted slightly by the
caller to achieve desired results. The SPICE window routine
wncond_c can be used to contract the result window.
3) If an error (typically cell overflow) occurs while performing
window arithmetic, the error will be diagnosed by a routine
in the call tree of this routine.
4) If the relational operator `relate' is not recognized, an
error is signaled by a routine in the call tree of this
routine.
5) If the aberration correction specifier contains an
unrecognized value, an error is signaled by a routine in the
call tree of this routine.
6) If `adjust' is negative, an error is signaled by a routine in
the call tree of this routine.
7) If either of the input body names do not map to NAIF ID
codes, an error is signaled by a routine in the call tree of
this routine.
8) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
9) If any input string argument pointer is null, the error
SPICE(NULLPOINTER) will be signaled.
10) If any input string argument is empty, the error
SPICE(EMPTYSTRING) will be signaled.
11) If the workspace interval count 'nintvls' is less than 1, the
error SPICE(VALUEOUTOFRANGE) will be signaled.
12) If the required amount of workspace memory cannot be
allocated, the error SPICE(MALLOCFAILURE) will be
signaled.
Appropriate SPK and PCK kernels must be loaded by the
calling program before this routine is called.
The following data are required:
- SPK data: the calling application must load ephemeris data
for the targets, observer, and any intermediate objects in
a chain connecting the targets and observer that cover the time
period specified by the window CNFINE. If aberration
corrections are used, the states of target and observer
relative to the solar system barycenter must be calculable
from the available ephemeris data. Typically ephemeris data
are made available by loading one or more SPK files using
FURNSH.
- PCK data: bodies modeled as triaxial ellipsoids must have
semi-axis lengths provided by variables in the kernel pool.
Typically these data are made available by loading a text
PCK file using FURNSH.
- If non-inertial reference frames are used, then PCK
files, frame kernels, C-kernels, and SCLK kernels may be
needed.
Such kernel data are normally loaded once per program
run, NOT every time this routine is called.
This routine provides a simpler, but less flexible interface
than does the routine gfevnt_c for conducting searches for
observer-target vector coordinate value events. Applications
that require support for progress reporting, interrupt
handling, non-default step or refinement functions, or non-default
convergence tolerance should call gfevnt_c rather than this routine.
This routine determines a set of one or more time intervals
within the confinement window when the selected coordinate of
the observer-target vector satisfies a caller-specified
constraint. The resulting set of intervals is returned as a SPICE
window.
Below we discuss in greater detail aspects of this routine's
solution process that are relevant to correct and efficient
use of this routine in user applications.
The Search Process
==================
Regardless of the type of constraint selected by the caller, this
routine starts the search for solutions by determining the time
periods, within the confinement window, over which the specified
coordinate function is monotone increasing and monotone
decreasing. Each of these time periods is represented by a SPICE
window. Having found these windows, all of the coordinate
function's local extrema within the confinement window are known.
Absolute extrema then can be found very easily.
Within any interval of these "monotone" windows, there will be at
most one solution of any equality constraint. Since the boundary
of the solution set for any inequality constraint is contained in
the union of
- the set of points where an equality constraint is met
- the boundary points of the confinement window
the solutions of both equality and inequality constraints can be
found easily once the monotone windows have been found.
Step Size
=========
The monotone windows (described above) are found using a two-step
search process. Each interval of the confinement window is
searched as follows: first, the input step size is used to
determine the time separation at which the sign of the rate of
change of coordinate will be sampled. Starting at
the left endpoint of an interval, samples will be taken at each
step. If a change of sign is found, a root has been bracketed; at
that point, the time at which the time derivative of the coordinate
is zero can be found by a refinement process, for example,
using a binary search.
Note that the optimal choice of step size depends on the lengths
of the intervals over which the coordinate function is monotone:
the step size should be shorter than the shortest of these
intervals (within the confinement window).
The optimal step size is *not* necessarily related to the lengths
of the intervals comprising the result window. For example, if
the shortest monotone interval has length 10 days, and if the
shortest result window interval has length 5 minutes, a step size
of 9.9 days is still adequate to find all of the intervals in the
result window. In situations like this, the technique of using
monotone windows yields a dramatic efficiency improvement over a
state-based search that simply tests at each step whether the
specified constraint is satisfied. The latter type of search can
miss solution intervals if the step size is longer than the
shortest solution interval.
Having some knowledge of the relative geometry of the target and
observer can be a valuable aid in picking a reasonable step size.
In general, the user can compensate for lack of such knowledge by
picking a very short step size; the cost is increased computation
time.
Note that the step size is not related to the precision with which
the endpoints of the intervals of the result window are computed.
That precision level is controlled by the convergence tolerance.
Convergence Tolerance
=====================
As described above, the root-finding process used by this routine
involves first bracketing roots and then using a search process to
locate them. "Roots" include times when extrema are attained and
times when the geometric quantity function is equal to a reference
value or adjusted extremum. All endpoints of the intervals comprising
the result window are either endpoints of intervals of the confinement
window or roots.
Once a root has been bracketed, a refinement process is used to
narrow down the time interval within which the root must lie.
This refinement process terminates when the location of the root
has been determined to within an error margin called the
"convergence tolerance." The convergence tolerance used by this
routine is set via the parameter SPICE_GF_CNVTOL.
The value of SPICE_GF_CNVTOL is set to a "tight" value so that the
tolerance doesn't limit the accuracy of solutions found by this
routine. In general the accuracy of input data will be the limiting
factor.
The user may change the convergence tolerance from the default
SPICE_GF_CNVTOL value by calling the routine gfstol_c, e.g.
gfstol_c( tolerance value in seconds )
Call gfstol_c prior to calling this routine. All subsequent
searches will use the updated tolerance value.
Searches over time windows of long duration may require use of
larger tolerance values than the default: the tolerance must be
large enough so that it, when added to or subtracted from the
confinement window's lower and upper bounds, yields distinct time
values.
Setting the tolerance tighter than SPICE_GF_CNVTOL is unlikely to be
useful, since the results are unlikely to be more accurate.
Making the tolerance looser will speed up searches somewhat,
since a few convergence steps will be omitted. However, in most
cases, the step size is likely to have a much greater effect
on processing time than would the convergence tolerance.
The Confinement Window
======================
The simplest use of the confinement window is to specify a time
interval within which a solution is sought. However, the
confinement window can, in some cases, be used to make searches
more efficient. Sometimes it's possible to do an efficient search
to reduce the size of the time period over which a relatively
slow search of interest must be performed.
Practical use of the coordinate search capability would likely
consist of searches over multiple coordinate constraints to find
time intervals that satisfies the constraints. An effective
technique to accomplish such a search is to use the result
window from one search as the confinement window of the next.
Longitude and Right Ascension
=============================
The cyclic nature of the longitude and right ascension coordinates
produces branch cuts at +/- 180 degrees longitude and 0-360
longitude. Round-off error may cause solutions near these branches
to cross the branch. Use of the SPICE routine wncond_c will contract
solution windows by some epsilon, reducing the measure of the
windows and eliminating the branch crossing. A one millisecond
contraction will in most cases eliminate numerical round-off caused
branch crossings.
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.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: standard.tm
This meta-kernel is intended to support operation of SPICE
example programs. The kernels shown here should not be
assumed to contain adequate or correct versions of data
required by SPICE-based user applications.
In order for an application to use this meta-kernel, the
kernels referenced here must be present in the user's
current working directory.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
de421.bsp Planetary ephemeris
pck00009.tpc Planet orientation and
radii
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00009.tpc',
'naif0009.tls' )
\begintext
Example(1):
Find the time during 2007 for which the latitude of the
Earth-Sun vector in IAU_EARTH frame has the maximum value,
i.e. the latitude of the Tropic of Cancer.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "SpiceUsr.h"
#define MAXWIN 750
#define TIMFMT "YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND"
#define TIMLEN 41
int main( int argc, char **argv )
{
/.
Create the needed windows. Note, one window
consists of two values, so the total number
of cell values to allocate is twice
the number of intervals.
./
SPICEDOUBLE_CELL ( result, 2*MAXWIN );
SPICEDOUBLE_CELL ( cnfine, 2 );
SpiceDouble begtim;
SpiceDouble endtim;
SpiceDouble step;
SpiceDouble adjust;
SpiceDouble refval;
SpiceDouble beg;
SpiceDouble end;
SpiceChar begstr [ TIMLEN ];
SpiceChar endstr [ TIMLEN ];
SpiceChar * relate = "ABSMAX";
SpiceChar * crdsys = "LATITUDINAL";
SpiceChar * coord = "LATITUDE";
SpiceChar * targ = "SUN";
SpiceChar * obsrvr = "EARTH";
SpiceChar * frame = "IAU_EARTH";
SpiceChar * abcorr = "NONE";
SpiceInt count;
SpiceInt i;
/.
Load kernels.
./
furnsh_c( "standard.tm" );
/.
Store the time bounds of our search interval in
the cnfine confinement window.
./
str2et_c( "2007 JAN 01", &begtim );
str2et_c( "2008 JAN 01", &endtim );
wninsd_c ( begtim, endtim, &cnfine );
/.
The latitude varies relatively slowly, ~46 degrees during the
year. The extrema occur approximately every six months.
Search using a step size less than half that value (180 days).
For this example use ninety days (in units of seconds).
./
step = (90.)*spd_c();
adjust = 0.;
refval = 0;
/.
List the beginning and ending points in each interval
if result contains data.
./
gfposc_c ( targ,
frame,
abcorr,
obsrvr,
crdsys,
coord,
relate,
refval,
adjust,
step,
MAXWIN,
&cnfine,
&result );
count = wncard_c( &result );
/.
Display the results.
./
if (count == 0 )
{
printf ( "Result window is empty.\n\n" );
}
else
{
for ( i = 0; i < count; i++ )
{
/.
Fetch the endpoints of the Ith interval
of the result window.
./
wnfetd_c ( &result, i, &beg, &end );
if ( beg == end )
{
timout_c ( beg, TIMFMT, TIMLEN, begstr );
printf ( "Event time: %s\n", begstr );
}
else
{
timout_c ( beg, TIMFMT, TIMLEN, begstr );
timout_c ( end, TIMFMT, TIMLEN, endstr );
printf ( "Interval %d\n", i + 1);
printf ( "From : %s \n", begstr );
printf ( "To : %s \n", endstr );
printf( " \n" );
}
}
}
kclear_c();
return( 0 );
}
The program outputs:
Event time: 2007-JUN-21 17:54:13.166910 (TDB)
Example(2):
A minor modification of the program listed in Example 1; find the
time during 2007 for which the latitude of the Earth-Sun vector
in IAU_EARTH frame has the minimum value, i.e. the latitude of
the Tropic of Capricorn.
Edit the example program, assign:
SpiceChar * relate = "ABSMIN";
The program outputs:
Event time: 2007-DEC-22 06:04:32.630160 (TDB)
Example(3):
Find the time during 2007 for which the Z component of the
Earth-Sun vector in IAU_EARTH frame has value 0, i.e. crosses
the equatorial plane (this also defines a zero latitude).
The search should return two times, one for an ascending
passage and one for descending.
Edit the example program, assign:
SpiceChar * relate = "=";
SpiceChar * crdsys = "RECTANGULAR";
SpiceChar * coord = "Z";
Note, this RELATE operator refers to the REFVAL value,
assigned to 0.D0 for this example.
The program outputs:
Event time: 2007-MAR-21 00:01:25.495120 (TDB)
Event time: 2007-SEP-23 09:46:39.574124 (TDB)
Example(4):
Find the times between Jan 1, 2007 and Jan 1, 2008 corresponding
to the apoapsis on the Moon's orbit around the Earth (note, the
GFDIST routine can also perform this search).
Edit the example program, assign:
This search requires a change in the step size since the Moon's
orbit about the earth (earth-moon barycenter) has a twenty-eight
day period. Use a step size something less than half that value.
In this case, we use twelve days.
SpiceChar * relate = "LOCMAX";
SpiceChar * crdsys = "SPHERICAL";
SpiceChar * coord = "RADIUS";
SpiceChar * targ = "MOON";
SpiceChar * frame = "J2000";
step = 12.*spd_c();
The program outputs:
Event time: 2007-JAN-10 16:26:18.805837 (TDB)
Event time: 2007-FEB-07 12:39:35.078525 (TDB)
Event time: 2007-MAR-07 03:38:07.334769 (TDB)
Event time: 2007-APR-03 08:38:55.222606 (TDB)
Event time: 2007-APR-30 10:56:49.847027 (TDB)
Event time: 2007-MAY-27 22:03:28.857783 (TDB)
Event time: 2007-JUN-24 14:26:23.639351 (TDB)
Event time: 2007-JUL-22 08:43:50.135565 (TDB)
Event time: 2007-AUG-19 03:28:33.538169 (TDB)
Event time: 2007-SEP-15 21:07:13.964698 (TDB)
Event time: 2007-OCT-13 09:52:30.819372 (TDB)
Event time: 2007-NOV-09 12:32:50.070555 (TDB)
Event time: 2007-DEC-06 16:54:31.225504 (TDB)
Example(5):
Find times between Jan 1, 2007 and Jan 1, 2008 when the latitude
(elevation) of the observer-target vector between DSS 17 and the
Moon, as observed in the DSS 17 topocentric (station) frame,
exceeds 83 degrees.
This search uses a step size of four hours since the time
for all declination zero-to-max-to-zero passes within
the search window exceeds eight hours.
This search requires kernels not included in the standard.tm
meta kernel.
Kernel name Contents
----------- --------
earthstns_itrf93_050714.bsp SPK for DSN Station
Locations
earth_topo_050714.tf Topocentric DSN stations
frame definitions
earth_000101_080120_071029.bpc High precision earth PCK
Edit the example program, assign:
SpiceChar * relate = ">";
SpiceChar * crdsys = "LATITUDINAL";
SpiceChar * coord = "LATITUDE";
SpiceChar * targ = "MOON";
SpiceChar * obsrvr = "DSS-17";
SpiceChar * frame = "DSS-17_TOPO";
furnsh_c ("earthstns_itrf93_050714.bsp");
furnsh_c ("earth_topo_050714.tf");
furnsh_c ("earth_000101_080120_071029.bpc");
step = (4./24.)*spd_c();
refval = 83. * rpd_c();
The program outputs:
Interval 1
From : 2007-FEB-26 03:18:48.229806 (TDB)
To : 2007-FEB-26 03:31:29.734169 (TDB)
Interval 2
From : 2007-MAR-25 01:12:38.551183 (TDB)
To : 2007-MAR-25 01:23:53.908601 (TDB)
1) The kernel files to be used by this routine must be loaded
(normally via the CSPICE routine furnsh_c) before this routine
is called.
2) This routine has the side effect of re-initializing the
coordinate quantity utility package. Callers may
need to re-initialize the package after calling this routine.
None.
N.J. Bachman (JPL)
E.D. Wright (JPL)
-CSPICE Version 1.0.2, 31-JUL-2014 (EDW)
Edit to header, replaced ' character with character " to indicate
C strings.
Edit to header, correct Required Reading entry eliminating ".REQ"
suffix.
-CSPICE Version 1.0.1, 28-FEB-2013 (NJB) (EDW)
Header was updated to discuss use of gfstol_c.
Edit to comments to correct search description.
Edits to Example section, proper description of "standard.tm"
meta kernel.
-CSPICE Version 1.0.1, 26-AUG-2009 (EDW)
Correction of several typos.
-CSPICE Version 1.0.0, 10-FEB-2009 (NJB) (EDW)
GF position coordinate search
Link to routine gfposc_c source file gfposc_c.c
|