void limbpt_c ( ConstSpiceChar * method,
ConstSpiceChar * target,
SpiceDouble et,
ConstSpiceChar * fixref,
ConstSpiceChar * abcorr,
ConstSpiceChar * corloc,
ConstSpiceChar * obsrvr,
ConstSpiceDouble refvec[3],
SpiceDouble rolstp,
SpiceInt ncuts,
SpiceDouble schstp,
SpiceDouble soltol,
SpiceInt maxn,
SpiceInt npts [],
SpiceDouble points[][3],
SpiceDouble epochs[],
SpiceDouble tangts[][3] )
Find limb points on a target body. The limb is the set of points
of tangency on the target of rays emanating from the observer.
The caller specifies half-planes bounded by the observer-target
center vector in which to search for limb points.
The surface of the target body may be represented either by a
triaxial ellipsoid or by topographic data.
CK
DSK
FRAMES
NAIF_IDS
PCK
SPK
TIME
GEOMETRY
Variable I/O Description
-------- --- --------------------------------------------------
method I Computation method.
target I Name of target body.
et I Epoch in ephemeris seconds past J2000 TDB.
fixref I Body-fixed, body-centered target body frame.
abcorr I Aberration correction.
corloc I Aberration correction locus.
obsrvr I Name of observing body.
refvec I Reference vector for cutting half-planes.
rolstp I Roll angular step for cutting half-planes.
ncuts I Number of cutting half-planes.
schstp I Angular step size for searching.
soltol I Solution convergence tolerance.
maxn I Maximum number of entries in output arrays.
npts O Counts of limb points corresponding to cuts.
points O Limb points.
epochs O Times associated with limb points.
tangts O Tangent vectors emanating from the observer.
method is a short string providing parameters defining
the computation method to be used. In the syntax
descriptions below, items delimited by brackets
are optional.
`method' may be assigned the following values:
"TANGENT/DSK/UNPRIORITIZED[/SURFACES = <surface list>]"
The limb point computation uses topographic data
provided by DSK files (abbreviated as "DSK data"
below) to model the surface of the target body. A
limb point is defined as the point of tangency, on
the surface represented by the DSK data, of a ray
emanating from the observer.
Limb points are generated within a specified set
of "cutting" half-planes that have as an edge the
line containing the observer-target vector.
Multiple limb points may be found within a given
half-plane, if the target body shape allows for
this.
The surface list specification is optional. The
syntax of the list is
<surface 1> [, <surface 2>...]
If present, it indicates that data only for the
listed surfaces are to be used; however, data need
not be available for all surfaces in the list. If
the list is absent, loaded DSK data for any
surface associated with the target body are used.
The surface list may contain surface names or
surface ID codes. Names containing blanks must
be delimited by double quotes, for example
SURFACES = \"Mars MEGDR 128 PIXEL/DEG\"
If multiple surfaces are specified, their names
or IDs must be separated by commas.
See the Particulars section below for details
concerning use of DSK data.
This is the highest-accuracy method supported by
this subroutine. It generally executes much more
slowly than the "GUIDED" method described below.
"GUIDED/DSK/UNPRIORITIZED[/SURFACES = <surface list>]"
This method uses DSK data as described above, but
limb points generated by this method are "guided"
so as to lie in the limb plane of the target
body's reference ellipsoid, on the target body's
surface. This method produces a unique limb point
for each cutting half-plane. If multiple limb
point candidates lie in a given cutting
half-plane, the outermost one is chosen.
This method may be used only with the "CENTER"
aberration correction locus (see the description
of `refloc' below).
Limb points generated by this method are
approximations; they are generally not true
ray-surface tangent points. However, these
approximations can be generated much more quickly
than tangent points.
"TANGENT/ELLIPSOID"
"GUIDED/ELLIPSOID"
Both of these methods generate limb points on the
target body's reference ellipsoid. The "TANGENT"
option may be used with any aberration correction
locus, while the "GUIDED" option may be used only
with the "CENTER" locus (see the description of
`refloc' below).
When the locus is set to "CENTER", these methods
produce the same results.
Neither case nor white space are significant in
`method', except within double-quoted strings. For
example, the string " eLLipsoid/tAnGenT " is valid.
Within double-quoted strings, blank characters are
significant, but multiple consecutive blanks are
considered equivalent to a single blank. Case is
not significant. So
\"Mars MEGDR 128 PIXEL/DEG\"
is equivalent to
\" mars megdr 128 pixel/deg \"
but not to
\"MARS MEGDR128PIXEL/DEG\"
target is the name of the target body. The target body is
an extended ephemeris object.
The string `target' is case-insensitive, and leading
and trailing blanks in `target' are not significant.
Optionally, you may supply a string containing the
integer ID code for the object. For example both
"MOON" and "301" are legitimate strings that indicate
the Moon is the target body.
When the target body's surface is represented by a
tri-axial ellipsoid, this routine assumes that a
kernel variable representing the ellipsoid's radii is
present in the kernel pool. Normally the kernel
variable would be defined by loading a PCK file.
et is the epoch of participation of the observer,
expressed as TDB seconds past J2000 TDB: `et' is
the epoch at which the observer's state is computed.
When aberration corrections are not used, `et' is also
the epoch at which the position and orientation of
the target body are computed.
When aberration corrections are used, the position
and orientation of the target body are computed at
et-lt, where lt is the one-way light time between the
aberration correction locus and the observer. The
locus is specified by the input argument `corloc'.
See the descriptions of `abcorr' and `corloc' below for
details.
fixref is the name of a body-fixed reference frame centered
on the target body. `fixref' may be any such frame
supported by the SPICE system, including built-in
frames (documented in the Frames Required Reading)
and frames defined by a loaded frame kernel (FK). The
string `fixref' is case-insensitive, and leading and
trailing blanks in `fixref' are not significant.
The output limb points in the array `points' and the
output observer-target tangent vectors in the array
`tangts' are expressed relative to this reference frame.
abcorr indicates the aberration corrections to be applied
when computing the target's position and orientation.
Corrections are applied at the location specified by
the aberration correction locus argument `corloc',
which is described below.
For remote sensing applications, where apparent limb
points seen by the observer are desired, normally
either of the corrections
"LT+S"
"CN+S"
should be used. The correction "NONE" may be suitable
for cases in which the target is very small and the
observer is close to, and has small velocity relative
to, the target (e.g. comet Churyumov-Gerasimenko and
the Rosetta Orbiter).
These and the other supported options are described
below. `abcorr' may be any of the following:
"NONE" Apply no correction. Return the
geometric limb points on the target
body.
Let `lt' represent the one-way light time between the
observer and the aberration correction locus. The
following values of `abcorr' apply to the "reception"
case in which photons depart from the locus at the
light-time corrected epoch et-lt and *arrive* at the
observer's location at `et':
"LT" Correct for one-way light time (also
called "planetary aberration") using a
Newtonian formulation. This correction
yields the locus at the moment it
emitted photons arriving at the
observer at `et'.
The light time correction uses an
iterative solution of the light time
equation. The solution invoked by the
"LT" option uses one iteration.
Both the target position as seen by the
observer, and rotation of the target
body, are corrected for light time.
"LT+S" Correct for one-way light time and
stellar aberration using a Newtonian
formulation. This option modifies the
locus obtained with the "LT" option to
account for the observer's velocity
relative to the solar system
barycenter. These corrections yield
points on the apparent limb.
"CN" Converged Newtonian light time
correction. In solving the light time
equation, the "CN" correction iterates
until the solution converges. Both the
position and rotation of the target
body are corrected for light time.
"CN+S" Converged Newtonian light time and
stellar aberration corrections. This
option produces a solution that is at
least as accurate at that obtainable
with the "LT+S" option. Whether the
"CN+S" solution is substantially more
accurate depends on the geometry of the
participating objects and on the
accuracy of the input data. In all
cases this routine will execute more
slowly when a converged solution is
computed.
corloc is a string specifying the aberration correction
locus: the point or set of points for which
aberration corrections are performed. `corloc' may be
assigned the values:
"CENTER"
Light time and stellar aberration corrections
are applied to the vector from the observer to
the center of the target body. The one way
light time from the target center to the
observer is used to determine the epoch at
which the target body orientation is computed.
This choice is appropriate for small target
objects for which the light time from the
surface to the observer varies little across
the entire target. It may also be appropriate
for large, nearly ellipsoidal targets when the
observer is very far from the target.
Computation speed for this option is faster
than for the "ELLIPSOID LIMB" option.
"ELLIPSOID LIMB"
Light time and stellar aberration corrections
are applied to individual limb points on the
reference ellipsoid. For a limb point on the
surface described by topographic data, lying
in a specified cutting half-plane, the unique
reference ellipsoid limb point in the same
half-plane is used as the locus of the
aberration corrections.
This choice is appropriate for large target
objects for which the light time from the limb
to the observer is significantly different
from the light time from the target center to
the observer.
Because aberration corrections are repeated for
individual limb points, computational speed for
this option is relatively slow.
obsrvr is the name of the observing body. The observing body
is an ephemeris object: it typically is a spacecraft,
the earth, or a surface point on the earth. `obsrvr' is
case-insensitive, and leading and trailing blanks in
`obsrvr' are not significant. Optionally, you may
supply a string containing the integer ID code for
the object. For example both "MOON" and "301" are
legitimate strings that indicate the Moon is the
observer.
refvec,
rolstp,
ncuts are, respectively, a reference vector, a roll step
angle, and a count of cutting half-planes.
`refvec' defines the first of a sequence of cutting
half-planes in which limb points are to be found.
Each cutting half-plane has as its edge the line
containing the observer-target vector; the first
half-plane contains `refvec'.
`refvec' is expressed in the body-fixed reference frame
designated by `fixref'.
`rolstp' is an angular step by which to roll the
cutting half-planes about the observer-target vector.
The first half-plane is aligned with `refvec'; the ith
half-plane is rotated from `refvec' about the
observer-target vector in the counter-clockwise
direction by (i-1)*rolstp. Units are radians.
`rolstp' should be set to
2*pi/ncuts
to generate an approximately uniform distribution of
limb points along the limb.
`ncuts' is the number of cutting half-planes used to
find limb points; the angular positions of
consecutive half-planes increase in the positive
sense (counterclockwise) about the target-observer
vector and are distributed roughly equally about that
vector: each half-plane has angular separation of
approximately
`rolstp' radians
from each of its neighbors. When the aberration
correction locus is set to "CENTER", the angular
separation is the value above, up to round-off. When
the locus is "ELLIPSOID LIMB", the separations are
less uniform due to differences in the aberration
corrections used for the respective limb points.
schstp,
soltol are used only for DSK-based surfaces. These inputs
are, respectively, the search angular step size and
solution convergence tolerance used to find tangent
rays and associated limb points within each cutting
half plane. These values are used when the `method'
argument includes the "TANGENT" option. In this case,
limb points are found by a two-step search process:
1) Bracketing: starting with the direction
opposite the observer-target vector, rays
emanating from the observer are generated
within the half-plane at successively greater
angular separations from the initial direction,
where the increment of angular separation is
`schstp'. The rays are tested for intersection
with the target surface. When a transition
between non-intersection to intersection is
found, the angular separation of a tangent ray
has been bracketed.
2) Root finding: each time a tangent ray is
bracketed, a search is done to find the angular
separation from the starting direction at which
a tangent ray exists. The search terminates
when successive rays are separated by no more
than `soltol'. When the search converges, the
last ray-surface intersection point found in
the convergence process is considered to be a
limb point.
`schstp' and `soltol' have units of radians.
Target bodies with simple surfaces---for example,
convex shapes---will have a single limb point within
each cutting half-plane. For such surfaces, `schstp'
can be set large enough so that only one bracketing
step is taken. A value greater than pi, for example
4.0, is recommended.
Target bodies with complex surfaces can have
multiple limb points within a given cutting
half-plane. To find all limb points, `schstp' must be
set to a value smaller than the angular separation
of any two limb points in any cutting half-plane,
where the vertex of the angle is the observer.
`schstp' must not be too small, or the search will be
excessively slow.
For both kinds of surfaces, `soltol' must be chosen so
that the results will have the desired precision.
Note that the choice of `soltol' required to meet a
specified bound on limb point height errors depends
on the observer-target distance.
maxn is the maximum number of limb points that can be
stored in the output array `points'.
npts is an array of counts of limb points within the
specified set of cutting half-planes. The Ith
element of `npts' is the limb point count in the Ith
half-plane. `npts' should be declared with length
at least `ncuts'.
For most target bodies, there will be one limb point
per half-plane. For complex target shapes, the limb
point count in a given half-plane can be greater
than one (see example 3 below), and it can be zero.
points is an array containing the limb points found by this
routine. Sets of limb points associated with
half-planes are ordered by the indices of the
half-planes in which they're found. The limb points
in a given half-plane are ordered by decreasing
angular separation from the observer-target
direction; the outermost limb point in a given
half-plane is the first of that set.
The limb points for the half-plane containing `refvec'
occupy array elements
points[ 0 ][0] through
points[ npts[0]-1 ][2]
Limb points for the second half plane occupy
elements
points[ npts[0] ][0] through
points[ npts[0]+npts[1]-1 ][2]
and so on.
`points' should be declared with dimensions
[maxn][3]
Limb points are expressed in the reference frame
designated by `fixref'. For each limb point, the
orientation of the frame is evaluated at the epoch
corresponding to the limb point; the epoch is
provided in the output array `epochs' (described
below).
Units of the limb points are km.
epochs is an array of epochs associated with the limb
points, accounting for light time if aberration
corrections are used. `epochs' contains one element
for each limb point. `epochs' should be declared
with length
maxn
The element
epochs[i]
is associated with the limb point
points[i][j], j = 0 to 2
If `corloc' is set to "CENTER", all values of `epochs'
will be the epoch associated with the target body
center. That is, if aberration corrections are used,
and if `lt' is the one-way light time from the target
center to the observer, the elements of `epochs' will
all be set to
et - lt
If `corloc' is set to "ELLIPSOID LIMB", all values of
`epochs' for the limb points in a given half plane
will be those for the reference ellipsoid limb point
in that half plane. That is, if aberration
corrections are used, and if lt[i] is the one-way
light time to the observer from the reference
ellipsoid limb point in the ith half plane, the
elements of `epochs' for that half plane will all be
set to
et - lt[i]
tangts is an array of tangent vectors connecting the
observer to the limb points. The tangent vectors are
expressed in the frame designated by `fixref'. For the
Ith vector, the orientation of the frame is
evaluated at the Ith epoch provided in the output
array `epochs' (described above).
`tangts' should be declared with dimensions
[maxn][3]
The elements
tangts[i][j], j = 0 to 2
are associated with the limb point
points[i][j], j = 0 to 2
Units of the tangent vectors are km.
None.
1) If the specified aberration correction is unrecognized, the
error will be signaled by a routine in the call tree of this
routine. If transmission corrections are commanded, the error
SPICE(INVALIDOPTION) will be signaled.
2) If either the target or observer input strings cannot be
converted to an integer ID code, the error
SPICE(IDCODENOTFOUND) is signaled.
3) If `obsrvr' and `target' map to the same NAIF integer ID code,
the error SPICE(BODIESNOTDISTINCT) is signaled.
4) If the input target body-fixed frame `fixref' is not
recognized, the error SPICE(NOFRAME) is signaled. A frame
name may fail to be recognized because a required frame
specification kernel has not been loaded; another cause is a
misspelling of the frame name.
5) If the input frame `fixref' is not centered at the target body,
the error SPICE(INVALIDFRAME) is signaled.
6) If the input argument `method' is not recognized, the error
SPICE(INVALIDMETHOD) is signaled by this routine, or the
error is signaled by a routine in the call tree of this
routine.
7) If `method' contains an invalid limb type, the error
SPICE(INVALIDLIMBTYPE) will be signaled.
8) If the target and observer have distinct identities but are
at the same location the error SPICE(NOSEPARATION) is
signaled.
9) If insufficient ephemeris data have been loaded prior to
calling limbpt_c, the error will be signaled by a routine in
the call tree of this routine. When light time correction is
used, sufficient ephemeris data must be available to
propagate the states of both observer and target to the solar
system barycenter.
10) If the computation method requires an ellipsoidal target
shape and triaxial radii of the target body have not been
loaded into the kernel pool prior to calling limbpt_c, the
error will be diagnosed and signaled by a routine in the call
tree of this routine.
If the radii are available in the kernel pool but the count
of radii values is not three, the error SPICE(BADRADIUSCOUNT)
will be signaled.
When the target shape is modeled by topographic data, radii
of the reference triaxial ellipsoid are still required if
the aberration correction locus is "ELLIPSOID LIMB" or if
the limb point generation method is "GUIDED".
11) The target must be an extended body. If the target body's
shape is modeled as an ellipsoid, and if any of the radii of
the target body are non-positive, the error will be diagnosed
and signaled by routines in the call tree of this routine.
12) If PCK data specifying the target body-fixed frame
orientation have not been loaded prior to calling limbpt_c,
the error will be diagnosed and signaled by a routine in the
call tree of this routine.
13) If `method' specifies that the target surface is represented by
DSK data, and no DSK files are loaded for the specified
target, the error is signaled by a routine in the call tree
of this routine.
14) If the array bound `maxn' is less than 1, the error
SPICE(INVALIDSIZE) will be signaled.
15) If the number of cutting half-planes specified by `ncuts'
is negative or greater than `maxn', the error
SPICE(INVALIDCOUNT) will be signaled.
16) If the aberration correction locus is not recognized, the
error SPICE(INVALIDLOCUS) will be signaled.
17) If the aberration correction locus is "ELLIPSOID LIMB"
but limb type is not "TANGENT", the error
SPICE(BADLIMBLOCUSMIX) will be signaled.
18) If the reference vector `refvec' is the zero vector, the
error SPICE(ZEROVECTOR) will be signaled.
19) If the reference vector `refvec' and the observer target
vector are linearly dependent, the error
SPICE(DEGENERATECASE) will be signaled.
20) If the limb computation uses the target ellipsoid limb
plane, and the limb plane normal and reference vector
`refvec' are linearly dependent, the error
SPICE(DEGENERATECASE) will be signaled.
21) If the limb points cannot all be stored in the output `points'
array, the error SPICE(OUTOFROOM) will be signaled.
22) If the surface is represented by DSK data, and if the search
step is non-positive, the error SPICE(INVALIDSEARCHSTEP) will
be signaled.
23) If the surface is represented by DSK data, and if the search
tolerance is non-positive, the error SPICE(INVALIDTOLERANCE)
will be signaled.
24) If the roll step is non-positive and NCUTS is greater
than 1, the error SPICE(INVALIDROLLSTEP) will be signaled.
25) If any input string argument pointer is null, the error
SPICE(NULLPOINTER) will be signaled.
26) If any input string argument is empty, the error
SPICE(EMPTYSTRING) will be signaled.
Appropriate kernels must be loaded by the calling program before
this routine is called.
The following data are required:
- SPK data: ephemeris data for target and observer must be
loaded. 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 via furnsh_c.
- Target body orientation data: these may be provided in a text
or binary PCK file. In some cases, target body orientation
may be provided by one more more CK files. In either case,
data are made available by loading the files via furnsh_c.
- Shape data for the target body:
PCK data:
If the target body shape is modeled as an ellipsoid,
triaxial radii for the target body must be loaded into
the kernel pool. Typically this is done by loading a
text PCK file via furnsh_c.
Triaxial radii are also needed if the target shape is
modeled by DSK data but one or both of the "GUIDED" limb
definition method or the "ELLIPSOID LIMB" aberration
correction locus are selected.
DSK data:
If the target shape is modeled by DSK data, DSK files
containing topographic data for the target body must be
loaded. If a surface list is specified, data for at
least one of the listed surfaces must be loaded.
The following data may be required:
- Frame data: if a frame definition is required to convert the
observer and target states to the body-fixed frame of the
target, that definition must be available in the kernel
pool. Typically the definition is supplied by loading a
frame kernel via furnsh_c.
- Surface name-ID associations: if surface names are specified
in `method', the association of these names with their
corresponding surface ID codes must be established by
assignments of the kernel variables
NAIF_SURFACE_NAME
NAIF_SURFACE_CODE
NAIF_SURFACE_BODY
Normally these associations are made by loading a text
kernel containing the necessary assignments. An example
of such a set of assignments is
NAIF_SURFACE_NAME += 'Mars MEGDR 128 PIXEL/DEG'
NAIF_SURFACE_CODE += 1
NAIF_SURFACE_BODY += 499
- SCLK data: if the target body's orientation is provided by
CK files, an associated SCLK kernel must be loaded.
In all cases, kernel data are normally loaded once per program
run, NOT every time this routine is called.
Using DSK data
==============
DSK loading and unloading
-------------------------
DSK files providing data used by this routine are loaded by
calling furnsh_c and can be unloaded by calling unload_c or
kclear_c. See the documentation of furnsh_c for limits on numbers
of loaded DSK files.
For run-time efficiency, it's desirable to avoid frequent
loading and unloading of DSK files. When there is a reason to
use multiple versions of data for a given target body---for
example, if topographic data at varying resolutions are to be
used---the surface list can be used to select DSK data to be
used for a given computation. It is not necessary to unload
the data that are not to be used. This recommendation presumes
that DSKs containing different versions of surface data for a
given body have different surface ID codes.
DSK data priority
-----------------
A DSK coverage overlap occurs when two segments in loaded DSK
files cover part or all of the same domain---for example, a
given longitude-latitude rectangle---and when the time
intervals of the segments overlap as well.
When DSK data selection is prioritized, in case of a coverage
overlap, if the two competing segments are in different DSK
files, the segment in the DSK file loaded last takes
precedence. If the two segments are in the same file, the
segment located closer to the end of the file takes
precedence.
When DSK data selection is unprioritized, data from competing
segments are combined. For example, if two competing segments
both represent a surface as sets of triangular plates, the
union of those sets of plates is considered to represent the
surface.
Currently only unprioritized data selection is supported.
Because prioritized data selection may be the default behavior
in a later version of the routine, the UNPRIORITIZED keyword is
required in the `method' argument.
Syntax of the `method' input argument
-------------------------------------
The keywords and surface list in the `method' argument
are called "clauses." The clauses may appear in any
order, for example
TANGENT/DSK/UNPRIORITIZED/<surface list>
DSK/TANGENT/<surface list>/UNPRIORITIZED
UNPRIORITIZED/<surface list>/DSK/TANGENT
The simplest form of the `method' argument specifying use of
DSK data is one that lacks a surface list, for example:
"TANGENT/DSK/UNPRIORITIZED"
"GUIDED/DSK/UNPRIORITIZED"
For applications in which all loaded DSK data for the target
body are for a single surface, and there are no competing
segments, the above strings suffice. This is expected to be
the usual case.
When, for the specified target body, there are loaded DSK
files providing data for multiple surfaces for that body, the
surfaces to be used by this routine for a given call must be
specified in a surface list, unless data from all of the
surfaces are to be used together.
The surface list consists of the string
SURFACES =
followed by a comma-separated list of one or more surface
identifiers. The identifiers may be names or integer codes in
string format. For example, suppose we have the surface
names and corresponding ID codes shown below:
Surface Name ID code
------------ -------
"Mars MEGDR 128 PIXEL/DEG" 1
"Mars MEGDR 64 PIXEL/DEG" 2
"Mars_MRO_HIRISE" 3
If data for all of the above surfaces are loaded, then
data for surface 1 can be specified by either
"SURFACES = 1"
or
"SURFACES = \"Mars MEGDR 128 PIXEL/DEG\""
Double quotes are used to delimit the surface name because
it contains blank characters.
To use data for surfaces 2 and 3 together, any
of the following surface lists could be used:
"SURFACES = 2, 3"
"SURFACES = \"Mars MEGDR 64 PIXEL/DEG\", 3"
"SURFACES = 2, Mars_MRO_HIRISE"
"SURFACES = \"Mars MEGDR 64 PIXEL/DEG\", Mars_MRO_HIRISE"
An example of a `method' argument that could be constructed
using one of the surface lists above is
"NADIR/DSK/UNPRIORITIZED/SURFACES= \"Mars MEGDR 64 PIXEL/DEG\",3"
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 apparent limb points on Phobos as seen from Mars.
Due to Phobos' irregular shape, the TANGENT limb point
definition will used. It suffices to compute light time and
stellar aberration corrections for the center of Phobos, so
the "CENTER" aberration correction locus will be used. Use
converged Newtonian light time and stellar aberration
corrections in order to model the apparent position and
orientation of Phobos.
For comparison, compute limb points using both ellipsoid
and topographic shape models.
Use the target body-fixed +Z axis as the reference direction
for generating cutting half-planes. This choice enables the
user to see whether the first limb point is near the target's
north pole.
For each option, use just three cutting half-planes, in order
to keep the volume of output manageable. In most applications,
the number of cuts and the number of resulting limb points
would be much greater.
Use the meta-kernel below to load the required SPICE
kernels.
KPL/MK
File: limbpt_ex1.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
--------- --------
de430.bsp Planetary ephemeris
mar097.bsp Mars satellite ephemeris
pck00010.tpc Planet orientation and
radii
naif0011.tls Leapseconds
phobos512.bds DSK based on
Gaskell ICQ Q=512
Phobos plate model
\begindata
PATH_SYMBOLS = "GEN"
PATH_VALUES = '/ftp/pub/naif/generic_kernels'
KERNELS_TO_LOAD = ( 'de430.bsp',
'mar097.bsp',
'pck00010.tpc',
'naif0011.tls',
'$GEN/dsk/phobos/phobos512.bds' )
\begintext
Example code begins here.
/.
limbpt_c example 1
Find limb points on Phobos as seen from Mars.
Compute limb points using the tangent definition.
Perform aberration corrections for the target center.
Use both ellipsoid and DSK shape models.
./
#include <stdio.h>
#include "SpiceUsr.h"
int main()
{
/.
Local constants
./
#define META "limbpt_ex1.tm"
#define MTHLEN 51
#define NMETH 2
#define MAXN 10000
/.
Local variables
./
SpiceChar * abcorr;
SpiceChar * corloc;
SpiceChar * fixref;
SpiceChar * obsrvr;
SpiceChar method [NMETH][MTHLEN] =
{ "TANGENT/ELLIPSOID",
"TANGENT/DSK/UNPRIORITIZED" };
SpiceChar * target;
SpiceDouble delrol;
SpiceDouble et;
SpiceDouble points [MAXN][3];
SpiceDouble roll;
SpiceDouble schstp;
SpiceDouble soltol;
SpiceDouble tangts [MAXN][3];
SpiceDouble trgeps [MAXN];
SpiceDouble z [3] = { 0.0, 0.0, 1.0 };
SpiceInt i;
SpiceInt j;
SpiceInt k;
SpiceInt ncuts;
SpiceInt npts [MAXN];
SpiceInt start;
/.
Load kernel files via the meta-kernel.
./
furnsh_c ( META );
/.
Set target, observer, and target body-fixed,
body-centered reference frame.
./
obsrvr = "MARS";
target = "PHOBOS";
fixref = "IAU_PHOBOS";
/.
Set aberration correction and correction locus.
./
abcorr = "CN+S";
corloc = "CENTER";
/.
Convert the UTC request time string seconds past
J2000, TDB.
./
str2et_c ( "2008 AUG 11 00:00:00", &et );
/.
Compute a set of limb points using light time and
stellar aberration corrections. Use both ellipsoid
and DSK shape models. Use a step size of 100
microradians to ensure we don't miss the limb.
Set the convergence tolerance to 100 nanoradians,
which will limit the height error to about 1 meter.
Compute 3 limb points for each computation method.
./
schstp = 1.0e-4;
soltol = 1.0e-7;
ncuts = 3;
printf ( "\n"
"Observer: %s\n"
"Target: %s\n"
"Frame: %s\n"
"\n"
"Number of cuts: %d\n",
obsrvr,
target,
fixref,
(int)ncuts );
delrol = twopi_c() / ncuts;
for ( i = 0; i < NMETH; i++ )
{
limbpt_c ( method[i], target, et, fixref,
abcorr, corloc, obsrvr, z,
delrol, ncuts, schstp, soltol,
MAXN, npts, points, trgeps,
tangts );
/.
Write the results.
./
printf ( "\n\n"
"Computation method = %s\n"
"Locus = %s\n",
method[i],
corloc );
start = 0;
for ( j = 0; j < ncuts; j++ )
{
roll = j * delrol;
printf ( "\n"
" Roll angle (deg) = %21.9f\n"
" Target epoch = %21.9f\n"
" Number of limb points at this "
"roll angle: %d\n",
roll * dpr_c(),
trgeps[j],
npts[j] );
printf ( " Limb points\n" );
for ( k = 0; k < npts[j]; k++ )
{
printf ( " %20.9f %20.9f %20.9f\n",
points[k+start][0],
points[k+start][1],
points[k+start][2] );
}
start += npts[j];
}
}
printf ( "\n" );
return ( 0 );
}
When this program was executed on a PC/Linux/gcc 64-bit
platform, the output was:
Observer: MARS
Target: PHOBOS
Frame: IAU_PHOBOS
Number of cuts: 3
Computation method = TANGENT/ELLIPSOID
Locus = CENTER
Roll angle (deg) = 0.000000000
Target epoch = 271684865.152078211
Number of limb points at this roll angle: 1
Limb points
0.016445326 -0.000306114 9.099992715
Roll angle (deg) = 120.000000000
Target epoch = 271684865.152078211
Number of limb points at this roll angle: 1
Limb points
-0.204288375 -9.235230829 -5.333237706
Roll angle (deg) = 240.000000000
Target epoch = 271684865.152078211
Number of limb points at this roll angle: 1
Limb points
0.242785221 9.234520095 -5.333231253
Computation method = TANGENT/DSK/UNPRIORITIZED
Locus = CENTER
Roll angle (deg) = 0.000000000
Target epoch = 271684865.152078211
Number of limb points at this roll angle: 1
Limb points
-0.398901673 0.007425178 9.973720555
Roll angle (deg) = 120.000000000
Target epoch = 271684865.152078211
Number of limb points at this roll angle: 1
Limb points
-0.959300281 -8.537573427 -4.938700447
Roll angle (deg) = 240.000000000
Target epoch = 271684865.152078211
Number of limb points at this roll angle: 1
Limb points
-1.380536729 9.714334047 -5.592916790
2) Find apparent limb points on Mars as seen from the earth.
Compare results using different computation options.
Use both the "TANGENT" and "GUIDED" limb point definitions. For
the tangent limb points, use the "ELLIPSOID LIMB" aberration
correction locus; for the guided limb points, use the "CENTER"
locus. For the "GUIDED" limb points, also compute the distance
of each point from the corresponding point computed using the
"TANGENT" definition.
For comparison, compute limb points using both ellipsoid and
topographic shape models.
Check the limb points by computing the apparent emission
angles at each limb point.
For the ellipsoid shape model, we expect emission angles very
close to 90 degrees, since each illumination angle calculation
is done using aberration corrections for the limb point at
which the angles are measured.
Use the target body-fixed +Z axis as the reference direction
for generating cutting half-planes. This choice enables the
user to see whether the first limb point is near the target's
north pole.
For each option, use just three cutting half-planes, in order
to keep the volume of output manageable. In most applications,
the number of cuts and the number of resulting limb points
would be much greater.
Use the meta-kernel shown below.
KPL/MK
File: limbpt_ex2.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
--------- --------
de430.bsp Planetary ephemeris
mar097.bsp Mars satellite ephemeris
pck00010.tpc Planet orientation and
radii
naif0011.tls Leapseconds
megr90n000cb_plate.bds DSK plate model based on
MGS MOLAR MEGDR DEM,
resolution 4
pixels/degree.
\begindata
KERNELS_TO_LOAD = ( 'de430.bsp',
'mar097.bsp',
'pck00010.tpc',
'naif0011.tls',
'megr90n000cb_plate.bds' )
\begintext
Example code begins here.
/.
limbpt_c example 2
Find limb points on Mars as seen from the earth.
Compute limb points using both the tangent and
"guided" definitions.
For the tangent limb points, perform aberration
corrections for the reference ellipsoid limb.
Check limb points by computing emission angles
at each point.
Use both ellipsoid and DSK shape models.
./
#include <stdio.h>
#include "SpiceUsr.h"
int main()
{
/.
Local constants
./
#define META "limbpt_ex2.tm"
#define CORLEN 21
#define MTHLEN 51
#define NMETH 3
#define MAXN 10000
/.
Local variables
./
SpiceChar * abcorr;
ConstSpiceChar * corloc [NMETH] =
{ "ELLIPSOID LIMB",
"ELLIPSOID LIMB",
"CENTER" };
SpiceChar * fixref;
ConstSpiceChar * ilumth [NMETH] =
{ "ELLIPSOID",
"DSK/UNPRIORITIZED",
"DSK/UNPRIORITIZED" };
ConstSpiceChar * method [NMETH] =
{ "TANGENT/ELLIPSOID",
"TANGENT/DSK/UNPRIORITIZED",
"GUIDED/DSK/UNPRIORITIZED" };
SpiceChar * obsrvr;
SpiceChar * target;
SpiceDouble alt;
SpiceDouble delrol;
SpiceDouble dist;
SpiceDouble emissn;
SpiceDouble et;
SpiceDouble f;
SpiceDouble lat;
SpiceDouble lon;
SpiceDouble lt;
SpiceDouble phase;
static SpiceDouble points [MAXN][3];
static SpiceDouble svpnts [MAXN][3];
SpiceDouble pos [3];
SpiceDouble radii [3];
SpiceDouble re;
SpiceDouble roll;
SpiceDouble rp;
SpiceDouble schstp;
SpiceDouble solar;
SpiceDouble soltol;
SpiceDouble srfvec [3];
static SpiceDouble tangts [MAXN][3];
SpiceDouble trgepc;
static SpiceDouble trgeps [MAXN];
SpiceDouble z [3] = { 0.0, 0.0, 1.0 };
SpiceInt i;
SpiceInt j;
SpiceInt k;
SpiceInt m;
SpiceInt n;
SpiceInt ncuts;
static SpiceInt npts [MAXN];
SpiceInt start;
/.
Load kernel files via the meta-kernel.
./
furnsh_c ( META );
/.
Set target, observer, and target body-fixed,
body-centered reference frame.
./
obsrvr = "EARTH";
target = "MARS";
fixref = "IAU_MARS";
/.
Set aberration correction. We'll set the correction
locus below.
./
abcorr = "CN+S";
/.
Convert the UTC request time string seconds past
J2000, TDB.
./
str2et_c ( "2008 AUG 11 00:00:00", &et );
/.
Look up the target body's radii. We'll use these to
convert Cartesian to planetographic coordinates. Use
the radii to compute the flattening coefficient of
the reference ellipsoid.
./
bodvrd_c ( target, "RADII", 3, &n, radii );
/.
Compute the flattening coefficient for planetodetic
coordinates
./
re = radii[0];
rp = radii[2];
f = ( re - rp ) / re;
/.
Compute a set of limb points using light time and
stellar aberration corrections. Use both ellipsoid
and DSK shape models.
Obtain the observer-target distance at ET.
./
spkpos_c ( target, et, "J2000", abcorr,
obsrvr, pos, < );
dist = vnorm_c( pos );
/.
Set the angular step size so that a single step will
be taken in the root bracketing process; that's all
that is needed since we don't expect to have multiple
limb points in any cutting half-plane.
./
schstp = 4.0;
/.
Set the convergence tolerance to minimize the height
error. We can't achieve the 1 millimeter precision
suggested by the formula because the earth-Mars
distance is about 3.5e8 km. Compute 3 limb points
for each computation method.
./
soltol = 1.0e-6/dist;
/.
Set the number of cutting half-planes and roll step.
./
ncuts = 3;
delrol = twopi_c() / ncuts;
printf ( "\n"
"Observer: %s\n"
"Target: %s\n"
"Frame: %s\n"
"\n"
"Number of cuts: %d\n",
obsrvr,
target,
fixref,
(int)ncuts );
for ( i = 0; i < NMETH; i++ )
{
limbpt_c ( method[i], target, et, fixref,
abcorr, corloc[i], obsrvr, z,
delrol, ncuts, schstp, soltol,
MAXN, npts, points, trgeps,
tangts );
/.
Write the results.
./
printf ( "\n"
"Computation method = %s\n"
"Locus = %s\n",
method[i],
corloc[i] );
start = 0;
for ( j = 0; j < ncuts; j++ )
{
roll = j * delrol;
printf ( "\n"
" Roll angle (deg) = %21.9f\n"
" Target epoch = %21.9f\n"
" Number of limb points at this "
"roll angle: %d\n",
roll * dpr_c(),
trgeps[j],
npts[j] );
for ( k = 0; k < npts[j]; k++ )
{
printf ( " Limb point planetodetic "
"coordinates:\n" );
recgeo_c ( points[start+k], re, f,
&lon, &lat, &alt );
printf ( " Longitude (deg): %21.9f\n"
" Latitude (deg): %21.9f\n"
" altitude (km): %21.9f\n",
lon*dpr_c(), lat*dpr_c(), alt );
/.
Get illumination angles for this limb point.
./
m = start + k;
ilumin_c ( ilumth[i], target, et,
fixref, abcorr, obsrvr,
points[m], &trgepc, srfvec,
&phase, &solar, &emissn );
printf ( " Emission angle (deg): %21.9f\n",
emissn*dpr_c() );
if ( i == 1 )
{
vequ_c ( points[m], svpnts[m] );
}
else if ( i == 2 )
{
dist = vdist_c ( points[m], svpnts[m] );
printf ( " Distance error (km): "
"%21.9f\n",
dist );
}
}
start += npts[j];
}
printf( "\n" );
}
return ( 0 );
}
When this program was executed on a PC/Linux/gcc 64-bit
platform, the output was:
Observer: EARTH
Target: MARS
Frame: IAU_MARS
Number of cuts: 3
Computation method = TANGENT/ELLIPSOID
Locus = ELLIPSOID LIMB
Roll angle (deg) = 0.000000000
Target epoch = 271683700.368869901
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): -19.302258950
Latitude (deg): 64.005620446
altitude (km): -0.000000000
Emission angle (deg): 90.000000000
Roll angle (deg) = 120.000000000
Target epoch = 271683700.368948162
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): 85.029135674
Latitude (deg): -26.912378799
altitude (km): 0.000000000
Emission angle (deg): 90.000000000
Roll angle (deg) = 240.000000000
Target epoch = 271683700.368949771
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): -123.633654215
Latitude (deg): -26.912378799
altitude (km): -0.000000000
Emission angle (deg): 90.000000000
Computation method = TANGENT/DSK/UNPRIORITIZED
Locus = ELLIPSOID LIMB
Roll angle (deg) = 0.000000000
Target epoch = 271683700.368869901
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): -19.302258949
Latitude (deg): 63.893637432
altitude (km): -3.667553958
Emission angle (deg): 89.979580513
Roll angle (deg) = 120.000000000
Target epoch = 271683700.368948162
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): 85.434644181
Latitude (deg): -26.705411232
altitude (km): -0.044832382
Emission angle (deg): 88.089500425
Roll angle (deg) = 240.000000000
Target epoch = 271683700.368949771
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): -123.375003592
Latitude (deg): -27.043096738
altitude (km): 3.695628489
Emission angle (deg): 89.875890611
Computation method = GUIDED/DSK/UNPRIORITIZED
Locus = CENTER
Roll angle (deg) = 0.000000000
Target epoch = 271683700.368922532
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): -19.302259163
Latitude (deg): 64.005910146
altitude (km): -3.676424552
Emission angle (deg): 89.979580513
Distance error (km): 6.664208540
Roll angle (deg) = 120.000000000
Target epoch = 271683700.368922532
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): 85.029135792
Latitude (deg): -26.912405352
altitude (km): -0.328988915
Emission angle (deg): 91.525256314
Distance error (km): 24.686472888
Roll angle (deg) = 240.000000000
Target epoch = 271683700.368922532
Number of limb points at this roll angle: 1
Limb point planetodetic coordinates:
Longitude (deg): -123.633653487
Latitude (deg): -26.912086524
altitude (km): 3.626058850
Emission angle (deg): 89.809897171
Distance error (km): 15.716056568
3) Find apparent limb points on comet Churyumov-Gerasimenko
as seen from the Rosetta orbiter.
This computation is an example of a case for which some
of the cutting half-planes contain multiple limb points.
Use the "TANGENT" limb definition, since the target shape
is not well approximated by its reference ellipsoid.
Use the "CENTER" aberration correction locus since the
light time difference across the object is small.
Use the meta-kernel shown below.
KPL/MK
File: limbpt_ex3.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
paths of the kernels referenced here must be adjusted to
be compatible with the user's host computer directory
structure.
The names and contents of the kernels referenced
by this meta-kernel are as follows:
File name Contents
--------- --------
DE405.BSP Planetary ephemeris
NAIF0011.TLS Leapseconds
ROS_CG_M004_NSPCESA_N_V1.BDS DSK plate model based on
Rosetta NAVCAM data
RORB_DV_145_01_______00216.BSP Rosetta orbiter
ephemeris
CORB_DV_145_01_______00216.BSP Comet Churyumov-
Gerasimenko ephemeris
ROS_CG_RAD_V10.TPC Comet Churyumov-
Gerasimenko radii
ROS_V25.TF Comet C-G frame kernel
(includes SCLK
parameters)
CATT_DV_145_01_______00216.BC Comet C-G C-kernel
\begindata
PATH_VALUES = (
'/ftp/pub/naif/pds/data/+'
'ro_rl-e_m_a_c-spice-6-v1.0/rossp_1000/DATA'
)
PATH_SYMBOLS = (
'KERNELS'
)
KERNELS_TO_LOAD = (
'$KERNELS/SPK/DE405.BSP'
'$KERNELS/LSK/NAIF0011.TLS'
'$KERNELS/SPK/RORB_DV_145_01_______00216.BSP'
'$KERNELS/SPK/CORB_DV_145_01_______00216.BSP'
'$KERNELS/PCK/ROS_CG_RAD_V10.TPC'
'$KERNELS/FK/ROS_V25.TF'
'$KERNELS/CK/CATT_DV_145_01_______00216.BC'
'$KERNELS/DSK/ROS_CG_M004_NSPCESA_N_V1.BDS'
)
\begintext
Example code begins here.
/.
limbpt_c example 3
Find limb points on comet Churyumov-Gerasimenko
as seen from the Rosetta orbiter.
Compute limb points using the tangent definition.
Perform aberration corrections for the target center.
Use both ellipsoid and DSK shape models.
Display only limb points lying in half-planes that
contain multiple limb points.
./
#include <stdio.h>
#include "SpiceUsr.h"
int main()
{
/.
Local constants
./
#define META "limbpt_ex3.tm"
#define CORLEN 21
#define MTHLEN 51
#define MAXN 10000
/.
Local variables
./
SpiceChar * abcorr;
SpiceChar * corloc;
SpiceChar * fixref;
ConstSpiceChar * method =
{ "TANGENT/DSK/UNPRIORITIZED" };
SpiceChar * obsrvr;
SpiceChar * target;
SpiceDouble angle;
SpiceDouble axis [3];
SpiceDouble delrol;
SpiceDouble et;
SpiceDouble lt;
static SpiceDouble points [MAXN][3];
SpiceDouble refvec [3];
SpiceDouble roll;
SpiceDouble schstp;
SpiceDouble soltol;
static SpiceDouble tangts [MAXN][3];
static SpiceDouble trgeps [MAXN];
SpiceDouble trgpos [3];
SpiceDouble xvec [3] = { 1.0, 0.0, 0.0 };
SpiceInt i;
SpiceInt j;
SpiceInt ncuts;
static SpiceInt npts [MAXN];
SpiceInt start;
/.
Load kernel files via the meta-kernel.
./
furnsh_c ( META );
/.
Set target, observer, and target body-fixed,
body-centered reference frame.
./
obsrvr = "ROSETTA";
target = "CHURYUMOV-GERASIMENKO";
fixref = "67P/C-G_CK";
/.
Set aberration correction and correction locus.
./
abcorr = "CN+S";
corloc = "CENTER";
/.
Convert the UTC request time string seconds past
J2000, TDB.
./
str2et_c ( "2015 MAY 10 00:00:00", &et );
/.
Compute a set of limb points using light time and
stellar aberration corrections. Use a step size
corresponding to a 1 meter height error to ensure
we don't miss the limb. Set the convergence tolerance
to 1/100 of this amount, which will limit the height
convergence error to about 1 cm.
./
spkpos_c ( target, et, fixref, abcorr,
obsrvr, trgpos, < );
schstp = 1.e-2 / vnorm_c( trgpos );
soltol = schstp / 100.0;
/.
Set the reference vector to the start of a
region of the roll domain on which we know
(from an external computation) that we'll
find multiple limb points in some half planes.
Compute 30 limb points, starting with the
half-plane containing the reference vector.
./
vminus_c ( trgpos, axis );
angle = 310.0 * rpd_c();
vrotv_c ( xvec, axis, angle, refvec );
ncuts = 30;
delrol = twopi_c() / 1000.0;
printf ( "\n"
"Observer: %s\n"
"Target: %s\n"
"Frame: %s\n"
"\n"
"Number of cuts: %d\n",
obsrvr,
target,
fixref,
(int)ncuts );
limbpt_c ( method, target, et, fixref,
abcorr, corloc, obsrvr, refvec,
delrol, ncuts, schstp, soltol,
MAXN, npts, points, trgeps,
tangts );
/.
Write the results.
./
printf ( "\n\n"
"Computation method = %s\n"
"Locus = %s\n",
method,
corloc );
start = 0;
for ( i = 0; i < ncuts; i++ )
{
roll = i * delrol;
printf ( "\n"
" Roll angle (deg) = %21.9f\n"
" Target epoch = %21.9f\n"
" Number of limb points at this "
"roll angle: %d\n",
roll * dpr_c(),
trgeps[i],
npts[i] );
if ( npts[i] > 1 )
{
printf ( " Limb points\n" );
for ( j = 0; j < npts[i]; j++ )
{
printf( "%21.9f %21.9f %21.9f\n",
points[start+j][0],
points[start+j][1],
points[start+j][2] );
}
}
start += npts[i];
}
printf( "\n" );
return ( 0 );
}
When this program was executed on a PC/Linux/gcc 64-bit
platform, the output was (only the first three and last three
limb points are shown here):
Observer: ROSETTA
Target: CHURYUMOV-GERASIMENKO
Frame: 67P/C-G_CK
Number of cuts: 30
Computation method = TANGENT/DSK/UNPRIORITIZED
Locus = CENTER
Roll angle (deg) = 0.000000000
Target epoch = 484488067.184933782
Number of limb points at this roll angle: 3
Limb points
1.320416231 -0.347379011 1.445260615
0.970350318 0.201685071 0.961996205
0.436720618 0.048224590 0.442280714
Roll angle (deg) = 0.360000000
Target epoch = 484488067.184933782
Number of limb points at this roll angle: 3
Limb points
1.330290293 -0.352340416 1.438802587
0.965481808 0.202131806 0.946190003
0.453917030 0.082062880 0.447624224
Roll angle (deg) = 0.720000000
Target epoch = 484488067.184933782
Number of limb points at this roll angle: 3
Limb points
1.339037339 -0.357848188 1.431256926
0.962159098 0.192370269 0.934342086
0.459160821 0.082273840 0.447880429
...
Roll angle (deg) = 9.720000000
Target epoch = 484488067.184933782
Number of limb points at this roll angle: 3
Limb points
1.568112677 -0.674947784 1.254880628
0.709857306 -0.111495634 0.547778706
0.491633785 -0.142729847 0.386229224
Roll angle (deg) = 10.080000000
Target epoch = 484488067.184933782
Number of limb points at this roll angle: 3
Limb points
1.585230837 -0.663993935 1.249957484
0.633077981 -0.300058272 0.502702168
0.254736344 -0.760250955 0.266785439
Roll angle (deg) = 10.440000000
Target epoch = 484488067.184933782
Number of limb points at this roll angle: 3
Limb points
1.599387477 -0.661757808 1.243621216
0.633255406 -0.293319746 0.495438969
0.271959251 -0.761967204 0.274619198
None.
None.
N.J. Bachman (JPL)
-CSPICE Version 1.0.0, 05-APR-2017 (NJB)
find limb points on target body
Link to routine limbpt_c source file limbpt_c.c
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