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Index Page limbpt_c
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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
       limbpt_c ( Limb points on an extended object )

       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]  )
#### Abstract
       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.
#### Required_Reading
       CK
       DSK
       FRAMES
       NAIF_IDS
       PCK
       SPK
       TIME
#### Keywords
       GEOMETRY
#### Brief_I/O
       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.
#### Detailed_Input
       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 routine. 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 `corloc' 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
                         `corloc' 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 two iterations.

                                 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.

                   The following values of `abcorr' apply to the
                   "transmission" case in which photons depart from the
                   observer's location at `et' and arrive at the aberration
                   correction locus at the light-time corrected epoch
                   et+lt:

                      "XLT"      Correct for one-way light time (also
                                 called "planetary aberration") using a
                                 Newtonian formulation. This correction
                                 yields the locus at the moment it
                                 receives photons departing from 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 two iterations.

                                 Both the target position as seen by the
                                 observer, and rotation of the target
                                 body, are corrected for light time.

                      "XLT+S"    Correct for one-way transmission light
                                 time and stellar aberration using a
                                 Newtonian formulation. This option
                                 modifies the locus obtained with the "XLT"
                                 option to account for the observer's
                                 velocity relative to the solar system
                                 barycenter. These corrections yield points
                                 on the apparent limb.

                      "XCN"      Converged transmission Newtonian light
                                 time correction. In solving the light time
                                 equation, the "XCN" correction iterates
                                 until the solution converges. Both the
                                 position and rotation of the target body
                                 are corrected for light time.

                      "XCN+S"    Converged transmission Newtonian light
                                 time and stellar aberration corrections.
                                 This option produces a solution that is at
                                 least as accurate at that obtainable with
                                 the `XLT+S' option. Whether the "XCN+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'.
#### Detailed_Output
       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.
#### Parameters
       None.
#### Exceptions
       1)  If the specified aberration correction is unrecognized, an
           error is signaled by a routine in the call tree of this
           routine.

       2)  If either the target or observer input strings cannot be
           converted to an integer ID code, the error
           SPICE(IDCODENOTFOUND) is signaled by a routine in the call
           tree of this routine.

       3)  If `obsrvr' and `target' map to the same NAIF integer ID code, the
           error SPICE(BODIESNOTDISTINCT) is signaled by a routine in the
           call tree of this routine.

       4)  If the input target body-fixed frame `fixref' is not recognized,
           the error SPICE(NOFRAME) is signaled by a routine in the call
           tree of this routine. 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 by a routine in the
           call tree of this routine.

       6)  If the input argument `method' is not recognized, the error
           SPICE(INVALIDMETHOD) is signaled by either this routine or a
           routine in the call tree of this routine.

       7)  If `method' contains an invalid limb type, the error
           SPICE(INVALIDLIMBTYPE) is signaled by a routine in the call
           tree of this routine.

       8)  If the target and observer have distinct identities but are
           at the same location, the error SPICE(NOSEPARATION) is
           signaled by a routine in the call tree of this routine.

       9)  If insufficient ephemeris data have been loaded prior to
           calling limbpt_c, an error is 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, an error is
           signaled by a routine in the call tree of this routine.

           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) If the radii are available in the kernel pool but the count
           of radii values is not three, the error SPICE(BADRADIUSCOUNT)
           is signaled by a routine in the call tree of this routine.

       12) If the target body's shape is modeled as an ellipsoid, and if
           any of the radii of the target body are non-positive, an error
           is signaled by a routine in the call tree of this routine. The
           target must be an extended body.

       13) If PCK data specifying the target body-fixed frame orientation
           have not been loaded prior to calling limbpt_c, an error is
           signaled by a routine in the call tree of this routine.

       14) If `method' specifies that the target surface is represented by
           DSK data, and no DSK files are loaded for the specified
           target, an error is signaled by a routine in the call tree
           of this routine.

       15) If the array bound `maxn' is less than 1, the error
           SPICE(INVALIDSIZE) is signaled by a routine in the call tree
           of this routine.

       16) If the number of cutting half-planes specified by `ncuts' is
           negative or greater than `maxn', the error SPICE(INVALIDCOUNT)
           is signaled by a routine in the call tree of this routine.

       17) If the aberration correction locus is not recognized, the
           error SPICE(INVALIDLOCUS) is signaled by a routine in the call
           tree of this routine.

       18) If the aberration correction locus is "ELLIPSOID LIMB" but
           limb type is not "TANGENT", the error SPICE(BADLIMBLOCUSMIX)
           is signaled by a routine in the call tree of this routine.

       19) If the reference vector `refvec' is the zero vector, the error
           SPICE(ZEROVECTOR) is signaled by a routine in the call tree of
           this routine.

       20) If the reference vector `refvec' and the observer target vector
           are linearly dependent, the error SPICE(DEGENERATECASE) is
           signaled by a routine in the call tree of this routine.

       21) 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) is
           signaled by a routine in the call tree of this routine.

       22) If the limb points cannot all be stored in the output `points'
           array, the error SPICE(OUTOFROOM) is signaled by a routine in
           the call tree of this routine.

       23) If the surface is represented by DSK data, and if the search
           step is non-positive, the error SPICE(INVALIDSEARCHSTEP) is
           signaled by a routine in the call tree of this routine.

       24) If the surface is represented by DSK data, and if the search
           tolerance is non-positive, the error SPICE(INVALIDTOLERANCE)
           is signaled by a routine in the call tree of this routine.

       25) If the roll step is non-positive and `ncuts' is greater than 1,
           the error SPICE(INVALIDROLLSTEP) is signaled by a routine in
           the call tree of this routine.

       26) If any of the `method', `target', `fixref', `abcorr', `corloc'
           or `obsrvr' input string pointers is null, the error
           SPICE(NULLPOINTER) is signaled.

       27) If any of the `method', `target', `fixref', `abcorr', `corloc'
           or `obsrvr' input strings has zero length, the error
           SPICE(EMPTYSTRING) is signaled.
#### Files
       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.
#### Particulars
       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"
#### 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 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 shown 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

                KERNELS_TO_LOAD = ( 'de430.bsp',
                                    'mar097.bsp',
                                    'pck00010.tpc',
                                    'naif0011.tls',
                                    'phobos512.bds' )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program limbpt_ex1

             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 Mac/Intel/cc/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 to load the required SPICE
          kernels.

             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

             End of meta-kernel

          Example code begins here.

          /.
             Program limbpt_ex1

             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, &lt              );

             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 Mac/Intel/cc/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 to load the required SPICE
          kernels.

             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

               KERNELS_TO_LOAD = ( 'DE405.BSP'
                                   'NAIF0011.TLS'
                                   'RORB_DV_145_01_______00216.BSP'
                                   'CORB_DV_145_01_______00216.BSP'
                                   'ROS_CG_RAD_V10.TPC'
                                   'ROS_V25.TF'
                                   'CATT_DV_145_01_______00216.BC'
                                   'ROS_CG_M004_NSPCESA_N_V1.BDS'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program limbpt_ex1

             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, &lt            );

             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 6 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  = 6;
             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 Mac/Intel/cc/64-bit
          platform, the output was:

          Observer:       ROSETTA
          Target:         CHURYUMOV-GERASIMENKO
          Frame:          67P/C-G_CK

          Number of cuts: 6

          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) =           1.080000000
               Target epoch  =   484488067.184933782
               Number of limb points at this roll angle: 3
                Limb points
                    1.346729151           -0.365488231            1.423051540
                    0.960760394            0.183652804            0.924323093
                    0.464582286            0.084076587            0.447930141

            Roll angle (deg) =           1.440000000
               Target epoch  =   484488067.184933782
               Number of limb points at this roll angle: 3
                Limb points
                    1.351235771           -0.380664224            1.413164272
                    0.960268777            0.176953543            0.914876859
                    0.466284590            0.079312729            0.445564308

            Roll angle (deg) =           1.800000000
               Target epoch  =   484488067.184933782
               Number of limb points at this roll angle: 3
                Limb points
                    1.358042184           -0.390349186            1.404421386
                    0.959495690            0.170340551            0.905212642
                    0.370611049           -0.167047205            0.395076979
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
#### Version
       -CSPICE Version 2.0.0, 01-NOV-2021 (NJB) (JDR)

           Added support for transmission aberration corrections.

           Corrected description of iteration count for non-converged
           corrections.

           Edited the header to comply with NAIF standard. Reduced
           the number of cuts to present in the output in Example #3.

       -CSPICE Version 1.0.0, 05-APR-2017 (NJB)
#### Index_Entries
       find limb points on target body
#### Link to routine limbpt_c source file limbpt_c.c

    Fri Dec 31 18:41:09 2021