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Index Page sincpt_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
       sincpt_c ( Surface intercept )

       void sincpt_c ( ConstSpiceChar      * method,
                       ConstSpiceChar      * target,
                       SpiceDouble           et,
                       ConstSpiceChar      * fixref,
                       ConstSpiceChar      * abcorr,
                       ConstSpiceChar      * obsrvr,
                       ConstSpiceChar      * dref,
                       ConstSpiceDouble      dvec   [3],
                       SpiceDouble           spoint [3],
                       SpiceDouble         * trgepc,
                       SpiceDouble           srfvec [3],
                       SpiceBoolean        * found       )
#### Abstract
       Compute, for a given observer and a ray emanating from the
       observer, the surface intercept of the ray on a target body at
       a specified epoch, optionally corrected for light time and
       stellar aberration.

       The surface of the target body may be represented by a triaxial
       ellipsoid or by topographic data provided by DSK files.

       This routine supersedes srfxpt_c.
#### Required_Reading
       CK
       DSK
       FRAMES
       NAIF_IDS
       PCK
       SCLK
       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 TDB seconds past J2000 TDB.
       fixref     I   Body-fixed, body-centered target body frame.
       abcorr     I   Aberration correction flag.
       obsrvr     I   Name of observing body.
       dref       I   Reference frame of ray's direction vector.
       dvec       I   Ray's direction vector.
       spoint     O   Surface intercept point on the target body.
       trgepc     O   Intercept epoch.
       srfvec     O   Vector from observer to intercept point.
       found      O   Flag indicating whether intercept was found.
#### 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:

                      "ELLIPSOID"

                         The intercept computation uses a triaxial
                         ellipsoid to model the surface of the target
                         body. The ellipsoid's radii must be available
                         in the kernel pool.

                      "DSK/UNPRIORITIZED[/SURFACES = <surface list>]"

                         The intercept computation uses topographic data
                         to model the surface of the target body. These
                         data must be provided by loaded DSK files.

                         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 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 escaped 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.

                   Neither case nor white space are significant in
                   `method', except within double-quoted strings. For
                   example, the string " eLLipsoid " 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. `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 ephemeris 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 state 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 or et+lt, where `lt' is the one-way light time
                   between the intercept point and the observer, and the
                   sign applied to `lt' depends on the selected
                   correction. See the description of `abcorr' 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 intercept point `spoint' and the observer-to-
                   intercept vector `srfvec' will be expressed relative to
                   this reference frame.

       abcorr      indicates the aberration corrections to be applied
                   when computing the target's position and orientation.

                   For remote sensing applications, where the apparent
                   surface intercept point seen by the observer is
                   desired, normally the correction

                      "CN+S"

                   should be used. This and the other supported options
                   are described below. `abcorr' may be any of the
                   following:

                      "NONE"     Apply no correction. Return the
                                 geometric surface intercept point on the
                                 target body.

                   Let `lt' represent the one-way light time between the
                   observer and the surface intercept point (note: NOT
                   between the observer and the target body's center).
                   The following values of `abcorr' apply to the
                   "reception" case in which photons depart from the
                   intercept point's location 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 location of the surface
                                 intercept point 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
                                 surface intercept obtained with the
                                 "LT" option to account for the
                                 observer's velocity relative to the
                                 solar system barycenter. These
                                 computations yield the apparent surface
                                 intercept point.

                      "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.

                                 For reception-case applications
                                 involving intercepts near the target
                                 body limb, this option should be used.

                   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
                   intercept point at the light-time corrected epoch
                   et+lt:

                      "XLT"      "Transmission" case: correct for
                                 one-way light time using a Newtonian
                                 formulation. This correction yields the
                                 intercept location at the moment it
                                 receives photons emitted from the
                                 observer's location at `et'.

                                 The light time correction uses an
                                 iterative solution of the light time
                                 equation. The solution invoked by the
                                 "XLT" option uses one iteration.

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

                      "XLT+S"    "Transmission" case: correct for
                                 one-way light time and stellar
                                 aberration using a Newtonian
                                 formulation. This option modifies the
                                 intercept obtained with the "XLT"
                                 option to account for the observer's
                                 velocity relative to the solar system
                                 barycenter.

                      "XCN"      Converged Newtonian light time
                                 correction. This is the same as "XLT"
                                 correction but with further iterations
                                 to a converged Newtonian light time
                                 solution.

                      "XCN+S"    "Transmission" case: converged
                                 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.

                                 For transmission-case applications
                                 involving intercepts near the target
                                 body limb, this option should be used.

                   Case and embedded blanks are not significant in
                   `abcorr'. For example, the string

                     "Cn + s"

                   is valid.

       obsrvr      is the name of the observing body. This is typically
                   a spacecraft, the earth, or a surface point on the
                   earth or on another extended object.

                   The observer must be outside the target body.

                   `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.

       dref        is the name of the reference frame relative to which
                   the ray's direction vector is expressed. This may be
                   any 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 `dref' is case-insensitive, and
                   leading and trailing blanks in `dref' are not
                   significant.

                   When `dref' designates a non-inertial frame, the
                   orientation of the frame is evaluated at an epoch
                   dependent on the frame's center and, if the center is
                   not the observer, on the selected aberration
                   correction. See the description of the direction
                   vector `dvec' for details.

       dvec        is a ray direction vector emanating from the observer.
                   The intercept with the target body's surface of the ray
                   defined by the observer and `dvec' is sought.

                   `dvec' is specified relative to the reference frame
                   designated by `dref'.

                   Non-inertial reference frames are treated as follows:
                   if the center of the frame is at the observer's
                   location, the frame is evaluated at `et'. If the
                   frame's center is located elsewhere, then letting
                   `ltcent' be the one-way light time between the observer
                   and the central body associated with the frame, the
                   orientation of the frame is evaluated at et-ltcent,
                   et+ltcent, or `et' depending on whether the requested
                   aberration correction is, respectively, for received
                   radiation, transmitted radiation, or is omitted.
                   `ltcent' is computed using the method indicated by
                   `abcorr'.
#### Detailed_Output
       spoint      is the surface intercept point on the target body of
                   the ray defined by the observer and the direction
                   vector. If the ray intersects the target body in
                   multiple points, the selected intersection point is
                   the one closest to the observer. The output argument
                   `found' (see below) indicates whether an intercept was
                   found.

                   `spoint' is expressed in Cartesian coordinates,
                   relative to the target body-fixed frame designated by
                   `fixref'. The body-fixed target frame is evaluated at
                   the intercept epoch `trgepc' (see description below).

                   When light time correction is used, the duration of
                   light travel between `spoint' to the observer is
                   considered to be the one way light time. When both light
                   time and stellar aberration corrections are used,
                   `spoint' is computed such that, when the vector from the
                   observer to `spoint' is corrected for light time and
                   stellar aberration, the resulting vector lies on the ray
                   defined by the observer's location and `dvec'.

                   The components of `spoint' are given in units of km.

       trgepc      is the "intercept epoch." `trgepc' is defined as
                   follows: letting `lt' be the one-way light time between
                   the observer and the intercept point, `trgepc' is the
                   epoch et-lt, et+lt, or `et' depending on whether the
                   requested aberration correction is, respectively, for
                   received radiation, transmitted radiation, or
                   omitted. `lt' is computed using the method indicated by
                   `abcorr'.

                   `trgepc' is expressed as TDB seconds past J2000 TDB.

       srfvec      is the vector from the observer's position at `et' to
                   the aberration-corrected (or optionally, geometric)
                   position of `spoint', where the aberration corrections
                   are specified by `abcorr'. `srfvec' is expressed in the
                   target body-fixed reference frame designated by
                   `fixref', evaluated at `trgepc'.

                   The components of `srfvec' are given in units of km.

                   One can use the CSPICE function vnorm_c to obtain the
                   distance between the observer and `spoint':

                      dist = vnorm_c ( srfvec );

                   The observer's position `obspos', relative to the
                   target body's center, where the center's position is
                   corrected for aberration effects as indicated by
                   `abcorr', can be computed via the call:

                      vsub_c ( spoint, srfvec, obspos );

                   To transform the vector `srfvec' from a reference frame
                   `fixref' at time `trgepc' to a time-dependent reference
                   frame `ref' at time `et', the routine pxfrm2_c should be
                   called. Let `xform' be the 3x3 matrix representing the
                   rotation from the reference frame `fixref' at time
                   `trgepc' to the reference frame `ref' at time `et'. Then
                   `srfvec' can be transformed to the result `refvec' as
                   follows:

                       pxfrm2_c ( fixref, ref,    trgepc, et, xform );
                       mxv_c    ( xform,  srfvec, refvec );

                   The second example in the -Examples header section
                   below presents a complete program that demonstrates
                   this procedure.

       found       is a logical flag indicating whether or not the ray
                   intersects the target. If an intersection exists `found'
                   will be returned as SPICETRUE. If the ray misses the
                   target, `found' will be returned as SPICEFALSE.
#### 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' cannot be parsed, an error
           is signaled by either this routine or a routine in the
           call tree of this routine.

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

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

       9)  If the computation method specifies an ellipsoidal target
           shape and triaxial radii of the target body have not been
           loaded into the kernel pool prior to calling sincpt_c, an error
           is signaled by a routine in the call tree of this routine.

       10) The target must be an extended body: 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.

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

       12) If the reference frame designated by `dref' is not recognized
           by the SPICE frame subsystem, the error SPICE(NOFRAME)
           is signaled by a routine in the call tree of this routine.

       13) If the direction vector `dvec' is the zero vector, the error
           SPICE(ZEROVECTOR) 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 `method' specifies that the target surface is represented
           by DSK data, and DSK data are not available for a portion of
           the target body's surface, an intercept might not be found.
           This routine does not revert to using an ellipsoidal surface
           in this case.

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

       17) If any of the `method', `target', `fixref', `abcorr', `obsrvr'
           or `dref' 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. Ephemeris
          data are made available by loading one or more SPK files via
          furnsh_c.

       -  PCK data: if the computation method is specified as
          "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.

       -  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.

       The following data may be required:

       -  DSK data: if `method' indicates that DSK data are to be used,
          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.

       -  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 assignments is

             NAIF_SURFACE_NAME += 'Mars MEGDR 128 PIXEL/DEG'
             NAIF_SURFACE_CODE += 1
             NAIF_SURFACE_BODY += 499

       -  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. Similarly, the frame definition required to map
          between the frame designated by `dref' and the target
          body-fixed frame must be available. Typically the
          definitions of frames not already built-in to SPICE are
          supplied by loading a frame kernel.

       -  CK data: if the frame to which `dref' refers is fixed to a
          spacecraft instrument or structure, at least one CK file
          will be needed to permit transformation of vectors between
          that frame and both the J2000 and the target body-fixed
          frames.

       -  SCLK data: if a CK file is needed, an associated SCLK
          kernel is required to enable conversion between encoded SCLK
          (used to time-tag CK data) and barycentric dynamical time
          (TDB).

       In all cases, kernel data are normally loaded once per program
       run, NOT every time this routine is called.
#### Particulars
       Given a ray defined by a direction vector and the location of an
       observer, sincpt_c computes the surface intercept point of the ray
       on a specified target body. sincpt_c also determines the vector
       from the observer to the surface intercept point. If the ray
       intersects the target in multiple locations, the intercept
       closest to the observer is selected.

       When aberration corrections are used, this routine finds the
       value of `spoint' such that, if `spoint' is regarded as an ephemeris
       object, after the selected aberration corrections are applied to
       the vector from the observer to `spoint', the resulting vector is
       parallel to the direction vector `dvec'.

       This routine computes light time corrections using light time
       between the observer and the surface intercept point, as opposed
       to the center of the target. Similarly, stellar aberration
       corrections done by this routine are based on the direction of
       the vector from the observer to the light-time corrected
       intercept point, not to the target center. This technique avoids
       errors due to the differential between aberration corrections
       across the target body. Therefore it's valid to use aberration
       corrections with this routine even when the observer is very
       close to the intercept point, in particular when the
       observer-intercept point distance is much less than the
       observer-target center distance. It's also valid to use stellar
       aberration corrections even when the intercept point is near or
       on the limb (as may occur in occultation computations using a
       point target).

       When comparing surface intercept point computations with results
       from sources other than SPICE, it's essential to make sure the
       same geometric definitions are used.

       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 a set 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

             "DSK/<surface list>/UNPRIORITIZED"
             "DSK/UNPRIORITIZED/<surface list>"
             "UNPRIORITIZED/<surface list>/DSK"

          The simplest form of the `method' argument specifying use of
          DSK data is one that lacks a surface list, for example:

             "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 string suffices. 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\""

          Escaped 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

             "DSK/UNPRIORITIZED/SURFACES = \"Mars MEGDR 64 PIXEL/DEG\", 3"

          Round-off errors and mitigating algorithms
          ------------------------------------------

          When topographic data are used to represent the surface of a
          target body, round-off errors can produce some results that
          may seem surprising.

          Note that, since the surface in question might have mountains,
          valleys, and cliffs, the points of intersection found for
          nearly identical sets of inputs may be quite far apart from
          each other: for example, a ray that hits a mountain side in a
          nearly tangent fashion may, on a different host computer, be
          found to miss the mountain and hit a valley floor much farther
          from the observer, or even miss the target altogether.

          Round-off errors can affect segment selection: for example, a
          ray that is expected to intersect the target body's surface
          near the boundary between two segments might hit either
          segment, or neither of them; the result may be
          platform-dependent.

          A similar situation exists when a surface is modeled by a set
          of triangular plates, and the ray is expected to intersect the
          surface near a plate boundary.

          To avoid having the routine fail to find an intersection when
          one clearly should exist, this routine uses two "greedy"
          algorithms:

             1) If the ray passes sufficiently close to any of the
                boundary surfaces of a segment (for example, surfaces of
                maximum and minimum longitude or latitude), that segment
                is tested for an intersection of the ray with the
                surface represented by the segment's data.

                This choice prevents all of the segments from being
                missed when at least one should be hit, but it could, on
                rare occasions, cause an intersection to be found in a
                segment other than the one that would be found if higher
                precision arithmetic were used.

             2) For type 2 segments, which represent surfaces as
                sets of triangular plates, each plate is expanded very
                slightly before a ray-plate intersection test is
                performed. The default plate expansion factor is

                   1 + 1.e-10

                In other words, the sides of the plate are lengthened by
                1/10 of a micron per km. The expansion keeps the centroid
                of the plate fixed.

                Plate expansion prevents all plates from being missed
                in cases where clearly at least one should be hit.

                As with the greedy segment selection algorithm, plate
                expansion can occasionally cause an intercept to be
                found on a different plate than would be found if higher
                precision arithmetic were used. It also can occasionally
                cause an intersection to be found when the ray misses
                the target by a very small distance.

          Aberration corrections
          ----------------------

          For irregularly shaped target bodies, the distance between the
          observer and the nearest surface intercept need not be a
          continuous function of time; hence the one-way light time
          between the intercept and the observer may be discontinuous as
          well. In such cases, the computed light time, which is found
          using an iterative algorithm, may converge slowly or not at all.
          In all cases, the light time computation will terminate, but
          the result may be less accurate than expected.
#### 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) The following program computes surface intercept points on Mars
          for the boresight and FOV boundary vectors of the MGS MOC
          narrow angle camera. The intercepts are computed for a single
          observation epoch. Converged Newtonian light time and stellar
          aberration corrections are used. For simplicity, camera
          distortion is ignored.

          Intercepts are computed using both triaxial ellipsoid and
          topographic surface models.

          The topographic model is based on data from the MGS MOLA DEM
          megr90n000cb, which has a resolution of 4 pixels/degree. A
          triangular plate model was produced by computing a 720 x 1440
          grid of interpolated heights from this DEM, then tessellating
          the height grid. The plate model is stored in a type 2 segment
          in the referenced DSK file.

          Use the meta-kernel shown below to load the required SPICE
          kernels.

             KPL/MK

             File: sincpt_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
                mgs_moc_v20.ti                   MGS MOC instrument
                                                 parameters
                mgs_sclkscet_00061.tsc           MGS SCLK coefficients
                mgs_sc_ext12.bc                  MGS s/c bus attitude
                mgs_ext12_ipng_mgs95j.bsp        MGS ephemeris
                megr90n000cb_plate.bds           Plate model based on
                                                 MEGDR DEM, resolution
                                                 4 pixels/degree.

             \begindata

                KERNELS_TO_LOAD = ( 'de430.bsp',
                                    'mar097.bsp',
                                    'pck00010.tpc',
                                    'naif0011.tls',
                                    'mgs_moc_v20.ti',
                                    'mgs_sclkscet_00061.tsc',
                                    'mgs_sc_ext12.bc',
                                    'mgs_ext12_ipng_mgs95j.bsp',
                                    'megr90n000cb_plate.bds'      )
             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program sincpt_ex1
          ./
          #include <stdio.h>
          #include <string.h>
          #include "SpiceUsr.h"
          #include "SpiceZmc.h"

          int main()
          {
             /.
             Local parameters
             ./
             #define META                "sincpt_ex1.tm"
             #define ABCLEN              20
             #define LNSIZE              81
             #define NAMLEN              33
             #define TIMLEN              51
             #define SHPLEN              81
             #define NCORNR               4
             #define NMETH                2

             /.
             Local variables
             ./
             SpiceBoolean            found;

             SpiceChar             * abcorr          = "CN+S";
             SpiceChar             * camera          = "MGS_MOC_NA";
             SpiceChar               dref    [NAMLEN];
             SpiceChar             * fixref          = "IAU_MARS";
             SpiceChar             * methds  [NMETH] =
                                   {
                                      "Ellipsoid",
                                      "DSK/UNPRIORITIZED"
                                   };

             SpiceChar             * obsrvr  = "MGS";
             SpiceChar               shape   [SHPLEN];

             SpiceChar             * srftyp  [NMETH] =
                                   {
                                     "Ellipsoid",
                                     "MGS/MOLA topography, 4 pixel/deg"
                                   };

             SpiceChar             * target  = "Mars";
             SpiceChar               title   [LNSIZE];

             SpiceChar             * utc     = "2003 OCT 13 06:00:00 UTC";

             SpiceDouble             bounds  [NCORNR][3];
             SpiceDouble             bsight  [3];
             SpiceDouble             dist;
             SpiceDouble             dvec    [3];
             SpiceDouble             et;
             SpiceDouble             lat;
             SpiceDouble             lon;
             SpiceDouble             radius;
             SpiceDouble             spoint [3];
             SpiceDouble             srfvec [3];
             SpiceDouble             trgepc;

             SpiceInt                camid;
             SpiceInt                i;
             SpiceInt                k;
             SpiceInt                n;

             /.
             Load kernel files:
             ./
             furnsh_c ( META );

             /.
             Convert the UTC request time to ET (seconds past
             J2000, TDB).
             ./
             str2et_c ( utc, &et );

             /.
             Get the MGS MOC Narrow angle camera (MGS_MOC_NA)
             ID code. Then look up the field of view (FOV)
             parameters.
             ./
             bodn2c_c ( camera, &camid, &found );

             if ( !found )
             {
                 setmsg_c ( "Could not find ID code for "
                            "instrument #."               );
                 errch_c  ( "#", camera                   );
                 sigerr_c ( "SPICE(NOTRANSLATION)"        );
             }

             /.
             getfov_c will return the name of the camera-fixed frame
             in the string `dref', the camera boresight vector in
             the array `bsight', and the FOV corner vectors in the
             array `bounds'.
             ./
             getfov_c ( camid, NCORNR, SHPLEN, NAMLEN,
                        shape, dref,   bsight, &n,     bounds );

             printf ( "\n"
                      "Surface Intercept Locations for Camera\n"
                      "FOV Boundary and Boresight Vectors\n"
                      "\n"
                      "   Instrument:             %s\n"
                      "   Epoch:                  %s\n"
                      "   Aberration correction:  %s\n",
                      camera, utc, abcorr                             );

             /.
             Now compute and display the surface intercepts for the
             boresight and all of the FOV boundary vectors.
             ./

             for ( i = 0;  i <= NCORNR;  i++ )
             {
                if ( i < NCORNR )
                {
                   sprintf ( title, "Corner vector %d", (int)(i+1) );

                   vequ_c ( bounds[i], dvec );
                }
                else
                {
                   strcpy ( title,  "Boresight vector" );

                   vequ_c ( bsight, dvec );
                }

                printf ( "\n"
                         "%s\n", title );

                sprintf ( title, "  Vector in %s frame = ", dref );

                printf ( "\n"
                         "%s\n", title );

                if ( i < NCORNR )
                {
                    printf ( "   %18.10e %18.10e %18.10e\n",
                             bounds[i][0], bounds[i][1], bounds[i][2] );
                }
                else
                {
                   printf ( "   %18.10e %18.10e %18.10e\n",
                            bsight[0],    bsight[1],    bsight[2]    );
                }

                printf ( "\n"
                         "  Intercept:\n" );

                /.
                Compute the surface intercept point using
                the specified aberration corrections. Loop
                over the set of computation methods.
                ./
                for ( k = 0;  k < NMETH;  k++ )
                {

                   sincpt_c ( methds[k],
                              target,  et,     fixref, abcorr,
                              obsrvr,  dref,   dvec,   spoint,
                              &trgepc, srfvec, &found         );

                   if ( found )
                   {
                      /.
                      Compute range from observer to apparent intercept.
                      ./
                      dist = vnorm_c( srfvec );

                      /.
                      Convert rectangular coordinates to planetocentric
                      latitude and longitude. Convert radians to degrees.
                      ./
                      reclat_c ( spoint, &radius, &lon, &lat );

                      lon *= dpr_c ();
                      lat *= dpr_c ();

                      /.
                      Display the results.
                      ./
                      printf ( "\n"
                               "    Surface representation: %s\n"
                               "\n"
                               "     Radius                   (km)  = %18.10f\n"
                               "     Planetocentric Latitude  (deg) = %18.10f\n"
                               "     Planetocentric Longitude (deg) = %18.10f\n"
                               "     Range                    (km)  = %18.10f\n",
                               srftyp[k], radius,  lat,  lon,  dist            );
                   }
                   else
                   {
                       printf ( "\n"
                                "Intercept not found.\n"
                                "\n"                     );
                   }
                }
             }
             return ( 0 );
          }

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

          Surface Intercept Locations for Camera
          FOV Boundary and Boresight Vectors

             Instrument:             MGS_MOC_NA
             Epoch:                  2003 OCT 13 06:00:00 UTC
             Aberration correction:  CN+S

          Corner vector 1

            Vector in MGS_MOC_NA frame =
               1.8571383810e-06  -3.8015622659e-03   9.9999277403e-01

            Intercept:

              Surface representation: Ellipsoid

               Radius                   (km)  =    3384.9411357607
               Planetocentric Latitude  (deg) =     -48.4774823672
               Planetocentric Longitude (deg) =    -123.4740748197
               Range                    (km)  =     388.9830822570

              Surface representation: MGS/MOLA topography, 4 pixel/deg

               Radius                   (km)  =    3387.6408267726
               Planetocentric Latitude  (deg) =     -48.4922595600
               Planetocentric Longitude (deg) =    -123.4754119350
               Range                    (km)  =     386.1451004041

          Corner vector 2

            Vector in MGS_MOC_NA frame =
               1.8571383810e-06   3.8015622659e-03   9.9999277403e-01

            Intercept:

              Surface representation: Ellipsoid

               Radius                   (km)  =    3384.9396985743
               Planetocentric Latitude  (deg) =     -48.4816367789
               Planetocentric Longitude (deg) =    -123.3988187487
               Range                    (km)  =     388.9751000527

              Surface representation: MGS/MOLA topography, 4 pixel/deg

               Radius                   (km)  =    3387.6403704508
               Planetocentric Latitude  (deg) =     -48.4963866889
               Planetocentric Longitude (deg) =    -123.4007435481
               Range                    (km)  =     386.1361644332

          Corner vector 3

            Vector in MGS_MOC_NA frame =
              -1.8571383810e-06   3.8015622659e-03   9.9999277403e-01

            Intercept:

              Surface representation: Ellipsoid

               Radius                   (km)  =    3384.9396897287
               Planetocentric Latitude  (deg) =     -48.4816623489
               Planetocentric Longitude (deg) =    -123.3988219550
               Range                    (km)  =     388.9746411355

              Surface representation: MGS/MOLA topography, 4 pixel/deg

               Radius                   (km)  =    3387.6403603146
               Planetocentric Latitude  (deg) =     -48.4964120424
               Planetocentric Longitude (deg) =    -123.4007467292
               Range                    (km)  =     386.1357106985

          Corner vector 4

            Vector in MGS_MOC_NA frame =
              -1.8571383810e-06  -3.8015622659e-03   9.9999277403e-01

            Intercept:

              Surface representation: Ellipsoid

               Radius                   (km)  =    3384.9411269138
               Planetocentric Latitude  (deg) =     -48.4775079405
               Planetocentric Longitude (deg) =    -123.4740779752
               Range                    (km)  =     388.9826233195

              Surface representation: MGS/MOLA topography, 4 pixel/deg

               Radius                   (km)  =    3387.6408166345
               Planetocentric Latitude  (deg) =     -48.4922849169
               Planetocentric Longitude (deg) =    -123.4754150656
               Range                    (km)  =     386.1446466486

          Boresight vector

            Vector in MGS_MOC_NA frame =
               0.0000000000e+00   0.0000000000e+00   1.0000000000e+00

            Intercept:

              Surface representation: Ellipsoid

          [...]

          Warning: incomplete output. Only 100 out of 112 lines have been
          provided.

       2) Use sincpt_c to perform a consistency check on a sub-observer
          point computation.

          Use subpnt_c to find the sub-spacecraft point on Mars for the
          Mars Reconnaissance Orbiter spacecraft (MRO) at a specified time,
          using both the 'Ellipsoid/Near point' computation method and an
          ellipsoidal target shape, and the "DSK/Unprioritized/Nadir"
          method and a DSK-based shape model.

          Use both LT+S and CN+S aberration corrections to illustrate
          the differences.

          Convert the spacecraft to sub-observer point vector obtained from
          subpnt_c into the MRO_HIRISE_LOOK_DIRECTION reference frame at
          the observation time. Perform a consistency check with this
          vector: compare the Mars surface intercept of the ray emanating
          from the spacecraft and pointed along this vector with the
          sub-observer point.

          Perform the sub-observer point and surface intercept computations
          using both triaxial ellipsoid and topographic surface models.

          For this example, the topographic model is based on the MGS MOLA
          DEM megr90n000eb, which has a resolution of 16 pixels/degree.
          Eight DSKs, each covering longitude and latitude ranges of 90
          degrees, were made from this data set. For the region covered by
          a given DSK, a grid of approximately 1500 x 1500 interpolated
          heights was produced, and this grid was tessellated using
          approximately 4.5 million triangular plates, giving a total plate
          count of about 36 million for the entire DSK set.

          All DSKs in the set use the surface ID code 499001, so there is
          no need to specify the surface ID in the `method' strings passed
          to sincpt_c and subpnt_c.

          Use the meta-kernel shown below to load the required SPICE
          kernels.

             KPL/MK

             File name: sincpt_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
                mro_psp4_ssd_mro95a.bsp          MRO ephemeris
                mro_v11.tf                       MRO frame specifications
                mro_sclkscet_00022_65536.tsc     MRO SCLK coefficients
                                                 parameters
                mro_sc_psp_070925_071001.bc      MRO attitude
                megr90n000eb_*_plate.bds         Plate model DSKs based
                                                 on MEGDR DEM, resolution
                                                 16 pixels/degree.

             \begindata

                KERNELS_TO_LOAD = (

                   'de430.bsp',
                   'mar097.bsp',
                   'pck00010.tpc',
                   'naif0011.tls',
                   'mro_psp4_ssd_mro95a.bsp',
                   'mro_v11.tf',
                   'mro_sclkscet_00022_65536.tsc',
                   'mro_sc_psp_070925_071001.bc',
                   'megr90n000eb_LL000E00N_UR090E90N_plate.bds'
                   'megr90n000eb_LL000E90S_UR090E00S_plate.bds'
                   'megr90n000eb_LL090E00N_UR180E90N_plate.bds'
                   'megr90n000eb_LL090E90S_UR180E00S_plate.bds'
                   'megr90n000eb_LL180E00N_UR270E90N_plate.bds'
                   'megr90n000eb_LL180E90S_UR270E00S_plate.bds'
                   'megr90n000eb_LL270E00N_UR360E90N_plate.bds'
                   'megr90n000eb_LL270E90S_UR360E00S_plate.bds'  )

             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program sincpt_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main()
          {
             /.
             Local constants
             ./
             #define META            "sincpt_ex2.tm"
             #define NCORR           2
             #define NMETH           2

             /.
             Local variables
             ./
             SpiceBoolean            found;

             static SpiceChar      * abcorr[NCORR] =
                                     {
                                        "LT+S", "CN+S"
                                     };

             static SpiceChar      * fixref = "IAU_MARS";

             static SpiceChar      * sinmth[NMETH] =
                                     {
                                        "Ellipsoid",
                                        "DSK/Unprioritized"
                                     };

             static SpiceChar      * submth[NMETH] =
                                     {
                                        "Ellipsoid/Near point",
                                        "DSK/Unprioritized/Nadir"
                                     };

             static SpiceChar      * hiref;

             SpiceDouble             alt;
             SpiceDouble             et;
             SpiceDouble             lat;
             SpiceDouble             lon;
             SpiceDouble             mrovec [3];
             SpiceDouble             radius;
             SpiceDouble             spoint [3];
             SpiceDouble             srfvec [3];
             SpiceDouble             trgepc;
             SpiceDouble             xepoch;
             SpiceDouble             xform  [3][3];
             SpiceDouble             xpoint [3];
             SpiceDouble             xvec   [3];

             SpiceInt                i;
             SpiceInt                j;

             /.
             Load kernel files via the meta-kernel.
             ./
             furnsh_c ( META );

             /.
             Convert the TDB request time string to seconds past
             J2000, TDB.
             ./
             str2et_c ( "2007 SEP 30 00:00:00 TDB", &et );

             /.
             Compute the sub-spacecraft point using each method.
             Compute the results using both LT+S and CN+S aberration
             corrections.
             ./
             for ( i = 0;  i < NMETH;  i++ )
             {

                printf ( "\nSub-observer point computation "
                         "method = %s\n",  submth[i] );

                for ( j = 0;  j < NCORR;  j++ )
                {
                   subpnt_c ( submth[i],
                              "mars", et,     fixref,  abcorr[j],
                              "mro",  spoint, &trgepc, srfvec    );

                   /.
                   Compute the observer's altitude above `spoint'.
                   ./
                   alt = vnorm_c ( srfvec );

                   /.
                   Express `srfvec' in the MRO_HIRISE_LOOK_DIRECTION
                   reference frame at epoch `et'. Since `srfvec' is expressed
                   relative to the IAU_MARS frame at `trgepc', we must
                   call pxfrm2_c to compute the position transformation matrix
                   from IAU_MARS at `trgepc' to the MRO_HIRISE_LOOK_DIRECTION
                   frame at time `et'.

                   To make code formatting a little easier, we'll store
                   the long MRO reference frame name in a variable:
                   ./
                   hiref = "MRO_HIRISE_LOOK_DIRECTION";

                   pxfrm2_c ( "iau_mars", hiref,  trgepc, et, xform );
                   mxv_c    (  xform,     srfvec, mrovec            );

                   /.
                   Convert sub-observer point rectangular coordinates to
                   planetocentric latitude and longitude. Convert radians to
                   degrees.
                   ./
                   reclat_c ( spoint, &radius, &lon, &lat );

                   lon *= dpr_c();
                   lat *= dpr_c();

                   /.
                   Write the results.
                   ./
                   printf ( "\n"
                            "   Aberration correction = %s\n\n"
                            "      MRO-to-sub-observer vector in\n"
                            "      MRO HIRISE look direction frame\n"
                            "         X-component             (km) = %21.9f\n"
                            "         Y-component             (km) = %21.9f\n"
                            "         Z-component             (km) = %21.9f\n"
                            "      Sub-observer point radius  (km) = %21.9f\n"
                            "      Planetocentric latitude   (deg) = %21.9f\n"
                            "      Planetocentric longitude  (deg) = %21.9f\n"
                            "      Observer altitude          (km) = %21.9f\n",
                            abcorr[j],
                            mrovec[0],
                            mrovec[1],
                            mrovec[2],
                            radius,
                            lat,
                            lon,
                            alt         );

                   /.
                   Consistency check: find the surface intercept on
                   Mars of the ray emanating from the spacecraft and having
                   direction vector `mrovec' in the MRO HIRISE look direction
                   reference frame at `et'. Call the intercept point
                   `xpoint'. `xpoint' should coincide with `spoint', up to a
                   small round-off error.
                   ./
                   sincpt_c ( sinmth[i], "mars",  et,    "iau_mars",
                              abcorr[j], "mro",   hiref, mrovec,
                              xpoint,    &xepoch, xvec,  &found     );

                   if ( !found )
                   {
                      printf ( "Bug: no intercept\n" );
                   }
                   else
                   {
                      /.
                      Report the distance between `xpoint' and `spoint'.
                      ./
                      printf ( "      Intercept comparison error (km) = "
                               "%21.9f\n\n",
                               vdist_c( xpoint, spoint )                  );
                   }
                }
             }
             return ( 0 );
          }

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

          Sub-observer point computation method = Ellipsoid/Near point

             Aberration correction = LT+S

                MRO-to-sub-observer vector in
                MRO HIRISE look direction frame
                   X-component             (km) =           0.286933229
                   Y-component             (km) =          -0.260425939
                   Z-component             (km) =         253.816326385
                Sub-observer point radius  (km) =        3388.299078378
                Planetocentric latitude   (deg) =         -38.799836378
                Planetocentric longitude  (deg) =        -114.995297227
                Observer altitude          (km) =         253.816622175
                Intercept comparison error (km) =           0.000002144

             Aberration correction = CN+S

                MRO-to-sub-observer vector in
                MRO HIRISE look direction frame
                   X-component             (km) =           0.286933107
                   Y-component             (km) =          -0.260426683
                   Z-component             (km) =         253.816315915
                Sub-observer point radius  (km) =        3388.299078376
                Planetocentric latitude   (deg) =         -38.799836382
                Planetocentric longitude  (deg) =        -114.995297449
                Observer altitude          (km) =         253.816611705
                Intercept comparison error (km) =           0.000000001

          Sub-observer point computation method = DSK/Unprioritized/Nadir

             Aberration correction = LT+S

                MRO-to-sub-observer vector in
                MRO HIRISE look direction frame
                   X-component             (km) =           0.282372596
                   Y-component             (km) =          -0.256289313
                   Z-component             (km) =         249.784871247
                Sub-observer point radius  (km) =        3392.330239436
                Planetocentric latitude   (deg) =         -38.800230156
                Planetocentric longitude  (deg) =        -114.995297338
                Observer altitude          (km) =         249.785162334
                Intercept comparison error (km) =           0.000002412

             Aberration correction = CN+S

                MRO-to-sub-observer vector in
                MRO HIRISE look direction frame
                   X-component             (km) =           0.282372464
                   Y-component             (km) =          -0.256290075
                   Z-component             (km) =         249.784860121
                Sub-observer point radius  (km) =        3392.330239564
                Planetocentric latitude   (deg) =         -38.800230162
                Planetocentric longitude  (deg) =        -114.995297569
                Observer altitude          (km) =         249.785151209
                Intercept comparison error (km) =           0.000000001
#### Restrictions
       1)  A cautionary note: if aberration corrections are used, and
           if `dref' is the target body-fixed frame, the epoch at which
           that frame is evaluated is offset from `et' by the light time
           between the observer and the *center* of the target body.
           This light time normally will differ from the light time
           between the observer and intercept point. Consequently the
           orientation of the target body-fixed frame at `trgepc' will
           not match that of the target body-fixed frame at the epoch
           associated with `dref'. As a result, various derived quantities
           may not be as expected: for example, `srfvec' would not be
           parallel to `dvec'.

           In many applications the errors arising from this frame
           discrepancy may be insignificant; however a safe approach is
           to always use as `dref' a frame other than the target
           body-fixed frame.

       2)  This routine must not be used for cases where the observer
           is inside the target body. This routine does not attempt to
           detect this condition.

           If the observer is a point on a target surface described
           by DSK data, care must be taken to ensure the observer is
           sufficiently far outside the target. The routine should
           not be used for surfaces for which "outside" cannot be
           defined.
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       S.C. Krening        (JPL)
       B.V. Semenov        (JPL)
#### Version
       -CSPICE Version 2.0.1, 01-NOV-2021 (JDR) (NJB)

           Edited the header to comply with NAIF standard.

           Updated -Detailed_Input and -Restrictions sections to state that
           the observer must be outside the target body.

       -CSPICE Version 2.0.0, 05-APR-2017 (NJB) (SCK) (BVS)

           Updated to support use of DSKs.

       -CSPICE Version 1.0.2, 02-APR-2011 (NJB) (SCK)

           References to the new pxfrm2_c routine were added, which
           changed the Detailed Output section and the second example.

           Miscellaneous, minor header comment corrections were made.

       -CSPICE Version 1.0.1, 06-FEB-2009 (NJB)

           Typos in the Detailed Input section's description of `dref'
           were corrected. Incorrect frame name fixfrm was changed to
           fixref in documentation.

           In the header examples, meta-kernel names were updated to use
           the suffix

              ".tm"

       -CSPICE Version 1.0.0, 02-MAR-2008 (NJB)
#### Index_Entries
       find surface intercept point
       find intersection of ray and target body surface
       find intercept of ray on target body surface
#### Link to routine sincpt_c source file sincpt_c.c

    Fri Dec 31 18:41:12 2021