Index of Functions: A B C D E F G H I J K L M N O P Q R S T U V W X
Index Page subpnt_c
Table of contents
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
       subpnt_c ( Sub-observer point )

       void subpnt_c ( ConstSpiceChar       * method,
                       ConstSpiceChar       * target,
                       SpiceDouble            et,
                       ConstSpiceChar       * fixref,
                       ConstSpiceChar       * abcorr,
                       ConstSpiceChar       * obsrvr,
                       SpiceDouble            spoint [3],
                       SpiceDouble          * trgepc,
                       SpiceDouble            srfvec [3] )
#### Abstract
       Compute the rectangular coordinates of the sub-observer point 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 subpt_c.
#### Required_Reading
       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 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.
       spoint     O   Sub-observer point on the target body.
       trgepc     O   Sub-observer point epoch.
       srfvec     O   Vector from observer to sub-observer point.
#### 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:

                      "NEAR POINT/ELLIPSOID"

                         The sub-observer point computation uses a
                         triaxial ellipsoid to model the surface of the
                         target body. The sub-observer point is defined
                         as the nearest point on the target relative to
                         the observer.

                         The word "NADIR" may be substituted for the phrase
                         "NEAR POINT" in the string above.

                         For backwards compatibility, the older syntax

                            "Near point: ellipsoid"

                         is accepted as well.

                      "INTERCEPT/ELLIPSOID"

                         The sub-observer point computation uses a
                         triaxial ellipsoid to model the surface of the
                         target body. The sub-observer point is defined
                         as the target surface intercept of the line
                         containing the observer and the target's
                         center.

                         For backwards compatibility, the older syntax

                            "Intercept: ellipsoid"

                         is accepted as well.

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

                         The sub-observer point computation uses DSK data
                         to model the surface of the target body. The
                         sub-observer point is defined as the intercept, on
                         the surface represented by the DSK data, of the
                         line containing the observer and the nearest point
                         on the target's reference ellipsoid. If multiple
                         such intercepts exist, the one closest to the
                         observer is selected.

                         Note that this definition of the sub-observer
                         point is not equivalent to the "nearest point on
                         the surface to the observer." The phrase "NEAR
                         POINT" may NOT be substituted for "NADIR" in the
                         string above.

                         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.

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

                         The sub-observer point computation uses DSK data
                         to model the surface of the target body. The
                         sub-observer point is defined as the target
                         surface intercept of the line containing the
                         observer and the target's center.

                         If multiple such intercepts exist, the one closest
                         to the observer is selected.

                         The surface list specification is optional. The
                         syntax of the list is identical to that for the
                         NADIR option described above.

                      Neither case nor white space are significant in
                      `method', except within double-quoted strings. For
                      example, the string " eLLipsoid/nearpoint " 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 ephemeris object (its trajectory is given by
                   SPK data), and is an extended 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 or et+lt, where `lt' is the one-way light time
                   between the sub-observer 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 sub-observer point `spoint' and the
                   observer-to-sub-observer point 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
                   sub-observer point seen by the observer is desired,
                   normally either of the corrections

                      "LT+S"
                      "CN+S"

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

                      "NONE"     Apply no correction. Return the
                                 geometric sub-observer point on the
                                 target body.

                   Let `lt' represent the one-way light time between the
                   observer and the sub-observer 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
                   sub-observer 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 sub-observer
                                 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
                                 sub-observer point obtained with the
                                 "LT" option to account for the
                                 observer's velocity relative to the
                                 solar system barycenter. These
                                 corrections yield the apparent
                                 sub-observer 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.

                   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
                   sub-observer 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
                                 sub-observer 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
                                 "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.

                      "XLT+S"    "Transmission" case: correct for
                                 one-way light time and stellar
                                 aberration using a Newtonian
                                 formulation  This option modifies the
                                 sub-observer point 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.

                   Neither case nor white space are significant in
                   `abcorr'. For example, the string

                     "Lt + s"

                   is valid.

       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.
#### Detailed_Output
       spoint      is the sub-observer point on the target body.

                   For target shapes modeled by ellipsoids, the
                   sub-observer point is defined either as the point on
                   the target body that is closest to the observer, or
                   the target surface intercept of the line from the
                   observer to the target's center.

                   For target shapes modeled by topographic data
                   provided by DSK files, the sub-observer point is
                   defined as the target surface intercept of the line
                   from the observer to either the nearest point on the
                   reference ellipsoid, or to the target's center. If
                   multiple such intercepts exist, the one closest to
                   the observer is selected.

                   The input argument `method' selects the target shape
                   model and sub-observer point definition to be used.

                   `spoint' is expressed in Cartesian coordinates,
                   relative to the body-fixed target frame designated by
                   `fixref'. The body-fixed target frame is evaluated at
                   the sub-observer 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 aberration corrections are used, `spoint' is
                   computed using target body position and orientation
                   that have been adjusted for the corrections
                   applicable to `spoint' itself rather than to the target
                   body's center. In particular, if the stellar
                   aberration correction applicable to `spoint' is
                   represented by a shift vector S, then the light-time
                   corrected position of the target is shifted by S
                   before the sub-observer point is computed.

                   The components of `spoint' have units of km.

       trgepc      is the "sub-observer point epoch." `trgepc' is defined
                   as follows: letting `lt' be the one-way light time
                   between the observer and the sub-observer 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 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.
#### 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 this routine, or, the
           error is signaled by a routine in the call tree of this
           routine.

       7)  If the sub-observer point type is not specified or is not
           recognized, the error SPICE(INVALIDSUBTYPE) 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 (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.

       9)  If insufficient ephemeris data have been loaded prior to
           calling subpnt_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.

       10) 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 subpnt_c, an error
           is signaled by a routine in the call tree of this routine.

       11) The target must be an extended body, and must have a shape
           for which a sub-observer point can be defined.

           If the target body's shape is modeled by DSK data, the shape
           must be such that the specified sub-observer point
           definition is applicable. For example, if the target shape
           is a torus, both the NADIR and INTERCEPT definitions might
           be inapplicable, depending on the relative locations of the
           observer and target.

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

       13) If `method' specifies that the target surface is represented by
           DSK data, and no DSK files are loaded for the specified
           target, 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 the ray from the observer to the sub-observer
           point doesn't intersect the target body's surface, the error
           SPICE(SUBPOINTNOTFOUND) is signaled by a routine in the call
           tree of this routine.

       15) If the surface intercept on the target body's reference
           ellipsoid of the observer to target center vector cannot not
           be computed, the error SPICE(DEGENERATECASE) is signaled by a
           routine in the call tree of this routine. Note that this is a
           very rare case.

       16) If radii for `target' are not found in the kernel pool, an error
           is signaled by a routine in the call tree of this routine.

       17) If the size of the `target' body radii kernel variable is not
           three, an error is signaled by a routine in the call tree of
           this routine.

       18) If any of the three `target' body radii is less-than or equal to
           zero, an error is signaled by a routine in the call tree of
           this routine.

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

       20) If any of the `method', `target', `fixref', `abcorr' 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 the DSK NADIR method is
               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 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
       For ellipsoidal target bodies, there are two different popular
       ways to define the sub-observer point: "nearest point on the
       target to the observer" or "target surface intercept of the line
       containing observer and target." These coincide when the target
       is spherical and generally are distinct otherwise.

       For target body shapes modeled using topographic data provided by
       DSK files, the "surface intercept" notion is valid, but the
       "nearest point on the surface" computation is both inefficient to
       execute and may fail to yield a result that is "under" the
       observer in an intuitively clear way. The NADIR option for DSK
       shapes instead finds the surface intercept of a ray that passes
       through the nearest point on the target reference ellipsoid. For
       shapes modeled using topography, there may be multiple
       ray-surface intercepts; the closest one to the observer is
       selected.

       The NADIR definition makes sense only if the target shape is
       reasonably close to the target's reference ellipsoid. If the
       target is very different---the nucleus of comet
       Churyumov-Gerasimenko is an example---the intercept definition
       should be used.

       This routine computes light time corrections using light time
       between the observer and the sub-observer 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
       sub-observer 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 sub-observer point, in particular when the
       observer to sub-observer point distance is much less than the
       observer to target center distance.

       When comparing sub-observer 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 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

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

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

             "NADIR/DSK/UNPRIORITIZED"
             "INTERCEPT/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\""

          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

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

          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) Find the sub-Earth point on Mars for a specified time.

          Compute the sub-Earth points using both triaxial ellipsoid
          and topographic surface models. Topography data are provided by
          a DSK file. For the ellipsoid model, use both the "intercept"
          and "near point" sub-observer point definitions; for the DSK
          case, use both the "intercept" and "nadir" definitions.

          Display the locations of both the Earth and the sub-Earth
          point relative to the center of Mars, in the IAU_MARS
          body-fixed reference frame, using both planetocentric and
          planetographic coordinates.

          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: subpnt_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
                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',
                                    'megr90n000cb_plate.bds' )
             \begintext

             End of meta-kernel

          Example code begins here.

          /.
             Program subpnt_ex1
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main()
          {
             /.
             Local parameters
             ./
             #define META            "subpnt_ex1.tm"
             #define MTHLEN          81
             #define NMETH           4

             /.
             Local variables
             ./
             static SpiceChar      * method[NMETH] =
                                     {
                                        "Intercept/ellipsoid",
                                        "Near point/ellipsoid",
                                        "Intercept/DSK/Unprioritized",
                                        "Nadir/DSK/Unprioritized"
                                     };

             SpiceDouble             et;
             SpiceDouble             f;
             SpiceDouble             obspos [3];
             SpiceDouble             odist;
             SpiceDouble             opclat;
             SpiceDouble             opclon;
             SpiceDouble             opcrad;
             SpiceDouble             opgalt;
             SpiceDouble             opglat;
             SpiceDouble             opglon;
             SpiceDouble             radii  [3];
             SpiceDouble             re;
             SpiceDouble             rp;
             SpiceDouble             spclat;
             SpiceDouble             spclon;
             SpiceDouble             spcrad;
             SpiceDouble             spgalt;
             SpiceDouble             spglat;
             SpiceDouble             spglon;
             SpiceDouble             spoint [3];
             SpiceDouble             srfvec [3];
             SpiceDouble             trgepc;

             SpiceInt                i;
             SpiceInt                n;

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

             /.
             Convert the UTC request time string to 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 ( "MARS", "RADII", 3, &n, radii );

             /.
             Let `re and `rp' be, respectively, the equatorial and
             polar radii of the target.
             ./
             re = radii[0];
             rp = radii[2];

             f  = ( re - rp ) / re;

             /.
             Compute sub-observer point using light time and stellar
             aberration corrections. Use both ellipsoid and DSK
             shape models, and use all of the "near point,"
             "intercept," and "nadir" sub-observer point definitions.
             ./
             for ( i = 0;  i < NMETH;  i++ )
             {
                subpnt_c ( method[i],
                           "mars",  et,     "iau_mars", "cn+s",
                           "earth", spoint, &trgepc,    srfvec );
                /.
                Compute the observer's distance from `spoint'.
                ./
                odist = vnorm_c ( srfvec );

                /.
                Convert the sub-observer point's rectangular coordinates
                to planetographic longitude, latitude and altitude.
                Convert radians to degrees.
                ./
                recpgr_c ( "mars",  spoint,  re,     f,
                           &spglon, &spglat, &spgalt   );

                spglon *= dpr_c();
                spglat *= dpr_c();

                /.
                Convert sub-observer point's rectangular coordinates to
                planetocentric radius, longitude, and latitude. Convert
                radians to degrees.
                ./
                reclat_c ( spoint, &spcrad, &spclon, &spclat );

                spclon *= dpr_c();
                spclat *= dpr_c();

                /.
                Compute the observer's position relative to the center
                of the target, where the center's location has been
                adjusted using the aberration corrections applicable
                to the sub-point. Express the observer's location in
                planetographic coordinates.
                ./
                vsub_c ( spoint, srfvec, obspos );

                recpgr_c ( "mars",  obspos,  re,    f,
                           &opglon, &opglat, &opgalt   );

                opglon *= dpr_c ();
                opglat *= dpr_c ();

                /.
                Convert the observer's rectangular coordinates to
                planetocentric radius, longitude, and latitude.
                Convert radians to degrees.
                ./
                reclat_c ( obspos, &opcrad, &opclon, &opclat );

                opclon *= dpr_c();
                opclat *= dpr_c();

                /.
                Write the results.
                ./
                printf( "\n"
                        " Computation method = %s\n\n"
                        "  Observer altitude relative to spheroid (km) = %21.9f\n"
                        "  Length of SRFVEC                       (km) = %21.9f\n"
                        "  Sub-observer point altitude            (km) = %21.9f\n",
                        method[i],
                        opgalt,
                        odist,
                        spgalt  );

                printf( "  Sub-observer planetographic longitude (deg) = %21.9f\n"
                        "  Observer planetographic longitude     (deg) = %21.9f\n"
                        "  Sub-observer planetographic latitude  (deg) = %21.9f\n"
                        "  Observer planetographic latitude      (deg) = %21.9f\n",
                        spglon,
                        opglon,
                        spglat,
                        opglat  );

                printf( "  Sub-observer planetocentric longitude (deg) = %21.9f\n"
                        "  Observer planetocentric longitude     (deg) = %21.9f\n"
                        "  Sub-observer planetocentric latitude  (deg) = %21.9f\n"
                        "  Observer planetocentric latitude      (deg) = %21.9f\n"
                        "\n",
                        spclon,
                        opclon,
                        spclat,
                        opclat      );
             }
             return ( 0 );
          }

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

           Computation method = Intercept/ellipsoid

            Observer altitude relative to spheroid (km) =   349199089.540947139
            Length of SRFVEC                       (km) =   349199089.577642739
            Sub-observer point altitude            (km) =           0.000000000
            Sub-observer planetographic longitude (deg) =         199.302305029
            Observer planetographic longitude     (deg) =         199.302305029
            Sub-observer planetographic latitude  (deg) =          26.262401237
            Observer planetographic latitude      (deg) =          25.994936751
            Sub-observer planetocentric longitude (deg) =         160.697694971
            Observer planetocentric longitude     (deg) =         160.697694971
            Sub-observer planetocentric latitude  (deg) =          25.994934171
            Observer planetocentric latitude      (deg) =          25.994934171

           Computation method = Near point/ellipsoid

            Observer altitude relative to spheroid (km) =   349199089.540938556
            Length of SRFVEC                       (km) =   349199089.540938556
            Sub-observer point altitude            (km) =          -0.000000000
            Sub-observer planetographic longitude (deg) =         199.302305029
            Observer planetographic longitude     (deg) =         199.302305029
            Sub-observer planetographic latitude  (deg) =          25.994936751
            Observer planetographic latitude      (deg) =          25.994936751
            Sub-observer planetocentric longitude (deg) =         160.697694971
            Observer planetocentric longitude     (deg) =         160.697694971
            Sub-observer planetocentric latitude  (deg) =          25.729407227
            Observer planetocentric latitude      (deg) =          25.994934171

           Computation method = Intercept/DSK/Unprioritized

            Observer altitude relative to spheroid (km) =   349199089.541017234
            Length of SRFVEC                       (km) =   349199091.785406649
            Sub-observer point altitude            (km) =          -2.207669751
            Sub-observer planetographic longitude (deg) =         199.302304999
            Observer planetographic longitude     (deg) =         199.302304999
            Sub-observer planetographic latitude  (deg) =          26.262576677
            Observer planetographic latitude      (deg) =          25.994936751
            Sub-observer planetocentric longitude (deg) =         160.697695001
            Observer planetocentric longitude     (deg) =         160.697695001
            Sub-observer planetocentric latitude  (deg) =          25.994934171
            Observer planetocentric latitude      (deg) =          25.994934171

           Computation method = Nadir/DSK/Unprioritized

            Observer altitude relative to spheroid (km) =   349199089.541007638
            Length of SRFVEC                       (km) =   349199091.707172275
            Sub-observer point altitude            (km) =          -2.166164622
            Sub-observer planetographic longitude (deg) =         199.302305000
            Observer planetographic longitude     (deg) =         199.302305000
            Sub-observer planetographic latitude  (deg) =          25.994936752
            Observer planetographic latitude      (deg) =          25.994936751
            Sub-observer planetocentric longitude (deg) =         160.697695000
            Observer planetocentric longitude     (deg) =         160.697695000
            Sub-observer planetocentric latitude  (deg) =          25.729237570
            Observer planetocentric latitude      (deg) =          25.994934171

       2) 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: subpnt_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 subpnt_ex2
          ./
          #include <stdio.h>
          #include "SpiceUsr.h"

          int main()
          {
             /.
             Local constants
             ./
             #define META            "subpnt_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
       None.
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       S.C. Krening        (JPL)
#### Version
       -CSPICE Version 2.0.1, 01-NOV-2021 (JDR)

           Edited the header to comply with NAIF standard.

           Updated first example code to split printf statement in three
           in order to comply with ANSI-C maximum string literal of length.

           Added entries #16 and #17 in -Exceptions section.

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

           Fixed a few header comment typos.

           Updated to support surfaces represented by DSK data.

       -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)

           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 sub-observer point on target body
       find sub-spacecraft point on target body
       find nearest point to observer on target body
#### Link to routine subpnt_c source file subpnt_c.c

    Fri Dec 31 18:41:13 2021