Index Page termpt_c
A B C D E F G H I J K L M N O P Q R S T U V W X
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
       void termpt_c ( ConstSpiceChar      * method,
                       ConstSpiceChar      * ilusrc,
                       ConstSpiceChar      * target,
                       SpiceDouble           et,
                       ConstSpiceChar      * fixref,
                       ConstSpiceChar      * abcorr,
                       ConstSpiceChar      * corloc,
                       ConstSpiceChar      * obsrvr,
                       ConstSpiceDouble      refvec[3],
                       SpiceDouble           rolstp,
                       SpiceInt              ncuts,
                       SpiceDouble           schstp,
                       SpiceDouble           soltol,
                       SpiceInt              maxn,
                       SpiceInt              npts  [],
                       SpiceDouble           points[][3],
                       SpiceDouble           epochs[],
                       SpiceDouble           trmvcs[][3]  )
#### Abstract
       Find terminator points on a target body. The caller specifies
       half-planes, bounded by the illumination source center-target center
       vector, in which to search for terminator points.

       The terminator can be either umbral or penumbral. The umbral
       terminator is the boundary of the region on the target surface
       where no light from the source is visible. The penumbral
       terminator is the boundary of the region on the target surface
       where none of the light from the source is blocked by the target
       itself.

       The surface of the target body may be represented either by a
       triaxial ellipsoid or by topographic data.
#### Required_Reading
       CK
       DSK
       FRAMES
       NAIF_IDS
       PCK
       SPK
       TIME
#### Keywords
       DSK
       GEOMETRY
       SHADOW
       TERMINATOR
#### Brief_I/O
       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       method     I   Computation method.
       ilusrc     I   Illumination source.
       target     I   Name of target body.
       et         I   Epoch in ephemeris seconds past J2000 TDB.
       fixref     I   Body-fixed, body-centered target body frame.
       abcorr     I   Aberration correction.
       corloc     I   Aberration correction locus.
       obsrvr     I   Name of observing body.
       refvec     I   Reference vector for cutting half-planes.
       rolstp     I   Roll angular step for cutting half-planes.
       ncuts      I   Number of cutting planes.
       schstp     I   Angular step size for searching.
       soltol     I   Solution convergence tolerance.
       maxn       I   Maximum number of entries in output arrays.
       npts       O   Counts of terminator points corresponding to cuts.
       points     O   Terminator points.
       epochs     O   Times associated with terminator points.
       trmvcs     O   Terminator vectors emanating from the observer.
#### Detailed_Input
       method   is a short string providing parameters defining
                the computation method to be used. In the syntax
                descriptions below, items delimited by angle brackets
                "<>" are to be replaced by actual values. Items
                delimited by brackets "[]" are optional.

                `method' may be assigned the following values:

                   "<shadow>/<curve type>/<shape specification>"

                An example of such a string is

                   "UMBRAL/TANGENT/DSK/UNPRIORITIZED"

                In the `method' string

                   <shadow> may be either of the strings

                      "UMBRAL"    indicates the terminator is the
                                  boundary of the portion of the surface
                                  that receives no light from the
                                  illumination source. The shape of
                                  the source is modeled as a sphere.
                                  See the Particulars section below for
                                  details.

                      "PENUMBRAL" indicates the terminator is the
                                  boundary of the portion of the
                                  surface that receives all possible
                                  light from the illumination source.
                                  The shape of the source is modeled as
                                  a sphere.

                                  The penumbral terminator bounds the
                                  portion of the surface that is not
                                  subject to self-occultation of light from
                                  the illumination source. Given that the
                                  light source is modeled as a sphere, from
                                  any target surface point nearer to the
                                  source than the penumbral terminator, the
                                  source appears to be a lit disc. See the
                                  Particulars section below for details.

                   <curve type> may be either of the strings

                      "TANGENT'   for topographic (DSK) target models
                                  indicates that a terminator point is
                                  defined as the point of tangency, on
                                  the surface represented by the
                                  specified data, of a line also tangent
                                  to the illumination source.

                                  For ellipsoidal target models, a
                                  terminator point is a point of tangency
                                  of a plane that is also tangent to the
                                  illumination source. See the Particulars
                                  section below for details.

                                  Terminator points are generated within a
                                  specified set of "cutting" half-planes
                                  that have as an edge the line containing
                                  the illumination source center-target
                                  center vector. Multiple terminator points
                                  may be found within a given half-plane,
                                  if the target body shape allows for this.

                                  This is the highest-accuracy method
                                  supported by this subroutine. It
                                  generally executes much more slowly
                                  than the GUIDED method described
                                  below.

                      "GUIDED"    indicates that terminator points are
                                  "guided" so as to lie on rays emanating
                                  from the target body's center and passing
                                  through the terminator on the target
                                  body's reference ellipsoid. The
                                  terminator points are constrained to lie
                                  on the target body's surface. As with the
                                  "TANGENT" method (see above), cutting
                                  half-planes are used to generate
                                  terminator points.

                                  The GUIDED method produces a unique
                                  terminator point for each cutting
                                  half-plane. If multiple terminator
                                  point candidates lie in a given
                                  cutting half-plane, the outermost one
                                  is chosen.

                                  This method may be used only with the
                                  CENTER aberration correction locus
                                  (see the description of REFLOC below).

                                  Terminator points generated by this
                                  method are approximations; they are
                                  generally not true ray-surface tangent
                                  points. However, these approximations
                                  can be generated much more quickly
                                  than tangent points.

                   <shape specification> may be either of the strings

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

                         The DSK option indicates that terminator point
                         computation is to use topographic data provided by
                         DSK files (abbreviated as "DSK data" below) to
                         model the surface of the target body.

                         The surface list specification is optional. The
                         syntax of the list is

                            <surface 1> [, <surface 2>...]

                         If present, it indicates that data only for the
                         listed surfaces are to be used; however, data
                         need not be available for all surfaces in the
                         list. If the list is absent, loaded DSK data
                         for any surface associated with the target body
                         are used.

                         The surface list may contain surface names or
                         surface ID codes. Names containing blanks must
                         be delimited by double quotes, for example

                            "SURFACES = \"Mars MEGDR 128 PIXEL/DEG\""

                         If multiple surfaces are specified, their names
                         or IDs must be separated by commas.

                         See the Particulars section below for details
                         concerning use of DSK data.

                      "ELLIPSOID"

                         The ELLIPSOID shape option generates terminator
                         points on the target body's reference ellipsoid.
                         When the ELLIPSOID shape is selected, The TANGENT
                         curve option may be used with any aberration
                         correction locus, while the GUIDED option may be
                         used only with the CENTER locus (see the
                         description of REFLOC below).

                         When the locus is set to "CENTER", the
                         "TANGENT" and "GUIDED" curve options produce
                         the same results.

                   Neither case nor white space are significant in
                   `method', except within double-quoted strings. For
                   example, the string " eLLipsoid/tAnGenT " is valid.

                   Within double-quoted strings, blank characters are
                   significant, but multiple consecutive blanks are
                   considered equivalent to a single blank. Case is
                   not significant. So

                      \"Mars MEGDR 128 PIXEL/DEG\"

                   is equivalent to

                      \" mars megdr  128  pixel/deg \"

                   but not to

                      \"MARS MEGDR128PIXEL/DEG\"

       ilusrc      is the name of the illumination source. This source
                   may be any ephemeris object. Case, blanks, and
                   numeric values are treated in the same way as for the
                   input `target'.

                   The shape of the illumination source is considered
                   to be spherical. The radius of the sphere is the
                   largest radius of the source's reference ellipsoid.

       target      is the name of the target body. The target body is
                   an extended ephemeris object.

                   The string `target' is case-insensitive, and leading
                   and trailing blanks in `target' are not significant.
                   Optionally, you may supply a string containing the
                   integer ID code for the object. For example both
                   "MOON" and "301" are legitimate strings that indicate
                   the Moon is the target body.

                   When the target body's surface is represented by a
                   tri-axial ellipsoid, this routine assumes that a
                   kernel variable representing the ellipsoid's radii is
                   present in the kernel pool. Normally the kernel
                   variable would be defined by loading a PCK file.

       et          is the epoch of participation of the observer,
                   expressed as TDB seconds past J2000 TDB: `et' is
                   the epoch at which the observer's state is computed.

                   When aberration corrections are not used, `et' is also
                   the epoch at which the position and orientation of
                   the target body are computed.

                   When aberration corrections are used, the position
                   and orientation of the target body are computed at
                   et-lt, where `lt' is the one-way light time between the
                   aberration correction locus and the observer. The
                   locus is specified by the input argument `corloc'.
                   See the descriptions of `abcorr' and `corloc' below for
                   details.

       fixref      is the name of a body-fixed reference frame centered
                   on the target body. `fixref' may be any such frame
                   supported by the SPICE system, including built-in
                   frames (documented in the Frames Required Reading)
                   and frames defined by a loaded frame kernel (FK). The
                   string `fixref' is case-insensitive, and leading and
                   trailing blanks in `fixref' are not significant.

                   The output terminator points in the array `points' and
                   the output observer-terminator vectors in the array
                   `trmvcs' are expressed relative to this reference frame.

       abcorr      indicates the aberration corrections to be applied
                   when computing the target's position and orientation.
                   Corrections are applied at the location specified by
                   the aberration correction locus argument `corloc',
                   which is described below.

                   For remote sensing applications, where apparent
                   terminator points seen by the observer are 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 terminator points on the
                                 target body.

                   Let `lt' represent the one-way light time between the
                   observer and the aberration correction locus. The
                   following values of `abcorr' apply to the "reception"
                   case in which photons depart from the locus at the
                   light-time corrected epoch et-lt and *arrive* at the
                   observer's location at `et':

                      "LT"       Correct for one-way light time (also
                                 called "planetary aberration") using a
                                 Newtonian formulation. This correction
                                 yields the locus at the moment it
                                 emitted photons arriving at the
                                 observer at `et'.

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

                                 Both the target position as seen by the
                                 observer, and rotation of the target
                                 body, are corrected for light time. The
                                 position of the illumination source as
                                 seen from the target is corrected as
                                 well.

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

                      "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. The
                                 position of the illumination source as
                                 seen from the target is corrected as
                                 well.

                      "CN+S"     Converged Newtonian light time and
                                 stellar aberration corrections. This
                                 option produces a solution that is at
                                 least as accurate at that obtainable
                                 with the `LT+S" option. Whether the
                                 "CN+S" solution is substantially more
                                 accurate depends on the geometry of the
                                 participating objects and on the
                                 accuracy of the input data. In all
                                 cases this routine will execute more
                                 slowly when a converged solution is
                                 computed.

       corloc      is a string specifying the aberration correction
                   locus: the point or set of points for which
                   aberration corrections are performed. `corloc' may be
                   assigned the values:

                      "CENTER"

                          Light time and stellar aberration corrections
                          are applied to the vector from the observer to
                          the center of the target body. The one way
                          light time from the target center to the
                          observer is used to determine the epoch at
                          which the target body orientation is computed.

                          This choice is appropriate for small target
                          objects for which the light time from the
                          surface to the observer varies little across
                          the entire target. It may also be appropriate
                          for large, nearly ellipsoidal targets when the
                          observer is very far from the target.

                          Computation speed for this option is faster
                          than for the ELLIPSOID TERMINATOR option.

                      "ELLIPSOID TERMINATOR"

                          Light time and stellar aberration corrections
                          are applied to individual terminator points on
                          the reference ellipsoid. For a terminator
                          point on the surface described by topographic
                          data, lying in a specified cutting half-plane,
                          the unique reference ellipsoid terminator
                          point in the same half-plane is used as the
                          locus of the aberration corrections.

                          This choice is appropriate for large target
                          objects for which the light time from the
                          terminator to the observer is significantly
                          different from the light time from the target
                          center to the observer.

                          Because aberration corrections are repeated
                          for individual terminator points,
                          computational speed for this option is
                          relatively slow.

       obsrvr      is the name of the observing body. The observing body
                   is an ephemeris object: it typically is a spacecraft,
                   the earth, or a surface point on the earth. `obsrvr' is
                   case-insensitive, and leading and trailing blanks in
                   `obsrvr' are not significant. Optionally, you may
                   supply a string containing the integer ID code for
                   the object. For example both "MOON" and "301" are
                   legitimate strings that indicate the Moon is the
                   observer.

       refvec,
       rolstp,
       ncuts       are, respectively, a reference vector, a roll step
                   angle, and a count of cutting half-planes.

                   `refvec' defines the first of a sequence of cutting
                   half-planes in which terminator points are to be found.
                   Each cutting half-plane has as its edge the line
                   containing the target-illumination source vector; the
                   first half-plane contains `refvec'.

                   `refvec' is expressed in the body-fixed reference frame
                   designated by `fixref'.

                   `rolstp' is an angular step by which to roll the cutting
                   half-planes about the target-illumination source vector,
                   which we'll call the "axis." The ith half-plane is
                   rotated from `refvec' about the axis in the
                   counter-clockwise direction by i*rolstp. Units are
                   radians. `rolstp' should be set to

                      2*pi/ncuts

                   to generate an approximately uniform distribution of
                   points along the terminator.

                   `ncuts' is the number of cutting half-planes used to
                   find terminator points; the angular positions of
                   consecutive half-planes increase in the positive
                   (counterclockwise) sense about the axis and are
                   distributed roughly equally about that vector: each
                   half-plane has angular separation of approximately

                      `rolstp' radians

                   from each of its neighbors. When the aberration
                   correction locus is set to "CENTER", the angular
                   separation is the value above, up to round-off.
                   When the locus is "TANGENT", the separations are
                   less uniform due to differences in the aberration
                   corrections used for the respective terminator points.

       schstp,
       soltol      are used only for DSK-based surfaces. These inputs
                   are, respectively, the search angular step size and
                   solution convergence tolerance used to find tangent
                   rays and associated terminator points within each cutting
                   half plane. These values are used when the `method'
                   argument includes the TANGENT option. In this case,
                   terminator points are found by a two-step search
                   process:

                      1) Bracketing: starting with a direction
                         having sufficiently small angular separation from
                         the axis, rays emanating from the illumination
                         source are generated within the half-plane at
                         successively greater angular separations from the
                         axis, where the increment of angular separation is
                         `schstp'. The rays are tested for intersection
                         with the target surface. When a transition from
                         non-intersection to intersection is found, the
                         angular separation of a tangent ray has been
                         bracketed.

                      2) Root finding: each time a tangent ray is
                         bracketed, a search is done to find the angular
                         separation from the axis at which a tangent ray
                         exists. The search terminates when successive rays
                         are separated by no more than `soltol'. When the
                         search converges, the last ray-surface
                         intersection point found in the convergence
                         process is considered to be a terminator point.

                    `schstp' and `soltol' have units of radians.

                    Target bodies with simple surfaces---for example,
                    convex shapes---will have a single terminator point
                    within each cutting half-plane. For such surfaces,
                    `schstp' can be set large enough so that only one
                    bracketing step is taken. A value greater than pi,
                    for example 4., is recommended.

                    Target bodies with complex surfaces can have multiple
                    terminator points within a given cutting half-plane. To
                    find all terminator points, `schstp' must be set to a
                    value smaller than the minimum angular separation of any two
                    terminator points in any cutting half-plane, where the
                    vertex of the angle is on the illumination source.
                    `schstp' must not be too small, or the search will be
                    excessively slow.

                    For both kinds of surfaces, `soltol' must be chosen so
                    that the results will have the desired precision.
                    Note that the choice of `soltol' required to meet a
                    specified bound on terminator point height errors
                    depends on the illumination source-target distance.

       maxn         is the maximum number of terminator points that can
                    be stored in the output array `points'.
#### Detailed_Output
       npts         is an array of counts of terminator points within
                    the specified set of cutting half-planes. The Ith
                    element of `npts' is the terminator point count in the
                    Ith half-plane. `npts' should be declared with length
                    at least `ncuts'.

       points       is an array containing the terminator points found
                    by this routine. Terminator points are ordered by the
                    indices of the half-planes in which they're found. The
                    terminator points in a given half-plane are ordered by
                    decreasing angular separation from the illumination
                    source-target direction; the outermost terminator point
                    in a given half-plane is the first of that set.

                    The terminator points for the half-plane containing
                    `refvec' occupy array elements

                       points[ 0         ][0]          through
                       points[ npts[0]-1 ][2]

                    Terminator points for the second half plane occupy
                    elements

                       points[ npts[0]           ][0]  through
                       points[ npts[0]+npts[1]-1 ][2]

                    and so on.

                    `points' should be declared with dimensions

                       [maxn][3]

                    Terminator points are expressed in the reference
                    frame designated by `fixref'. For each terminator
                    point, the orientation of the frame is evaluated at
                    the epoch corresponding to the terminator point; the
                    epoch is provided in the output array `epochs'
                    (described below).

                    Units of the terminator points are km.

       epochs       is an array of epochs associated with the terminator
                    points, accounting for light time if aberration
                    corrections are used. `epochs' contains one element
                    for each terminator point. `epochs' should be declared
                    with length

                       maxn

                    The element

                       epochs[i]

                    is associated with the terminator point

                       points[i][j], j = 0 to 2

                    If `corloc' is set to "CENTER", all values of `epochs'
                    will be the epoch associated with the target body
                    center. That is, if aberration corrections are used,
                    and if `lt' is the one-way light time from the target
                    center to the observer, the elements of `epochs' will
                    all be set to

                       et - lt

                    If `corloc' is set to "ELLIPSOID TERMINATOR", all
                    values of `epochs' for the terminator points in a
                    given half plane will be those for the reference
                    ellipsoid terminator point in that half plane. That
                    is, if aberration corrections are used, and if lt(i)
                    is the one-way light time to the observer from the
                    reference ellipsoid terminator point in the ith half
                    plane, the elements of `epochs' for that half plane
                    will all be set to

                       et - lt[i]

       trmvcs       is an array of vectors connecting the observer to the
                    terminator points. The terminator vectors are expressed
                    in the frame designated by `fixref'. For the Ith
                    vector, the orientation of the frame is evaluated at
                    the Ith epoch provided in the output array `epochs'
                    (described above).

                    `trmvcs' should be declared with dimensions

                       [maxn][3]

                    The elements

                       trmvcs[i][j], j = 0 to 2

                    are associated with the terminator point

                       points[i][j], j = 0 to 2

                    Units of the terminator vectors are km.
#### Parameters
       None.
#### Exceptions
       1)  If the specified aberration correction is unrecognized, the
           error will be signaled by a routine in the call tree of this
           routine. If transmission corrections are commanded, the error
           SPICE(INVALIDOPTION) will be signaled.

       2)  If either the target or observer input strings cannot be
           converted to an integer ID code, the error
           SPICE(IDCODENOTFOUND) is signaled.

       3)  If `obsrvr' and `target' map to the same NAIF integer ID code,
           the error SPICE(BODIESNOTDISTINCT) is signaled.

       4)  If the input target body-fixed frame `fixref' is not
           recognized, the error SPICE(NOFRAME) is signaled. A frame
           name may fail to be recognized because a required frame
           specification kernel has not been loaded; another cause is a
           misspelling of the frame name.

       5)  If the input frame `fixref' is not centered at the target body,
           the error SPICE(INVALIDFRAME) is signaled.

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

       7)  If `method' contains an invalid terminator type, the error
           SPICE(INVALIDTERMTYPE) will be signaled.

       8)  If the target and observer have distinct identities but are
           at the same location the error SPICE(NOSEPARATION) is
           signaled.

       9)  If insufficient ephemeris data have been loaded prior to
           calling termpt_c, the error will be signaled by a routine in
           the call tree of this routine. When light time correction is
           used, sufficient ephemeris data must be available to
           propagate the states of both observer and target to the solar
           system barycenter.

      10)  If the computation method requires an ellipsoidal target
           shape and triaxial radii of the target body have not been
           loaded into the kernel pool prior to calling termpt_c, the
           error will be diagnosed and signaled by a routine in the call
           tree of this routine.

           When the target shape is modeled by topographic data, radii
           of the reference triaxial ellipsoid are still required if
           the aberration correction locus is ELLIPSOID TERMINATOR or if
           the terminator point generation method is GUIDED.

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

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

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

      14)  If the array bound `maxn' is less than 1, the error
           SPICE(INVALIDSIZE) will be signaled.

      15)  If the number of cutting half-planes specified by `ncuts'
           is negative or greater than `maxn', the error
           SPICE(INVALIDCOUNT) will be signaled.

      16)  If the aberration correction locus is not recognized, the
           error SPICE(INVALIDLOCUS) will be signaled.

      17)  If the reference vector `refvec' is the zero vector, the
           error SPICE(ZEROVECTOR) will be signaled.

      18)  If the reference vector `refvec' and the observer target
           vector are linearly dependent, the error
           SPICE(DEGENERATECASE) will be signaled.

      19)  If the terminator points cannot all be stored in the output
           `points' array, the error SPICE(OUTOFROOM) will be signaled.

      20)  If any input string argument pointer is null, the error
           SPICE(NULLPOINTER) will be signaled.

      21)  If any input string argument is empty, the error
           SPICE(EMPTYSTRING) will be 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 the target, observer, and
            illumination source must be loaded. If aberration corrections
            are used, the states of target and observer relative to the
            solar system barycenter must be calculable from the available
            ephemeris data. Typically ephemeris data are made available by
            loading one or more SPK files via furnsh_c.

          - Target body orientation data: these may be provided in a text
            or binary PCK file. In some cases, target body orientation
            may be provided by one more more CK files. In either case,
            data are made available by loading the files via furnsh_c.

          - Shape data for the target body:

              PCK data:

                 If the target body shape is modeled as an ellipsoid,
                 triaxial radii for the target body must be loaded into
                 the kernel pool. Typically this is done by loading a
                 text PCK file via furnsh_c.

                 Triaxial radii are also needed if the target shape is
                 modeled by DSK data but one or both of the GUIDED
                 terminator definition method or the ELLIPSOID
                 TERMINATOR aberration correction locus are selected.

              DSK data:

                 If the target shape is modeled by DSK data, DSK files
                 containing topographic data for the target body must be
                 loaded. If a surface list is specified, data for at
                 least one of the listed surfaces must be loaded.

          - Shape data for the illumination source:

              PCK data:

                 Triaxial radii for the illumination source must be
                 loaded into the kernel pool. Typically this is done by
                 loading a text PCK file via furnsh_c.

       The following data may be required:

          - Frame data: if a frame definition is required to convert the
            observer and target states to the body-fixed frame of the
            target, that definition must be available in the kernel
            pool. Typically the definition is supplied by loading a
            frame kernel via furnsh_c.

          - Surface name-ID associations: if surface names are specified
            in `method', the association of these names with their
            corresponding surface ID codes must be established by
            assignments of the kernel variables

               NAIF_SURFACE_NAME
               NAIF_SURFACE_CODE
               NAIF_SURFACE_BODY

            Normally these associations are made by loading a text
            kernel containing the necessary assignments. An example
            of such a set of assignments is

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

          - SCLK data: if the target body's orientation is provided by
            CK files, an associated SCLK kernel must be loaded.

       In all cases, kernel data are normally loaded once per program
       run, NOT every time this routine is called.
#### Particulars
       Terminator definition
       =====================

       The definitions of terminators used by this routine vary
       depending on the target surface model.

       In all cases, the surface of the illumination source is
       modeled as a sphere.

       Ellipsoidal target surface model
       --------------------------------

       The umbral terminator is the boundary of the set of target
       surface points at which the illumination source is completely
       below the local tangent plane: the entire illumination source is
       below the horizon as seen from any surface point on the far side,
       relative to the source, of the umbral terminator. At an umbral
       terminator point, the target surface tangent plane containing
       that point is tangent to the surface of the light source as well,
       and the outward normal vectors at the two points of tangency are
       parallel.

       The penumbral terminator is the boundary of the set of target
       surface points at which the illumination source is completely
       above the local tangent plane: the entire illumination source is
       above the horizon as seen from any surface point on the near
       side, relative to the source, of the penumbral terminator. At a
       penumbral terminator point, the target surface tangent plane
       containing that point is tangent to the surface of the light
       source as well, and the outward normal vectors at the two points
       of tangency are anti-parallel.

       Topographic target surface model (DSK case)
       -------------------------------------------

       The concept of a plane tangent to both a topographic target
       surface and an illumination source is problematic. If the target
       tangent point is required to lie in a given cutting half-plane
       bounded by the line containing the target-source vector, the
       desired plane may not exist. In general, planes tangent to both
       the illumination source and the target will rest upon the high
       points of the target surface.

       For topographic target surface models, this routine uses a
       modified terminator definition: terminator points are target
       surface points at which a line is tangent to both the target and
       the illumination source. The line is constrained to lie in the
       plane containing the specified cutting half-plane. The concepts
       of umbral and penumbral terminators still apply. For umbral
       terminator points, the common tangent line does not cross the
       target-source line; for penumbral points, it does.

       Note that for ellipsoids, the terminator definitions based on
       tangent lines are not equivalent to the definitions based on
       tangent planes. Typically, a plane tangent to the target
       ellipsoid at a point found by the method described above will not
       be tangent to the illumination source: it will be rotated about
       the common tangent line and "cut into" the sphere representing
       the light source. This implies that some of the source will be
       visible at umbral terminator points and some will be blocked at
       penumbral terminator points: both umbral and penumbral terminator
       points found by this method will lie in a region bounded by the
       true terminators.

       The two definitions are equivalent for spherical targets.

       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

             UMBRAL/TANGENT/DSK/UNPRIORITIZED/<surface list>
             DSK/UMBRAL/TANGENT/<surface list>/UNPRIORITIZED
             UNPRIORITIZED/<surface list>/DSK/TANGENT/UMBRAL

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

             "PENUMBRAL/TANGENT/DSK/UNPRIORITIZED"
             "UMBRAL/GUIDED/DSK/UNPRIORITIZED"

          For applications in which all loaded DSK data for the target
          body are for a single surface, and there are no competing
          segments, the above strings suffice. This is expected to be
          the usual case.

          When, for the specified target body, there are loaded DSK
          files providing data for multiple surfaces for that body, the
          surfaces to be used by this routine for a given call must be
          specified in a surface list, unless data from all of the
          surfaces are to be used together.

          The surface list consists of the string

             SURFACES =

          followed by a comma-separated list of one or more surface
          identifiers. The identifiers may be names or integer codes in
          string format. For example, suppose we have the surface
          names and corresponding ID codes shown below:

             Surface Name                              ID code
             ------------                              -------
             "Mars MEGDR 128 PIXEL/DEG"                1
             "Mars MEGDR 64 PIXEL/DEG"                 2
             "Mars_MRO_HIRISE"                         3

          If data for all of the above surfaces are loaded, then
          data for surface 1 can be specified by either

             "SURFACES = 1"

          or

             "SURFACES = \"Mars MEGDR 128 PIXEL/DEG\""

          Double quotes are used to delimit the surface name because
          it contains blank characters.

          To use data for surfaces 2 and 3 together, any
          of the following surface lists could be used:

             "SURFACES = 2, 3"

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

             "SURFACES = 2, Mars_MRO_HIRISE"

             "SURFACES = \"Mars MEGDR 64 PIXEL/DEG\", Mars_MRO_HIRISE"

          An example of a `method' argument that could be constructed
          using one of the surface lists above is

          "UMBRAL/TANGENT/DSK/UNPRIORITIZED/SURFACES= \"Mars MEGDR 64 PIXEL/DEG\",3"
#### Examples
       The numerical results shown for these examples may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       1) Find apparent terminator points on Phobos as seen from Mars.
          Use the "umbral" shadow definition.

          Due to Phobos' irregular shape, the TANGENT terminator point
          definition will used. It suffices to compute light time and
          stellar aberration corrections for the center of Phobos, so
          the CENTER aberration correction locus will be used. Use
          converged Newtonian light time and stellar aberration
          corrections in order to model the apparent position and
          orientation of Phobos.

          For comparison, compute terminator points using both ellipsoid
          and topographic shape models.

          Use the target body-fixed +Z axis as the reference direction
          for generating cutting half-planes. This choice enables the
          user to see whether the first terminator point is near the
          target's north pole.

          For each option, use just three cutting half-planes in order
          to keep the volume of output manageable. In most applications,
          the number of cuts and the number of resulting terminator
          points would be much greater.

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

             KPL/MK

             File: termpt_ex1.tm

             This meta-kernel is intended to support operation of SPICE
             example programs. The kernels shown here should not be
             assumed to contain adequate or correct versions of data
             required by SPICE-based user applications.

             In order for an application to use this meta-kernel, the
             kernels referenced here must be present in the user's
             current working directory.

             The names and contents of the kernels referenced
             by this meta-kernel are as follows:

                File name                        Contents
                ---------                        --------
                de430.bsp                        Planetary ephemeris
                mar097.bsp                       Mars satellite ephemeris
                pck00010.tpc                     Planet orientation and
                                                 radii
                naif0011.tls                     Leapseconds
                phobos512.bds                    DSK based on
                                                 Gaskell ICQ Q=512
                                                 Phobos plate model
             \begindata

                PATH_SYMBOLS    = 'GEN'
                PATH_VALUES     = '/ftp/pub/naif/generic_kernels'

                KERNELS_TO_LOAD = ( 'de430.bsp',
                                    'mar097.bsp',
                                    'pck00010.tpc',
                                    'naif0011.tls',
                                    '$GEN/dsk/phobos/phobos512.bds' )
             \begintext

       Example code begins here.

          /.
          termpt_c example 1

             Find terminator points on Phobos as seen from Mars.

                Compute terminator points using the tangent
                definition, using the "umbral" shadow type.
                The sun is the illumination source. Perform
                aberration corrections for the target center.
                Use both ellipsoid and DSK shape models.
          ./

          #include <stdio.h>
          #include "SpiceUsr.h"

          int main()
          {
             /.
             Local constants
             ./
             #define META            "termpt_ex1.tm"
             #define MTHLEN          51
             #define NMETH            2
             #define MAXN         10000

             /.
             Local variables
             ./
             SpiceChar             * abcorr;
             SpiceChar             * corloc;
             SpiceChar             * fixref;
             SpiceChar             * ilusrc;
             SpiceChar             * obsrvr;
             SpiceChar             * target;

             SpiceChar               method [NMETH][MTHLEN] =

                               { "UMBRAL/TANGENT/ELLIPSOID",
                                 "UMBRAL/TANGENT/DSK/UNPRIORITIZED" };

             SpiceDouble             delrol;
             SpiceDouble             dist;
             SpiceDouble             et;
             SpiceDouble             lt;
             SpiceDouble             points  [MAXN][3];
             SpiceDouble             pos     [3];
             SpiceDouble             roll;
             SpiceDouble             schstp;
             SpiceDouble             soltol;
             SpiceDouble             trmvcs  [MAXN][3];
             SpiceDouble             trgeps  [MAXN];
             SpiceDouble             z       [3] = { 0.0, 0.0, 1.0 };

             SpiceInt                i;
             SpiceInt                j;
             SpiceInt                k;
             SpiceInt                ncuts;
             SpiceInt                npts    [MAXN];
             SpiceInt                start;

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

             /.
             Set illumination source, target, observer,
             and target body-fixed, body-centered reference frame.
             ./
             ilusrc = "SUN";
             obsrvr = "MARS";
             target = "PHOBOS";
             fixref = "IAU_PHOBOS";

             /.
             Set aberration correction and correction locus.
             ./
             abcorr = "CN+S";
             corloc = "CENTER";

             /.
             Convert the UTC request time string seconds past
             J2000, TDB.
             ./
             str2et_c ( "2008 AUG 11 00:00:00", &et );

             /.
             Compute a set of terminator points using light
             time and stellar aberration corrections. Use
             both ellipsoid and DSK shape models. Use an
             angular step size corresponding to a height of
             about 100 meters to ensure we don't miss the
             terminator. Set the convergence tolerance to limit
             the height convergence error to about 1 meter.
             Compute 3 terminator points for each computation
             method.

             Get the approximate light source-target distance
             at ET. We'll ignore the observer-target light
             time for this approximation.
             ./

             spkpos_c ( ilusrc, et, "J2000", abcorr,
                        target, pos, &lt            );

             dist   = vnorm_c( pos );

             schstp = 1.0e-1 / dist;
             soltol = 1.0e-3 / dist;
             ncuts  = 3;

             printf ( "\n"
                      "Light source:   %s\n"
                      "Observer:       %s\n"
                      "Target:         %s\n"
                      "Frame:          %s\n"
                      "\n"
                      "Number of cuts: %d\n",
                      ilusrc,
                      obsrvr,
                      target,
                      fixref,
                      (int)ncuts            );

             delrol = twopi_c() / ncuts;

             for ( i = 0;  i < NMETH;  i++ )
             {
                termpt_c ( method[i], ilusrc, target, et,
                           fixref,    abcorr, corloc, obsrvr,
                           z,         delrol, ncuts,  schstp,
                           soltol,    MAXN,   npts,   points,
                           trgeps,    trmvcs                  );
                /.
                Write the results.
                ./
                printf ( "\n"
                         "Computation method = %s\n"
                         "Locus              = %s\n"
                         "\n",
                         method[i],
                         corloc                     );

                start = 0;

                for ( j = 0;  j < ncuts;  j++ )
                {
                   roll = j * delrol;

                   printf ( "\n"
                            "  Roll angle (deg) = %17.9f\n"
                            "     Target epoch  = %17.9f\n"
                            "     Number of terminator points at "
                            "this roll angle: %d\n",
                            roll * dpr_c(),
                            trgeps[j],
                            npts[j]                            );

                   printf ( "      Terminator points:\n" );

                   for ( k = 0;  k < npts[j];  k++ )
                   {
                      printf ( " %20.9f %20.9f %20.9f\n",
                               points[k+start][0],
                               points[k+start][1],
                               points[k+start][2]        );
                   }

                   start += npts[j];
                }
             }
             printf ( "\n" );

             return ( 0 );
          }

       When this program was executed on a PC/Linux/gcc 64-bit
       platform, the output was:

          Light source:   SUN
          Observer:       MARS
          Target:         PHOBOS
          Frame:          IAU_PHOBOS

          Number of cuts: 3

          Computation method = UMBRAL/TANGENT/ELLIPSOID
          Locus              = CENTER

            Roll angle (deg) =       0.000000000
               Target epoch  = 271684865.152078211
               Number of terminator points at this roll angle: 1
                Terminator points:
                    2.040498332          5.012722925          8.047281838

            Roll angle (deg) =     120.000000000
               Target epoch  = 271684865.152078211
               Number of terminator points at this roll angle: 1
                Terminator points:
                  -11.058054707          0.167672089         -4.782740292

            Roll angle (deg) =     240.000000000
               Target epoch  = 271684865.152078211
               Number of terminator points at this roll angle: 1
                Terminator points:
                    8.195238564         -6.093889437         -5.122310498

          Computation method = UMBRAL/TANGENT/DSK/UNPRIORITIZED
          Locus              = CENTER

            Roll angle (deg) =       0.000000000
               Target epoch  = 271684865.152078211
               Number of terminator points at this roll angle: 1
                Terminator points:
                    1.626396122          3.995432317          8.853689531

            Roll angle (deg) =     120.000000000
               Target epoch  = 271684865.152078211
               Number of terminator points at this roll angle: 1
                Terminator points:
                  -11.186659739         -0.142366278         -4.646137201

            Roll angle (deg) =     240.000000000
               Target epoch  = 271684865.152078211
               Number of terminator points at this roll angle: 1
                Terminator points:
                    9.338447077         -6.091352469         -5.960849305

       2) Find apparent terminator points on Mars as seen from the
          earth.

          Use both the "umbral" and "penumbral" shadow definitions. Use
          only ellipsoid shape models for easier comparison. Find
          distances between corresponding terminator points on the
          umbral and penumbral terminators.

          Use the ELLIPSOID TERMINATOR aberration correction locus
          in order to perform separate aberration corrections for
          each terminator point. Because of the large size of Mars,
          corrections for the target center are less accurate.

          For each option, use just three cutting half-planes, in order
          to keep the volume of output manageable. In most applications,
          the number of cuts and the number of resulting terminator
          points would be much greater.

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

             KPL/MK

             File: termpt_ex2.tm

             This meta-kernel is intended to support operation of SPICE
             example programs. The kernels shown here should not be
             assumed to contain adequate or correct versions of data
             required by SPICE-based user applications.

             In order for an application to use this meta-kernel, the
             kernels referenced here must be present in the user's
             current working directory.

             The names and contents of the kernels referenced
             by this meta-kernel are as follows:

                File name                        Contents
                ---------                        --------
                de430.bsp                        Planetary ephemeris
                mar097.bsp                       Mars satellite ephemeris
                pck00010.tpc                     Planet orientation and
                                                 radii
                naif0011.tls                     Leapseconds
                megr90n000cb_plate.bds           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

       Example code begins here.

          /.
          termpt_c example 2

             Find terminator points on Mars as seen from the
             earth.

             Use only ellipsoid shape models. Use the
             ELLIPSOID TERMINATOR aberration correction
             locus.

             Use both UMBRAL and PENUMBRAL shadow definitions.
             Compute the distances between corresponding
             umbral and penumbral terminator points.

             Check terminator points by computing solar
             incidence angles at each point.
          ./

          #include <stdio.h>
          #include <math.h>
          #include "SpiceUsr.h"

          int main()
          {
             /.
             Local constants
             ./
             #define CORLEN          21
             #define META            "termpt_ex2.tm"
             #define MTHLEN          51
             #define NMETH            2
             #define MAXN         10000

             /.
             Local variables
             ./
             SpiceChar             * abcorr;

             SpiceChar               corloc [NMETH][CORLEN] =

                               { "ELLIPSOID TERMINATOR",
                                 "ELLIPSOID TERMINATOR" };

             SpiceChar             * fixref;

             SpiceChar               ilumth [NMETH][MTHLEN] =

                               { "ELLIPSOID",
                                 "ELLIPSOID" };

             SpiceChar             * ilusrc;
             SpiceChar             * obsrvr;
             SpiceChar             * target;

             SpiceChar               method [NMETH][MTHLEN] =

                            { "UMBRAL/TANGENT/ELLIPSOID",
                              "PENUMBRAL/TANGENT/ELLIPSOID" };

             SpiceDouble             adjang;
             SpiceDouble             alt;
             SpiceDouble             angsrc;
             SpiceDouble             delrol;
             SpiceDouble             dist;
             SpiceDouble             emissn;
             SpiceDouble             et;
             SpiceDouble             f;
             SpiceDouble             ilupos  [3];
             SpiceDouble             lat;
             SpiceDouble             lon;
             SpiceDouble             lt;
             SpiceDouble             phase;
             SpiceDouble             points  [MAXN][3];
             SpiceDouble             svpnts  [MAXN][3];
             SpiceDouble             tptilu  [3];
             SpiceDouble             radii   [3];
             SpiceDouble             re;
             SpiceDouble             roll;
             SpiceDouble             rp;
             SpiceDouble             schstp;
             SpiceDouble             solar;
             SpiceDouble             soltol;
             SpiceDouble             srcrad  [3];
             SpiceDouble             srfvec  [3];
             SpiceDouble             trmvcs  [MAXN][3];
             SpiceDouble             trgepc;
             SpiceDouble             trgeps  [MAXN];
             SpiceDouble             z       [3] = { 0.0, 0.0, 1.0 };

             SpiceInt                i;
             SpiceInt                j;
             SpiceInt                k;
             SpiceInt                m;
             SpiceInt                n;
             SpiceInt                ncuts;
             SpiceInt                npts    [MAXN];
             SpiceInt                start;

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

             /.
             Set illumination source, target, observer,
             and target body-fixed, body-centered reference frame.
             ./
             ilusrc = "SUN";
             obsrvr = "EARTH";
             target = "MARS";
             fixref = "IAU_MARS";

             /.
             Set the aberration correction.
             ./
             abcorr = "CN+S";

             /.
             Convert the UTC request time string seconds past
             J2000, TDB.
             ./
             str2et_c ( "2008 AUG 11 00:00:00", &et );

             /.
             Look up the target body's radii. We'll use these to
             convert Cartesian to planetographic coordinates. Use
             the radii to compute the flattening coefficient of
             the reference ellipsoid.
             ./
             bodvrd_c ( target, "RADII", 3, &n, radii );

             /.
             Compute the flattening coefficient for planetodetic
             coordinates
             ./
             re = radii[0];
             rp = radii[2];
             f  = ( re - rp ) / re;

             /.
             Get the radii of the illumination source as well.
             We'll use these radii to compute the angular radius
             of the source as seen from the terminator points.
             ./
             bodvrd_c ( ilusrc, "RADII", 3, &n, srcrad );

             /.
             Compute a set of terminator points using light time and
             stellar aberration corrections. Use both ellipsoid
             and DSK shape models.

             Get the approximate light source-target distance
             at ET. We'll ignore the observer-target light
             time for this approximation.
             ./
             spkpos_c ( ilusrc, et,     fixref, abcorr,
                        target, ilupos, &lt             );

             dist = vnorm_c( ilupos );

             /.
             Set the angular step size so that a single step will
             be taken in the root bracketing process; that's all
             that is needed since we don't expect to have multiple
             terminator points in any cutting half-plane.
             ./
             schstp = 4.0;

             /.
             Set the convergence tolerance to minimize the
             height error. We can't achieve the precision
             suggested by the formula because the sun-Mars
             distance is about 2.4e8 km. Compute 3 terminator
             points for each computation method.
             ./
             soltol = 1.e-7/dist;

             /.
             Set the number of cutting half-planes and roll step.
             ./
             ncuts  = 3;
             delrol = twopi_c() / ncuts;

             printf ( "\n"
                      "Light source:   %s\n"
                      "Observer:       %s\n"
                      "Target:         %s\n"
                      "Frame:          %s\n"
                      "\n"
                      "Number of cuts: %d\n",
                      ilusrc,
                      obsrvr,
                      target,
                      fixref,
                      (int)ncuts            );

             delrol = twopi_c() / ncuts;

             for ( i = 0;  i < NMETH;  i++ )
             {
                termpt_c ( method[i], ilusrc, target, et,
                           fixref,    abcorr, corloc, obsrvr,
                           z,         delrol, ncuts,  schstp,
                           soltol,    MAXN,   npts,   points,
                           trgeps,    trmvcs                  );
                /.
                Write the results.
                ./
                printf ( "\n\n"
                         "Computation method = %s\n"
                         "Locus              = %s\n",
                         method[i],
                         corloc[i]                  );

                start = 0;

                for ( j = 0;  j < ncuts;  j++ )
                {
                   roll = j * delrol;

                   printf ( "\n"
                            "   Roll angle (deg) = %17.9f\n"
                            "    Target epoch  = %17.9f\n"
                            "    Number of terminator points at "
                            "this roll angle: %d\n",
                            roll * dpr_c(),
                            trgeps[j],
                            npts[j]                            );

                   for ( k = 0;  k < npts[j];  k++ )
                   {
                      printf ( "    Terminator point planetodetic "
                               "coordinates:\n" );

                      m = k+start;

                      recgeo_c ( points[m], re, f,
                                 &lon,          &lat, &alt );

                      printf ( "      Longitude        (deg): %20.9f\n"
                               "      Latitude         (deg): %20.9f\n"
                               "      Altitude          (km): %20.9f\n",
                               lon * dpr_c(),
                               lat * dpr_c(),
                               alt                                     );

                      /.
                      Get illumination angles for this terminator point.
                      ./

                      illumg_c ( ilumth[i], target,  ilusrc, et,
                                 fixref,    abcorr,  obsrvr,
                                 points[m], &trgepc, srfvec,
                                 &phase,    &solar,  &emissn    );

                      printf ( "      Incidence angle  (deg): "
                               "%20.9f\n",   solar * dpr_c()    );

                      /.
                      Adjust the incidence angle for the angular
                      radius of the illumination source. Use the
                      epoch associated with the terminator point
                      for this lookup.
                      ./
                      spkpos_c ( ilusrc, trgeps[m], fixref,
                                 abcorr, target,    tptilu, &lt );

                      dist   = vnorm_c( tptilu );

                      angsrc = asin ( maxd_c( 3, srcrad[0],
                                                 srcrad[1],
                                                 srcrad[2] ) / dist );

                      if ( i == 0 )
                      {
                         /.
                         For points on the umbral terminator,
                         the ellipsoid outward normal is tilted
                         away from the terminator-source center
                         direction by the angular radius of the
                         source. Subtract this radius from the
                         illumination incidence angle to get the
                         angle between the local normal and the
                         direction to the corresponding tangent
                         point on the source.
                         ./
                         adjang = solar - angsrc;
                      }
                      else
                      {
                         /.
                         For the penumbral case, the outward
                         normal is tilted toward the illumination
                         source by the angular radius of the
                         source. Adjust the illumination
                         incidence angle for this.
                         ./
                         adjang = solar + angsrc;
                      }

                      printf ( "      Adjusted angle   (deg): "
                               "%20.9f\n",   adjang * dpr_c() );

                      if ( i == 0 )
                      {
                         /.
                         Save terminator points for comparison.
                         ./
                         vequ_c ( points[m], svpnts[m] );
                      }
                      else
                      {
                         /.
                         Compare terminator points with last
                         saved values.
                         ./
                         dist = vdist_c( points[m], svpnts[m] );

                         printf ( "      Distance offset  (km):  "
                                  "%20.9f\n",   dist             );
                      }
                   }
                   start += npts[j];
                }
             }
             printf ( "\n" );

             return ( 0 );
          }

       When this program was executed on a PC/Linux/gcc 64-bit
       platform, the output was:

          Light source:   SUN
          Observer:       EARTH
          Target:         MARS
          Frame:          IAU_MARS

          Number of cuts: 3

          Computation method = UMBRAL/TANGENT/ELLIPSOID
          Locus              = ELLIPSOID TERMINATOR

             Roll angle (deg) =       0.000000000
              Target epoch  = 271683700.369686902
              Number of terminator points at this roll angle: 1
              Terminator point planetodetic coordinates:
                Longitude        (deg):          4.189318082
                Latitude         (deg):         66.416132677
                Altitude          (km):          0.000000000
                Incidence angle  (deg):         90.163842885
                Adjusted angle   (deg):         89.999999980

             Roll angle (deg) =     120.000000000
              Target epoch  = 271683700.372003794
              Number of terminator points at this roll angle: 1
              Terminator point planetodetic coordinates:
                Longitude        (deg):        107.074551917
                Latitude         (deg):        -27.604435701
                Altitude          (km):          0.000000000
                Incidence angle  (deg):         90.163842793
                Adjusted angle   (deg):         89.999999888

             Roll angle (deg) =     240.000000000
              Target epoch  = 271683700.364983618
              Number of terminator points at this roll angle: 1
              Terminator point planetodetic coordinates:
                Longitude        (deg):        -98.695906077
                Latitude         (deg):        -27.604435700
                Altitude          (km):         -0.000000000
                Incidence angle  (deg):         90.163843001
                Adjusted angle   (deg):         90.000000096

          Computation method = PENUMBRAL/TANGENT/ELLIPSOID
          Locus              = ELLIPSOID TERMINATOR

             Roll angle (deg) =       0.000000000
              Target epoch  = 271683700.369747400
              Number of terminator points at this roll angle: 1
              Terminator point planetodetic coordinates:
                Longitude        (deg):          4.189317837
                Latitude         (deg):         66.743818467
                Altitude          (km):          0.000000000
                Incidence angle  (deg):         89.836157094
                Adjusted angle   (deg):         89.999999999
                Distance offset  (km):          19.483590936

             Roll angle (deg) =     120.000000000
              Target epoch  = 271683700.372064054
              Number of terminator points at this roll angle: 1
              Terminator point planetodetic coordinates:
                Longitude        (deg):        107.404259674
                Latitude         (deg):        -27.456458359
                Altitude          (km):          0.000000000
                Incidence angle  (deg):         89.836157182
                Adjusted angle   (deg):         90.000000087
                Distance offset  (km):          19.411414247

             Roll angle (deg) =     240.000000000
              Target epoch  = 271683700.365043879
              Number of terminator points at this roll angle: 1
              Terminator point planetodetic coordinates:
                Longitude        (deg):        -99.025614323
                Latitude         (deg):        -27.456458357
                Altitude          (km):          0.000000000
                Incidence angle  (deg):         89.836156972
                Adjusted angle   (deg):         89.999999877
                Distance offset  (km):          19.411437239
#### Restrictions
      None.
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman   (JPL)
#### Version
       -CSPICE Version 1.0.0, 05-APR-2017 (NJB)

       29-AUG-2016 (NJB)

          Original version.
#### Index_Entries
       find terminator points on target body
#### Link to routine termpt_c source file termpt_c.c

    Wed Apr  5 17:54:45 2017