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Procedure
Abstract
Required_Reading
Keywords
Brief_I/O
Detailed_Input
Detailed_Output
Parameters
Exceptions
Files
Particulars
Examples
Restrictions
Literature_References
Author_and_Institution
Version
Index_Entries

Procedure

   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