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cspice_termpt

Table of contents
Abstract
I/O
Parameters
Examples
Particulars
Exceptions
Files
Restrictions
Required_Reading
Literature_References
Author_and_Institution
Version
Index_Entries


Abstract


   CSPICE_TERMPT finds terminator points on a target body. The terminator
   is the set of points of tangency on the target body of planes tangent
   to both this body and to a light source. 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.

I/O


   Given:

      method   a short string providing parameters defining the computation
               method to be used.

               help, method
                  STRING = Scalar

               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.

                     '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.


                  <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-target 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 `corloc' 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 uses 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 `corloc' 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   the name of the illumination source.

               help, ilusrc
                  STRING = Scalar

               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   the name of the target body.

               help, target
                  STRING = Scalar

               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       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.

               help, et
                  DOUBLE = Scalar

               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-ltime, where `ltime' 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   the name of a body-fixed reference frame centered on the target
               body.

               help, fixref
                  STRING = Scalar

               `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.

               help, abcorr
                  STRING = Scalar

               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 `ltime' 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-ltime 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   a string specifying the aberration correction locus: the point
               or set of points for which aberration corrections are performed.

               help, corloc
                  STRING = Scalar

               `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   the name of the observing body.

               help, obsrvr
                  STRING = Scalar

               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.

               help, refvec
                  DOUBLE = Array[3]
               help, rolstp
                  DOUBLE = Scalar
               help, ncuts
                  LONG = Scalar

               `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   used only for DSK-based surfaces.

               help, schstp
                  DOUBLE = Scalar
               help, soltol
                  DOUBLE = Scalar

               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 surface of 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 starting direction at which
                     a tangent ray exists. The search terminates
                     when successive rays are separated by no more
                     than `soltol'. When the search converges, the
                     last ray-surface intersection point found in
                     the convergence process is considered to be a
                     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 4.0, 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 angular
               separation of any two terminator points in any
               cutting half-plane, where the vertex of the angle is
               near a point on the surface of 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     the maximum number of terminator points that can be stored in
               the output array `points'.

               help, maxn
                  LONG = Scalar

   the call:

      cspice_termpt, method, ilusrc, target, et,     fixref, abcorr,         $
                     corloc, obsrvr, refvec, rolstp, ncuts,  schstp,         $
                     soltol, maxn,   npts,   points, epochs, trmvcs

   returns:

      npts     an array of counts of terminator points within the specified set
               of cutting half-planes.

               help, npts
                  LONG = Array[maxn]

               The Ith element of `npts' is the terminator point count in the
               Ith half-plane.

      points   an array containing the terminator points found by this routine.

               help, points
                  DOUBLE = Array[3,maxn]

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

               Terminator points for the second half plane occupy
               elements

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

               and so on.

               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   an array of epochs associated with the terminator points,
               accounting for light time if aberration corrections are used.

               help, epochs
                  DOUBLE = Array[maxn]

               `epochs' contains one element for each terminator point.

               The element

                  epochs[i]

               is associated with the terminator point

                  points[j,i], 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 `ltime' is the one-way light time from the target
               center to the observer, the elements of `epochs' will
               all be set to

                  et - ltime

               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 ltime[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 - ltime[i]

      trmvcs   an array of vectors connecting the observer to the terminator
               points.

               help, trmvcs
                  DOUBLE = Array[3,maxn]

               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).

               The elements

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

               are associated with the terminator point

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

               Units of the terminator vectors are km.

Parameters


   None.

Examples


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   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 be 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 shown 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

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

         End of meta-kernel


      Example code begins here.


      ;;
      ;; 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.
      ;;
      PRO termpt_ex1

         MAXN = 10000

         method = [ 'UMBRAL/TANGENT/ELLIPSOID', $
                    'UMBRAL/TANGENT/DSK/UNPRIORITIZED' ]

         z = [ 0.D, 0.0, 1.0 ]

         ;;
         ;; Load kernel files via the meta-kernel.
         ;;
         cspice_furnsh, 'termpt_ex1.tm'

         ;;
         ;; 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 to seconds past
         ;; J2000, TDB.
         ;;
         cspice_str2et, '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.
         ;;

         cspice_spkpos, ilusrc, et, 'J2000', abcorr, target, pos, ltime

         dist   = norm( pos )

         schstp = 1.0d-1 / dist
         soltol = 1.0d-3 / dist
         ncuts  = 3L

         print
         print, 'Light source:   ', ilusrc
         print, 'Observer:       ', obsrvr
         print, 'Target:         ', target
         print, 'Frame:          ', fixref
         print
         print, 'Number of cuts: ', ncuts

         delrol = cspice_twopi()/ ncuts


         for i = 0, n_elements(method)-1L do begin

            cspice_termpt, method[i], ilusrc, target, et, fixref,   $
                           abcorr, corloc, obsrvr, z,               $
                           delrol, ncuts,  schstp,                  $
                           soltol, MAXN, npts, points, trgeps, trmvcs

            ;;
            ;; Write the results.
            ;;
            print
            print, 'Computation method = ', method[i]
            print, 'Locus              = ', corloc
            print

            strt = 0

            for j = 0, ncuts-1L do begin

               roll = j * delrol

               print
               print, '  Roll angle (deg) = ', roll * cspice_dpr()
               print, '     Target epoch  = ', trgeps[j]
               print, '     Number of terminator points at'+  $
                      ' this roll angle: ', npts[j]

               print, '      Terminator points:'

               for k = 0, npts[j]-1L do begin
                  print, format='(3(f20.9,A))', points[0:2, k+strt]
                endfor

                strt = npts[j] + strt

            endfor

          endfor

         ;;
         ;; It's always good form to unload kernels after use,
         ;; particularly in IDL due to data persistence.
         ;;
         cspice_kclear

      END


      When this program was executed on a Mac/Intel/IDL8.x/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) =        0.0000000
           Target epoch  =    2.7168487e+08
           Number of terminator points at this roll angle:            1
            Terminator points:
               2.040498332       5.0127229         8.047281838

        Roll angle (deg) =        120.00000
           Target epoch  =    2.7168487e+08
           Number of terminator points at this roll angle:            1
            Terminator points:
             -11.058054707      0.16767209        -4.782740292

        Roll angle (deg) =        240.00000
           Target epoch  =    2.7168487e+08
           Number of terminator points at this roll angle:            1
            Terminator points:
               8.195238564      -6.0938894        -5.122310498

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


        Roll angle (deg) =        0.0000000
           Target epoch  =    2.7168487e+08
           Number of terminator points at this roll angle:            1
            Terminator points:
               1.626396122       3.9954323         8.853689531

        Roll angle (deg) =        120.00000
           Target epoch  =    2.7168487e+08
           Number of terminator points at this roll angle:            1
            Terminator points:
             -11.186659739     -0.14236628        -4.646137201

        Roll angle (deg) =        240.00000
           Target epoch  =    2.7168487e+08
           Number of terminator points at this roll angle:            1
            Terminator points:
               9.338447077      -6.0913525        -5.960849305


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 cspice_furnsh and can be unloaded by calling cspice_unload or
      cspice_kclear. See the documentation of cspice_furnsh 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'

Exceptions


   1)  If the specified aberration correction is unrecognized, an
       error is signaled by a routine in the call tree of this
       routine.

   2)  If transmission corrections are commanded, the error
       SPICE(INVALIDOPTION) is signaled by a routine in the call tree
       of this routine.

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

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

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

   6)  If the input frame `fixref' is not centered at the target body,
       the error SPICE(INVALIDFRAME) is signaled by a routine in the
       call tree of this routine.

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

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

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

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

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

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

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

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

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

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

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

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

   18) If the GUIDED terminator type is used with the ELLIPSOID
       TERMINATOR aberration correction locus, the error
       SPICE(BADTERMLOCUSMIX) is signaled by a routine in the call
       tree of this routine.

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

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

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

   22) If `ncuts' is greater than 1, the roll step `rolstp' must be
       positive. Otherwise, the error SPICE(INVALIDROLLSTEP) is
       signaled by a routine in the call tree of this routine.

   23) If any of the input arguments, `method', `ilusrc', `target',
       `et', `fixref', `abcorr', `corloc', `obsrvr', `refvec',
       `rolstp', `ncuts', `schstp', `soltol' or `maxn', is undefined,
       an error is signaled by the IDL error handling system.

   24) If any of the input arguments, `method', `ilusrc', `target',
       `et', `fixref', `abcorr', `corloc', `obsrvr', `refvec',
       `rolstp', `ncuts', `schstp', `soltol' or `maxn', is not of the
       expected type, or it does not have the expected dimensions and
       size, an error is signaled by the Icy interface.

   25) If any of the output arguments, `npts', `points', `epochs' or
       `trmvcs', is not a named variable, an error is signaled by the
       Icy interface.

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
      cspice_furnsh.

   -  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 cspice_furnsh.

   -  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 cspice_furnsh.

            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 cspice_furnsh.

   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 cspice_furnsh.

   -  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.

Restrictions


   None.

Required_Reading


   CK.REQ
   DSK.REQ
   FRAMES.REQ
   ICY.REQ
   NAIF_IDS.REQ
   PCK.REQ
   SPK.REQ
   TIME.REQ

Literature_References


   None.

Author_and_Institution


   J. Diaz del Rio     (ODC Space)
   M. Liukis           (JPL)
   E.D. Wright         (JPL)

Version


   -Icy Version 1.1.0, 10-AUG-2021 (JDR)

       Changed the output argument name "tangts" to "trmvcs" for
       consistency with other routines. Changed the variable name used
       for light time to "ltime" in the header comments.

       Added -Parameters, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections. Updated
       -Particulars section.

       Edited the header to comply with NAIF standard. Added example's
       task description and meta-kernel.

       Removed reference to the routine's corresponding CSPICE header from
       -Abstract section.

       Added arguments' type and size information in the -I/O section.

   -Icy Version 1.0.0, 15-DEC-2016 (EDW) (ML)

Index_Entries


   find terminator points on target body



Fri Dec 31 18:43:08 2021