Module JNISpice
Package spice.basic

Class LimbPoint


  • public class LimbPoint
    extends Vector3
    Class LimbPoint supports limb point computations.

    LimbPoint instances consist of

    • An inherited Vector3 instance representing a limb point.
    • The epoch of participation of the target body.

      This is the observation epoch, minus the approximate one-way light time from the limb point to the observer, if aberration corrections are used. The way the light time is computed depends on the choice of aberration correction locus.

    • A vector from the observer to the limb point, expressed in the target body-fixed reference frame, evaluated at the epoch of participation of the target body.

    The principal computational method of this class is create(String,Body,Time,ReferenceFrame, AberrationCorrection,String,Body,Vector3,double, int,double,double,int). See the detailed documentation of this method for code examples.

    Files

    Appropriate SPICE kernels must be loaded by the calling program before methods of this class are called.

    The following data are required:

    • SPK data: the calling application must load ephemeris data for the target and observer. If aberration corrections are used, the states of the target body and of the 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 KernelDatabase.load(java.lang.String).
    • 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 KernelDatabase.load.
    • 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 KernelDatabase.load.
       
            Triaxial radii are also needed if the target shape is
            modeled by DSK data but one or both of the GUIDED limb
            definition method or the ELLIPSOID LIMB 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.
      

    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 KernelDatabase.load.
    • 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.

    Kernel data are normally loaded once per program run, NOT every time a method of this class is called.

    Class LimbPoint Particulars

    Using DSK data

    DSK loading and unloading

    DSK files providing data used by this class are loaded by calling KernelDatabase.load(java.lang.String) and can be unloaded by calling KernelDatabase.unload(java.lang.String) or KernelDatabase.clear(). See the documentation of KernelDatabase.load for limits on numbers of loaded DSK files. For run-time efficiency, it's desirable to avoid frequent loading and unloading of DSK files. When there is a reason to use multiple versions of data for a given target body---for example, if topographic data at varying resolutions are to be used---the surface list can be used to select DSK data to be used for a given computation. It is not necessary to unload the data that are not to be used. This recommendation presumes that DSKs containing different versions of surface data for a given body have different surface ID codes.

    DSK data priority

    A DSK coverage overlap occurs when two segments in loaded DSK files cover part or all of the same domain---for example, a given longitude-latitude rectangle---and when the time intervals of the segments overlap as well.

    When DSK data selection is prioritized, in case of a coverage overlap, if the two competing segments are in different DSK files, the segment in the DSK file loaded last takes precedence. If the two segments are in the same file, the segment located closer to the end of the file takes precedence.

    When DSK data selection is unprioritized, data from competing segments are combined. For example, if two competing segments both represent a surface as a set of triangular plates, the union of those sets of plates is considered to represent the surface.

    Currently only unprioritized data selection is supported. Because prioritized data selection may be the default behavior in a later version of the routine, the UNPRIORITIZED keyword is required in the `method' argument of the method `create'.

    Version and Date

    Version 1.0.0 11-JAN-2017 (NJB)

    • Field Detail

      • targetEpoch

        private TDBTime targetEpoch
      • tangentVector

        private Vector3 tangentVector
    • Constructor Detail

      • LimbPoint

        public LimbPoint​(Vector3 limbPoint,
                         Time targetEpoch,
                         Vector3 tangentVector)
                  throws SpiceException
        Create a limb point from a surface point, epoch, and observer-to limb point vector.
        Parameters:
        limbPoint - Vector3
        tangentVector - Vector3
        targetEpoch - Time
        Throws:
        SpiceException - exception
      • LimbPoint

        public LimbPoint()
        No-arguments constructor.
    • Method Detail

      • create

        public static LimbPoint[][] create​(java.lang.String method,
                                           Body target,
                                           Time et,
                                           ReferenceFrame fixref,
                                           AberrationCorrection abcorr,
                                           java.lang.String corloc,
                                           Body obsrvr,
                                           Vector3 refvec,
                                           double rolstp,
                                           int ncuts,
                                           double schstp,
                                           double soltol,
                                           int maxn)
                                    throws SpiceException
        Create an array of limb points on a specified target body, as seen from a specified observer.

        This is the principal method for constructing a representation of a limb.

        In the returned two-dimensional array, the ith row contains the limb points for the ith cutting half-plane. The rows do not necessarily have equal length.

        Inputs

           method   is a String instance providing parameters defining 
                    the computation method to be used. In the syntax 
                    descriptions below, items delimited by brackets 
                    are optional. 
         
                    `method' may be assigned the following values: 
         
                      "TANGENT/DSK/UNPRIORITIZED[/SURFACES = &ltsurface list&gt]" 
         
                          The limb point computation uses topographic data 
                          provided by DSK files (abbreviated as "DSK data" 
                          below) to model the surface of the target body. A 
                          limb point is defined as the point of tangency, on 
                          the surface represented by the DSK data, of a ray 
                          emanating from the observer. 
         
                          Limb points are generated within a specified set 
                          of "cutting" half-planes that have as an edge the 
                          line containing the observer-target vector. 
                          Multiple limb points may be found within a given 
                          half-plane, if the target body shape allows for 
                          this. 
         
                          The surface list specification is optional. The 
                          syntax of the list is 
         
                             &#60surface 1&#62 [, &#60surface 2&#62...] 
         
                          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. 
         
                          This is the highest-accuracy method supported by 
                          this subroutine. It generally executes much more 
                          slowly than the "GUIDED" method described below. 
                           
                           
                      "GUIDED/DSK/UNPRIORITIZED[/SURFACES = &#60surface list&#62]" 
         
                          This method uses DSK data as described above, but 
                          limb points generated by this method are "guided" 
                          so as to lie in the limb plane of the target 
                          body's reference ellipsoid, on the target body's 
                          surface. This method produces a unique limb point 
                          for each cutting half-plane. If multiple limb 
                          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). 
         
                          Limb 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. 
         
         
                      "TANGENT/ELLIPSOID" 
                      "GUIDED/ELLIPSOID" 
         
                          Both of these methods generate limb points on the 
                          target body's reference ellipsoid. The "TANGENT" 
                          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", these methods 
                          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\" 
         
                        
           target      is a Body instance identifying the target body. The 
                       target body is an extended ephemeris object. 
          
                       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 a Time instance representing the epoch of 
                       participation of the observer: `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 a ReferenceFrame instance representing
                       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 output limb points and observer-target tangent vectors
                       in the returned LimbPoint array are expressed relative 
                       to this reference frame. 
         
         
           abcorr      is an AberrationCorrection instance that
                       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 limb 
                       points seen by the observer are desired, normally 
                       either of the corrections 
                     
                          "LT+S"  
                          "CN+S" 
            
                       should be used. The correction "NONE" may be suitable 
                       for cases in which the target is very small and the 
                       observer is close to, and has small velocity relative 
                       to, the target (e.g. comet Churyumov-Gerasimenko and 
                       the Rosetta Orbiter). 
         
                       These and the other supported options are described 
                       below. `abcorr' may be any of the following: 
         
                          "NONE"     Apply no correction. Return the 
                                     geometric limb 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. 
         
                          "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 limb. 
         
                          "CN"       Converged Newtonian light time 
                                     correction. In solving the light time 
                                     equation, the "CN" correction iterates 
                                     until the solution converges. Both the 
                                     position and rotation of the target 
                                     body are corrected for light time. 
         
                          "CN+S"     Converged Newtonian light time and 
                                     stellar aberration corrections. This 
                                     option produces a solution that is at 
                                     least as accurate at that obtainable 
                                     with the "LT+S" option. Whether the 
                                     "CN+S" solution is substantially more 
                                     accurate depends on the geometry of the 
                                     participating objects and on the 
                                     accuracy of the input data. In all 
                                     cases this routine will execute more 
                                     slowly when a converged solution is 
                                     computed. 
         
         
           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 LIMB" option. 
         
                          "ELLIPSOID LIMB" 
         
                              Light time and stellar aberration corrections 
                              are applied to individual limb points on the 
                              reference ellipsoid. For a limb point on the 
                              surface described by topographic data, lying 
                              in a specified cutting half-plane, the unique 
                              reference ellipsoid limb 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 limb 
                              to the observer is significantly different 
                              from the light time from the target center to 
                              the observer. 
         
                              Because aberration corrections are repeated for 
                              individual limb points, computational speed for 
                              this option is relatively slow. 
         
         
           obsrvr      is a Body instance identifying
                       the observing body. The observing body 
                       is an ephemeris object: it typically is a spacecraft, 
                       the earth, or a surface point on the earth.  
         
         
           refvec, 
           rolstp, 
           ncuts       are, respectively, a reference vector, a roll step 
                       angle, and a count of cutting half-planes. 
         
                       `refvec' is a Vector3 instance that
                       defines the first of a sequence of cutting 
                       half-planes in which limb points are to be found. 
                       Each cutting half-plane has as its edge the line 
                       containing the observer-target 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 observer-target vector. 
                       The first half-plane is aligned with `refvec'; the ith 
                       half-plane is rotated from `refvec' about the 
                       observer-target vector in the counter-clockwise 
                       direction by (i-1)*rolstp. Units are radians. 
                       `rolstp' should be set to  
         
                          2*pi/ncuts  
         
                       to generate an approximately uniform distribution of 
                       limb points along the limb. 
         
                       `ncuts' is the number of cutting half-planes used to 
                       find limb points; the angular positions of 
                       consecutive half-planes increase in the positive 
                       sense (counterclockwise) about the target-observer 
                       vector 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 "ELLIPSOID LIMB", the separations are 
                       less uniform due to differences in the aberration 
                       corrections used for the respective limb 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 limb points within each cutting 
                       half plane. These values are used when the `method' 
                       argument includes the "TANGENT" option. In this case, 
                       limb points are found by a two-step search process: 
         
                          1) Bracketing: starting with the direction 
                             opposite the observer-target vector, rays 
                             emanating from the observer are generated 
                             within the half-plane at successively greater 
                             angular separations from the initial direction, 
                             where the increment of angular separation is 
                             `schstp'. The rays are tested for intersection 
                             with the target surface. When a transition 
                             between 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 
                             limb point. 
                            
            
                        `schstp' and `soltol' have units of radians. 
         
                        Target bodies with simple surfaces---for example, 
                        convex shapes---will have a single limb 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 limb points within a given cutting 
                        half-plane. To find all limb points, `schstp' must be 
                        set to a value smaller than the angular separation 
                        of any two limb points in any cutting half-plane, 
                        where the vertex of the angle is the observer. 
                        `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 limb point height errors depends 
                        on the observer-target distance. 
         
         
           maxn         is the maximum number of limb points that can be 
                        stored in the output array `points'.  
        

        Output

                        The returned LimbPoint array contains
                        the limb points found by this routine. The sets of limb 
                        points associated with the ith half-plane is contained
                        in the ith row of the returned array. The rows need not
                        have equal length. 
        
                        The limb points in a given half-plane are ordered by 
                        decreasing angular separation from the observer-target 
                        direction; the outermost limb point in a given half-plane 
                        is the first of that set. 
         
                        The limb points for the half-plane containing `refvec' 
                        occupy the first row of the output array 
         
                        Limb points are expressed in the reference frame 
                        designated by `fixref'. For each limb point, the 
                        orientation of the frame is evaluated at the epoch 
                        corresponding to the limb point.
        

        Method `create' Particulars

        Syntax of the `method' input argument

        The keywords and surface list in the `method' argument of `create' are called "clauses." The clauses may appear in any order, for example

         
                 TANGENT/DSK/UNPRIORITIZED/&#60surface list&#62
                 DSK/TANGENT/&#60surface list&#62/UNPRIORITIZED 
                 UNPRIORITIZED/&#60surface list&#62/DSK/TANGENT 
        
        The simplest form of the `method' argument specifying use of DSK data is one that lacks a surface list, for example:
                 "TANGENT/DSK/UNPRIORITIZED" 
                 "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
              "NADIR/DSK/UNPRIORITIZED/SURFACES= \"Mars MEGDR 64 PIXEL/DEG\",3" 
        

        Code 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 limb points on Phobos as seen from Mars.

          Due to Phobos' irregular shape, the TANGENT limb 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 limb 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 limb 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 limb points would be much greater.

        Use the meta-kernel shown below to load the required SPICE kernels.
        KPL/MK
        
        File: LimbPointEx1.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
          naif0012.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',
                              'naif0012.tls',
                              '$GEN/dsk/phobos/phobos512.bds' )
        \begintext
        
        
        Example code begins here.
        
        
        //
        // Program LimbPointEx1
        //
        
        import spice.basic.*;
        import static spice.basic.AngularUnits.*;
        import static java.lang.Math.PI;
        
        //
        // Find apparent limb points on Phobos as seen from Mars. 
        //
        public class LimbPointEx1
        {
           //
           // Load SPICE shared library.
           //
           static{ System.loadLibrary( "JNISpice" ); }
        
        
           public static void main( String[] args )
        
              throws SpiceException
           {
              //
              // Local constants
              //
              final String                      META   = "LimbPointEx1.tm";
        
              final int                         MAXN   = 10000;
              final int                         NMETH  = 2;
        
              //
              // Local variables
              //
              AberrationCorrection              abcorr = 
                                                   new AberrationCorrection( "CN+S" );
        
              Body                              obsrvr = new Body( "MARS"   );
              Body                              target = new Body( "PHOBOS" );
              
              LimbPoint[][]                     limbPoints;
        
              ReferenceFrame                    fixref =
                                                   new ReferenceFrame( "IAU_PHOBOS" );
        
              String[]                          methds = {
                                                            "TANGENT/ELLIPSOID",
                                                            "TANGENT/DSK/UNPRIORITIZED" 
                                                         };
        
              String                            corloc = "CENTER";
              String                            utc    = "2008 AUG 11 00:00:00 UTC";
        
              TDBTime                           et;
              TDBTime                           trgepc;
        
              Vector3                           z      = new Vector3( 0.0, 0.0, 1.0 );
        
              double                            delrol;  
              double[]                          pointArray;
              double                            roll;
              double                            schstp;
              double                            soltol;
        
              int                               i;
              int                               j;
              int                               k;
              int                               ncuts;
              int                               npts;
        
        
              try
              {
                 //
                 // Load kernels.
                 //
                 KernelDatabase.load( META );
        
                 //
                 // Convert the UTC request time to ET (seconds past
                 // J2000, TDB). 
                 //
                 et = new TDBTime( utc );
        
                 //
                 // Compute a set of limb points using light time and
                 // stellar aberration corrections. Use both ellipsoid
                 // and DSK shape models. Use a step size of 100
                 // microradians to ensure we don't miss the limb.
                 // Set the convergence tolerance to 100 nanoradians,
                 // which will limit the height error to about 1 meter.
                 // Compute 3 limb points for each computation method.
                 //
                 schstp = 1.0e-4;
                 soltol = 1.0e-7;
                 ncuts  = 3;
        
                 System.out.format ( "%n"                   +
                                     "Observer:       %s%n" +
                                     "Target:         %s%n" +
                                     "Frame:          %s%n" +
                                     "%n"                   +
                                     "Number of cuts: %d%n",
                                     obsrvr.getName(),
                                     target.getName(),
                                     fixref.getName(),
                                     ncuts                  );
        
                 delrol = 2*PI / ncuts;
        
                 for ( i = 0;  i &lt NMETH;  i++ )
                 {
                    //
                    // Compute a set of limb points using the current
                    // computation method.
                    //
                    limbPoints = 
        
                       LimbPoint.create( methds[i], target, et,     fixref,
                                         abcorr,    corloc, obsrvr, z,
                                         delrol,    ncuts,  schstp, soltol,
                                         MAXN                               );
                    //
                    // Write the results.
                    //
                    System.out.format ( "%n%n"                      +
                                        "Computation method = %s%n" +
                                        "Locus              = %s%n", 
                                        methds[i],
                                        corloc                       );
        
                    for ( j = 0;  j &lt ncuts;  j++ )
                    {
                       //
                       // Display the roll angle, target epoch, and limb point
                       // count for the current cutting half-plane. Note that
                       // the epoch associated with the first limb point applies
                       // to all points in the current half-plane.
                       //
                       roll   = j * delrol;
                       npts   = limbPoints[j].length;
                       trgepc = limbPoints[j][0].getTargetEpoch();
        
                       System.out.format ( "%n"                                  +
                                           "  Roll angle (deg) = %21.9f%n"       +
                                           "     Target epoch  = %21.9f%n"       +
                                           "     Number of limb points at this " +
                                           "roll angle: %d%n",
                                           roll * DPR,
                                           trgepc.getTDBSeconds(),
                                           npts                                    );
        
                       System.out.format ( "      Limb points%n" );
        
                       for ( k = 0;  k &lt npts;  k++ )
                       {
                          pointArray = limbPoints[j][k].toArray();
        
                          System.out.format ( " %20.9f %20.9f %20.9f%n",
                                              pointArray[0],
                                              pointArray[1],
                                              pointArray[2]               );
        
                       } // End of loop for current cut.
        
                    } // End of loop for limb, using current method.
                 
                 } // End of method loop.
                 
                 System.out.format ( "%n" );
        
              } // End of try block
        
              catch ( SpiceException exc )
              {
                 exc.printStackTrace();
              }
        
           } // End of main method 
        }
        
        

        When this program was executed on a PC/Linux/gcc/64-bit/java 1.5 platform, the output was:

        
        Observer:       MARS
        Target:         PHOBOS
        Frame:          IAU_PHOBOS
        
        Number of cuts: 3
        
        
        Computation method = TANGENT/ELLIPSOID
        Locus              = CENTER
        
          Roll angle (deg) =           0.000000000
             Target epoch  =   271684865.152078200
             Number of limb points at this roll angle: 1
              Limb points
                  0.016445326         -0.000306114          9.099992715
        
          Roll angle (deg) =         120.000000000
             Target epoch  =   271684865.152078200
             Number of limb points at this roll angle: 1
              Limb points
                 -0.204288375         -9.235230829         -5.333237706
        
          Roll angle (deg) =         240.000000000
             Target epoch  =   271684865.152078200
             Number of limb points at this roll angle: 1
              Limb points
                  0.242785221          9.234520095         -5.333231253
        
        
        Computation method = TANGENT/DSK/UNPRIORITIZED
        Locus              = CENTER
        
          Roll angle (deg) =           0.000000000
             Target epoch  =   271684865.152078200
             Number of limb points at this roll angle: 1
              Limb points
                 -0.398901673          0.007425178          9.973720555
        
          Roll angle (deg) =         120.000000000
             Target epoch  =   271684865.152078200
             Number of limb points at this roll angle: 1
              Limb points
                 -0.959300281         -8.537573427         -4.938700447
        
          Roll angle (deg) =         240.000000000
             Target epoch  =   271684865.152078200
             Number of limb points at this roll angle: 1
              Limb points
                 -1.380536729          9.714334047         -5.592916790
        
        

        Find apparent limb points on Mars as seen from the earth. Compare results using different computation options.

        Use both the "TANGENT" and "GUIDED" limb point definitions. For the tangent limb points, use the "ELLIPSOID LIMB" aberration correction locus; for the guided limb points, use the "CENTER" locus. For the "GUIDED" limb points, also compute the distance of each point from the corresponding point computed using the "TANGENT" definition.

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

        Check the limb points by computing the apparent emission angles at each limb point.

        For the ellipsoid shape model, we expect emission angles very close to 90 degrees, since each illumination angle calculation is done using aberration corrections for the limb point at which the angles are measured.

        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 limb 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 limb points would be much greater.

        Use the meta-kernel shown below.

        KPL/MK 
        
        File: LimbPointEx2.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 
           naif0012.tls                     Leapseconds 
           megr90n000cb_plate.bds           DSK plate model based on 
                                            MGS MOLAR MEGDR DEM,  
                                            resolution 4  
                                            pixels/degree. 
        
        \begindata 
        
           KERNELS_TO_LOAD = ( 'de430.bsp', 
                               'mar097.bsp', 
                               'pck00010.tpc', 
                               'naif0012.tls', 
                               'megr90n000cb_plate.bds' ) 
        \begintext 
        
        

        Example code begins here.

        
        //
        // Program LimbPointEx2
        //
        
        import spice.basic.*;
        import static spice.basic.AngularUnits.*;
        import static java.lang.Math.PI;
        
        //
        // Find apparent limb points on Mars as seen from Earth. 
        // Compare results using different computation options. 
        //
        public class LimbPointEx2
        {
           //
           // Load SPICE shared library.
           //
           static{ System.loadLibrary( "JNISpice" ); }
        
        
           public static void main( String[] args )
        
              throws SpiceException
           {
              //
              // Local constants
              //
              final String                      META   = "LimbPointEx2.tm";
        
              final int                         MAXN   = 10000;
              final int                         NMETH  = 3;
        
              //
              // Local variables
              //
              AberrationCorrection              abcorr = 
                                                   new AberrationCorrection( "CN+S" );
        
              Body                              obsrvr = new Body( "EARTH" );
              Body                              target = new Body( "MARS"  );
              
              GeodeticCoordinates               geoCoords;
        
              IlluminationAngles                iluAng;
        
              LimbPoint[][]                     limbPoints;
              LimbPoint[][]                     svPoints = new LimbPoint[MAXN][1];
        
              PositionRecord                    pr;
        
              ReferenceFrame                    fixref =
                                                   new ReferenceFrame( "IAU_MARS" );
        
              String[]                          corloc = {
                                                            "ELLIPSOID LIMB",
                                                            "ELLIPSOID LIMB",
                                                            "CENTER"
                                                         };
        
              String[]                          ilumth = { 
                                                            "ELLIPSOID",
                                                            "DSK/UNPRIORITIZED",
                                                            "DSK/UNPRIORITIZED"  
                                                         };
        
              String[]                          methds = {
                                                           "TANGENT/ELLIPSOID",
                                                           "TANGENT/DSK/UNPRIORITIZED",
                                                           "GUIDED/DSK/UNPRIORITIZED" 
                                                         };
        
              String                            utc    = "2008 AUG 11 00:00:00 UTC";
        
              TDBTime                           et;
              TDBTime                           trgepc;
        
              Vector3                           z      = new Vector3( 0.0, 0.0, 1.0 );
        
              double                            delrol;  
              double                            dist;
              double                            emissn;
              double                            f;
              double[]                          pointArray;
              double[]                          radii;
              double                            re;
              double                            rp;
              double                            roll;
              double                            schstp;
              double                            soltol;
        
              int                               i;
              int                               j;
              int                               k;
              int                               ncuts;
              int                               npts;
        
        
              try
              {
                 //
                 // Load kernels.
                 //
                 KernelDatabase.load( META );
        
                 //
                 // Convert the UTC request time to ET (seconds past
                 // J2000, TDB). 
                 //
                 et = new TDBTime( utc );
        
                 //
                 // 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.
                 // 
                 radii = target.getValues( "RADII" );
        
                 //
                 // Compute the flattening coefficient for planetodetic
                 // coordinates.
                 //
                 re = radii[0];
                 rp = radii[2];
                 f  = ( re - rp ) / re;
                
                 //
                 // Obtain the observer-target distance at `et'.
                 // 
                 pr   = new PositionRecord( target, et, fixref, abcorr, obsrvr );
        
                 dist = pr.norm();
         
                 //
                 // Compute a set of limb points using light time and
                 // stellar aberration corrections. Use both ellipsoid
                 // and DSK shape models.
                 //
                 //  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
                 // limb points in any cutting half-plane.
                 // 
                 schstp = 4.0;
        
                 //
                 // Set the convergence tolerance to minimize the height
                 // error. We can't achieve the 1 millimeter precision
                 // suggested by the formula because the earth-Mars
                 // distance is about 3.5e8 km. 
                 //
                 // Compute 3 limb points for each computation method.
                 //
                 soltol = 1.0e-6 / dist;
        
                 //
                 // Set the number of cutting half-planes and roll step.
                 //
                 ncuts  = 3;
                 delrol = ( 2 * Math.PI ) / ncuts;
        
                 System.out.format ( "%n"                   +
                                     "Observer:       %s%n" +
                                     "Target:         %s%n" +
                                     "Frame:          %s%n" +
                                     "%n"                   +
                                     "Number of cuts: %d%n",
                                     obsrvr.getName(),
                                     target.getName(),
                                     fixref.getName(),
                                     ncuts                  );
        
                 delrol = 2*PI / ncuts;
        
                 for ( i = 0;  i &lt NMETH;  i++ )
                 {
                    //
                    // Compute a set of limb points using the current
                    // computation method.
                    //
                    limbPoints = 
        
                       LimbPoint.create( methds[i], target,    et,     fixref,
                                         abcorr,    corloc[i], obsrvr, z,
                                         delrol,    ncuts,     schstp, soltol,
                                         MAXN                                 );
        
                    //
                    // If we're using the TANGENT/DSK/UNPRIORITIZED method,
                    // save the limb points for later use.
                    //
                    if ( i == 1 )
                    {
                       svPoints = new LimbPoint[ncuts][0];
        
                       for ( j = 0;  j &lt ncuts;  j++ )
                       {
                          npts        = limbPoints[j].length;
                          svPoints[j] = new LimbPoint[npts];
        
                          for ( k = 0;  k &lt npts;  k++ )
                          {
                             svPoints[j][k] = limbPoints[j][k];
                          }
                       }
                    }
        
                    //
                    // Write the results.
                    //
                    System.out.format ( "%n%n"                      +
                                        "Computation method = %s%n" +
                                        "Locus              = %s%n", 
                                        methds[i],
                                        corloc[i]                    );
        
                    for ( j = 0;  j &lt ncuts;  j++ )
                    {
                       //
                       // Display the roll angle, target epoch, and limb point
                       // count for the current cutting half-plane. Note that
                       // the epoch associated with the first limb point applies
                       // to all points in the current half-plane.
                       //
                       roll   = j * delrol;
                       npts   = limbPoints[j].length;
                       trgepc = limbPoints[j][0].getTargetEpoch();
        
                       System.out.format ( "%n"                                  +
                                           "  Roll angle (deg) = %21.9f%n"       +
                                           "     Target epoch  = %21.9f%n"       +
                                           "     Number of limb points at this " +
                                           "roll angle: %d%n",
                                           roll * DPR,
                                           trgepc.getTDBSeconds(),
                                           npts                                    );
        
        
                       for ( k = 0;  k &lt npts;  k++ )
                       {
                          geoCoords = new GeodeticCoordinates( limbPoints[j][k], re, f);
        
                          System.out.format ( "      Limb point planetodetic " +
                                              "coordinates:%n"                  );
        
                          System.out.format ( 
                                   "       Longitude      (deg): %21.9f%n" + 
                                   "       Latitude       (deg): %21.9f%n" + 
                                   "       altitude        (km): %21.9f5%n",
                                   geoCoords.getLongitude()*DPR, 
                                   geoCoords.getLatitude() *DPR, 
                                   geoCoords.getAltitude()                    );
                          //
                          // Get illumination angles for this limb point. 
                          //
                          iluAng = 
        
                             new IlluminationAngles ( ilumth[i], target, et,
                                                      fixref,    abcorr, obsrvr,
                                                      limbPoints[j][k]          );
        
                          System.out.format ( "       Emission angle (deg): %21.9f%n",
                                              iluAng.getEmissionAngle()*DPR           );
        
                          //
                          // Show the difference between the GUIDED and TANGENT
                          // results when a DSK model is used.
                          //
                          if ( i == 2 ) 
                          {
                             dist = limbPoints[j][k].dist( svPoints[j][k] );
        
                             System.out.format ( "       Distance error  (km): " +
                                                 "%21.9f%n",
                                                 dist                           );
                          }
        
                       } // End of loop for current cut.
        
                    } // End of loop for limb, using current method.
                 
                 } // End of method loop.
                 
                 System.out.format ( "%n" );
        
              } // End of try block
        
              catch ( SpiceException exc )
              {
                 exc.printStackTrace();
              }
        
           } // End of main method 
           
        }
        
        

        When this program was executed on a PC/Linux/gcc/64-bit/java 1.5 platform, the output was:

        
        Observer:       EARTH
        Target:         MARS
        Frame:          IAU_MARS
        
        Number of cuts: 3
        
        
        Computation method = TANGENT/ELLIPSOID
        Locus              = ELLIPSOID LIMB
        
          Roll angle (deg) =           0.000000000
             Target epoch  =   271683700.368869900
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):         -19.302258950
               Latitude       (deg):          64.005620446
               altitude        (km):          -0.0000000005
               Emission angle (deg):          90.000000000
        
          Roll angle (deg) =         120.000000000
             Target epoch  =   271683700.368948160
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):          85.029135674
               Latitude       (deg):         -26.912378799
               altitude        (km):           0.0000000005
               Emission angle (deg):          90.000000000
        
          Roll angle (deg) =         240.000000000
             Target epoch  =   271683700.368949800
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):        -123.633654215
               Latitude       (deg):         -26.912378799
               altitude        (km):          -0.0000000005
               Emission angle (deg):          90.000000000
        
        
        Computation method = TANGENT/DSK/UNPRIORITIZED
        Locus              = ELLIPSOID LIMB
        
          Roll angle (deg) =           0.000000000
             Target epoch  =   271683700.368869900
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):         -19.302258949
               Latitude       (deg):          63.893637432
               altitude        (km):          -3.6675539585
               Emission angle (deg):          89.979580513
        
          Roll angle (deg) =         120.000000000
             Target epoch  =   271683700.368948160
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):          85.434644181
               Latitude       (deg):         -26.705411232
               altitude        (km):          -0.0448323825
               Emission angle (deg):          88.089500425
        
          Roll angle (deg) =         240.000000000
             Target epoch  =   271683700.368949800
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):        -123.375003592
               Latitude       (deg):         -27.043096738
               altitude        (km):           3.6956284895
               Emission angle (deg):          89.875890611
        
        
        Computation method = GUIDED/DSK/UNPRIORITIZED
        Locus              = CENTER
        
          Roll angle (deg) =           0.000000000
             Target epoch  =   271683700.368922530
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):         -19.302259163
               Latitude       (deg):          64.005910146
               altitude        (km):          -3.6764245525
               Emission angle (deg):          89.979580513
               Distance error  (km):           6.664208540
        
          Roll angle (deg) =         120.000000000
             Target epoch  =   271683700.368922530
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):          85.029135792
               Latitude       (deg):         -26.912405352
               altitude        (km):          -0.3289889155
               Emission angle (deg):          91.525256314
               Distance error  (km):          24.686472888
        
          Roll angle (deg) =         240.000000000
             Target epoch  =   271683700.368922530
             Number of limb points at this roll angle: 1
              Limb point planetodetic coordinates:
               Longitude      (deg):        -123.633653487
               Latitude       (deg):         -26.912086524
               altitude        (km):           3.6260588505
               Emission angle (deg):          89.809897171
               Distance error  (km):          15.716056568
        
        

        Find apparent limb points on comet Churyumov-Gerasimenko as seen from the Rosetta orbiter.

        This computation is an example of a case for which some of the cutting half-planes contain multiple limb points.

        Use the "TANGENT" limb definition, since the target shape is not well approximated by its reference ellipsoid. Use the "CENTER" aberration correction locus since the light time difference across the object is small.

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

        KPL/MK
        
        File: LimbPointEx3.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
        paths of the kernels referenced here must be adjusted to
        be compatible with the user's host computer directory
        structure.
        
        The names and contents of the kernels referenced
        by this meta-kernel are as follows:
        
          File name                          Contents
          ---------                          --------
          DE405.BSP                          Planetary ephemeris
          NAIF0011.TLS                       Leapseconds
          ROS_CG_M004_NSPCESA_N_V1.BDS       DSK plate model based on
                                             Rosetta NAVCAM data
          RORB_DV_145_01_______00216.BSP     Rosetta orbiter
                                             ephemeris
          CORB_DV_145_01_______00216.BSP     Comet Churyumov-
                                             Gerasimenko ephemeris
          ROS_CG_RAD_V10.TPC                 Comet Churyumov-
                                             Gerasimenko radii
          ROS_V25.TF                         Comet C-G frame kernel
                                             (includes SCLK
                                             parameters)
          CATT_DV_145_01_______00216.BC      Comet C-G C-kernel
        
        
        \begindata
        
           PATH_VALUES     = (
        
              '/ftp/pub/naif/pds/data/+'
              'ro_rl-e_m_a_c-spice-6-v1.0/rossp_1000/DATA'
        
                             )
        
           PATH_SYMBOLS    = (
        
              'KERNELS'
                             )
        
           KERNELS_TO_LOAD = (
        
              '$KERNELS/SPK/DE405.BSP'
              '$KERNELS/LSK/NAIF0011.TLS'
              '$KERNELS/SPK/RORB_DV_145_01_______00216.BSP'
              '$KERNELS/SPK/CORB_DV_145_01_______00216.BSP'
              '$KERNELS/PCK/ROS_CG_RAD_V10.TPC'
              '$KERNELS/FK/ROS_V25.TF'
              '$KERNELS/CK/CATT_DV_145_01_______00216.BC'
              '$KERNELS/DSK/ROS_CG_M004_NSPCESA_N_V1.BDS'
        
                             )
        \begintext
        
        
        

        Example code begins here.

        
        //
        // Program LimbPointEx3
        //
        
        import spice.basic.*;
        import static spice.basic.AngularUnits.*;
        import static java.lang.Math.PI;
        
        //
        // Find limb points on comet Churyumov-Gerasimenko
        // as seen from the Rosetta orbiter.
        //
        public class LimbPointEx3
        {
           //
           // Load SPICE shared library.
           //
           static{ System.loadLibrary( "JNISpice" ); }
        
        
           public static void main( String[] args )
        
              throws SpiceException
           {
              //
              // Local constants
              //
              final String                      META   = "LimbPointEx3.tm";
        
              final int                         MAXN   = 10000;
              final int                         NMETH  = 2;
        
              //
              // Local variables
              //
              AberrationCorrection              abcorr = 
                                                   new AberrationCorrection( "CN+S" );
        
              Body                              obsrvr = new Body( "ROSETTA" );
        
              Body                              target =
        
                                                   new Body( "CHURYUMOV-GERASIMENKO" );
              
              LimbPoint[][]                     limbPoints;
        
              PositionVector                    trgpos;
        
              ReferenceFrame                    fixref =
                                                   new ReferenceFrame( "67P/C-G_CK" );
        
              String                            method = "TANGENT/DSK/UNPRIORITIZED";
        
              String                            corloc = "CENTER";
              String                            utc    = "2015 MAY 10 00:00:00 UTC";
        
              TDBTime                           et;
              TDBTime                           trgepc;
        
              Vector3                           axis;
              Vector3                           refvec;
              Vector3                           xvec   = new Vector3( 1.0, 0.0, 0.0 );
        
              double                            angle;
              double                            delrol;  
              double[]                          pointArray;
              double                            roll;
              double                            schstp;
              double                            soltol;
        
              int                               i;
              int                               j;
              int                               ncuts;
              int                               npts;
        
        
              try
              {
                 //
                 // Load kernels.
                 //
                 KernelDatabase.load( META );
        
                 //
                 // Convert the UTC request time to ET (seconds past
                 // J2000, TDB). 
                 //
                 et = new TDBTime( utc );
        
                 //
                 // Compute a set of limb points using light time and
                 // stellar aberration corrections. Use a step size 
                 // corresponding to a 1 meter height error to ensure 
                 // we don't miss the limb. Set the convergence tolerance 
                 // to 1/100 of this amount, which will limit the height 
                 // convergence error to about 1 cm.
                 //
                 trgpos = new PositionVector( target, et,    fixref, 
                                              abcorr, obsrvr        );
        
                 schstp = 1.0e-3 / trgpos.norm();
                 soltol = schstp / 100.0;
        
                 //
                 // Set the reference vector to the start of a
                 // region of the roll domain in which we know
                 // (from an external computation) that we'll
                 // find multiple limb points in some half planes.
                 // Compute 30 limb points, starting with the
                 // half-plane containing the reference vector.
                 //
                 axis   = trgpos.negate();
                 angle  = 310.0 * RPD;
        
                 refvec = xvec.rotate( axis, angle );
        
                 ncuts  = 30;
                 delrol = 2*PI / 1000.0;
               
        
                 System.out.format ( "%n"                   +
                                     "Observer:       %s%n" +
                                     "Target:         %s%n" +
                                     "Frame:          %s%n" +
                                     "%n"                   +
                                     "Number of cuts: %d%n",
                                     obsrvr.getName(),
                                     target.getName(),
                                     fixref.getName(),
                                     ncuts                  );
                 //
                 // Compute limb points.
                 //
                 limbPoints = LimbPoint.create( method, target, et,     fixref,
                                                abcorr, corloc, obsrvr, refvec, 
                                                delrol, ncuts,  schstp, soltol,
                                                MAXN                           );
                 //
                 // Write the results.
                 //
                 System.out.format ( "%n%n"                      +
                                     "Computation method = %s%n" +
                                     "Locus              = %s%n", 
                                     method,
                                     corloc                       );
        
                 for ( i = 0;  i &lt ncuts;  i++ )
                 {
                    //
                    // Display the roll angle, target epoch, and limb point
                    // count for the current cutting half-plane. Note that
                    // the epoch associated with the lowest-indexed limb point 
                    // applies to all points in the current half-plane.
                    //
                    roll   = i * delrol;
                    npts   = limbPoints[i].length;
                    trgepc = limbPoints[i][0].getTargetEpoch();
        
                    System.out.format ( "%n"                                  +
                                        "  Roll angle (deg) = %21.9f%n"       +
                                        "     Target epoch  = %21.9f%n"       +
                                        "     Number of limb points at this " +
                                        "roll angle: %d%n",
                                        roll * DPR,
                                        trgepc.getTDBSeconds(),
                                        npts                                    );
        
                    System.out.format ( "      Limb points%n" );
        
                    for ( j = 0;  j &lt npts;  j++ )
                    {
                       pointArray = limbPoints[i][j].toArray();
        
                       System.out.format ( " %20.9f %20.9f %20.9f%n",
                                           pointArray[0],
                                           pointArray[1],
                                           pointArray[2]               );
        
                    } // End of loop for current cut.
        
                 } // End of loop for limb.
                 
                 System.out.format ( "%n" );
        
              } // End of try block
        
              catch ( SpiceException exc )
              {
                 exc.printStackTrace();
              }
        
           } // End of main method 
           
        }
        
        

        When this program was executed on a PC/Linux/gcc/64-bit/java 1.5 platform, the output was (only the first three and last three limb points are shown here):

        
        Observer:       ROSETTA ORBITER
        Target:         CHURYUMOV-GERASIMENKO
        Frame:          67P/C-G_CK
        
        Number of cuts: 30
        
        
        Computation method = TANGENT/DSK/UNPRIORITIZED
        Locus              = CENTER
        
          Roll angle (deg) =           0.000000000
             Target epoch  =   484488067.184933800
             Number of limb points at this roll angle: 3
              Limb points
                  1.320362370         -0.347604560          1.445254172
                  0.970323084          0.201631414          0.961979719
                  0.436713864          0.048193273          0.442280570
        
          Roll angle (deg) =           0.360000000
             Target epoch  =   484488067.184933800
             Number of limb points at this roll angle: 3
              Limb points
                  1.330124598         -0.352820747          1.438735635
                  0.965299850          0.201734528          0.946088598
                  0.453749999          0.081575117          0.447557495
        
          Roll angle (deg) =           0.720000000
             Target epoch  =   484488067.184933800
             Number of limb points at this roll angle: 3
              Limb points
                  1.338848631         -0.358372459          1.431175507
                  0.961970200          0.192000406          0.934228157
                  0.458205425          0.079784540          0.447433687
        
             ...
        
          Roll angle (deg) =           9.720000000
             Target epoch  =   484488067.184933800
             Number of limb points at this roll angle: 3
              Limb points
                  1.567889849         -0.675587383          1.254779196
                  0.709821051         -0.111518380          0.547753702
                  0.491097248         -0.144183621          0.385975970
        
          Roll angle (deg) =          10.080000000
             Target epoch  =   484488067.184933800
             Number of limb points at this roll angle: 3
              Limb points
                  1.583510591         -0.668467845          1.249125044
                  0.633077981         -0.300058272          0.502702168
                  0.254698631         -0.760413229          0.266773664
        
          Roll angle (deg) =          10.440000000
             Target epoch  =   484488067.184933800
             Number of limb points at this roll angle: 3
              Limb points
                  1.599288724         -0.662045674          1.243576395
                  0.633123187         -0.293598781          0.495368615
                  0.271957881         -0.762004976          0.274621861
        
        
        Parameters:
        method - String
        maxn - int
        target - Body
        soltol - double
        et - Time
        schstp - double
        fixref - ReferenceFrame
        ncuts - int
        abcorr - AberrationCorrection
        rolstp - double
        corloc - String
        refvec - Vector3
        obsrvr - Body
        Returns:
        LimbPoint[][]
        Throws:
        SpiceException - exeption
      • getTargetEpoch

        public TDBTime getTargetEpoch()
        Return the target epoch from a LimbPoint instance.This method returns a deep copy.
        Returns:
        TDBTime
      • getTangentVector

        public Vector3 getTangentVector()
        Return the observer to limb point vector from a LimbPoint instance.This method returns a deep copy.
        Returns:
        Vector3