cspice_gfsep |
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## AbstractCSPICE_GFSEP determines the time intervals when the angular separation between the position vectors of two target bodies relative to an observer satisfies a numerical relationship. For important details concerning this module's function, please refer to the CSPICE routine gfsep_c. ## I/OGiven: Parameters- All parameters described here are declared in the header file SpiceGF.h. See that file for parameter values. SPICE_GF_CNVTOL is the convergence tolerance used for finding endpoints of the intervals comprising the result window. SPICE_GF_CNVTOL is used to determine when binary searches for roots should terminate: when a root is bracketed within an interval of length SPICE_GF_CNVTOL, the root is considered to have been found. The accuracy, as opposed to precision, of roots found by this routine depends on the accuracy of the input data. In most cases, the accuracy of solutions will be inferior to their precision. Arguments- targ1 the scalar string naming the first body of interest. You can also supply the integer ID code for the object as an integer string. For example both 'MOON' and '301' are legitimate strings that indicate the moon is the target body. shape1 the scalar string naming the geometric model used to represent the shape of the 'targ1' body. Models supported by this routine: 'SPHERE' Treat the body as a sphere with radius equal to the maximum value of BODYnnn_RADII 'POINT' Treat the body as a point; radius has value zero. The 'shape1' string lacks sensitivity to case, leading and trailing blanks. frame1 the scalar string naming the body-fixed reference frame corresponding to 'targ1'. ## ExamplesAny 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. Determine the times of local maxima of the angular separation between the moon and sun as observed from earth from Jan 1, 2007 to Jan 1 2008. MAXWIN = 1000 TIMFMT = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND' TIMLEN = 41 ;; ;; Load kernels. ;; cspice_furnsh, 'standard.tm' ;; ;; Store the time bounds of our search interval in ;; the cnfine confinement window. ;; cspice_str2et, [ '2007 JAN 01', '2008 JAN 01'], et cnfine = cspice_celld( 2 ) cspice_wninsd, et[0], et[1], cnfine ;; ;; Search using a step size of 6 days (in units of seconds). ;; step = 6.D*cspice_spd() adjust = 0.D refval = 0.D targ1 = 'MOON' shape1 = 'SPHERE' frame1 = 'NULL' targ2 = 'SUN' shape2 = 'SPHERE' frame2 = 'NULL' abcorr = 'NONE' relate = 'LOCMAX' obsrvr = 'EARTH' nintvls= MAXWIN result = cspice_celld( MAXWIN*2) ## ParticularsThis routine provides a simple interface for conducting searches for angular separation events. This routine determines a set of one or more time intervals within the confinement window for which the angular separation between the two bodies satisfies some defined relationship. The resulting set of intervals is returned as a Icy window. Below we discuss in greater detail aspects of this routine's solution process that are relevant to correct and efficient use of this routine in user applications. The Search Process ================== Regardless of the type of constraint selected by the caller, this routine starts the search for solutions by determining the time periods, within the confinement window, over which the specified angular separation function is monotone increasing and monotone decreasing. Each of these time periods is represented by a Icy window. Having found these windows, all of the angular separation function's local extrema within the confinement window are known. Absolute extrema then can be found very easily. Within any interval of these "monotone" windows, there will be at most one solution of any equality constraint. Since the boundary of the solution set for any inequality constraint is contained in the union of - the set of points where an equality constraint is met - the boundary points of the confinement window the solutions of both equality and inequality constraints can be found easily once the monotone windows have been found. Step Size ========= The monotone windows (described above) are found using a two-step search process. Each interval of the confinement window is searched as follows: first, the input step size is used to determine the time separation at which the sign of the rate of change of angular separation (angular separation rate) will be sampled. Starting at the left endpoint of an interval, samples will be taken at each step. If a change of sign is found, a root has been bracketed; at that point, the time at which the angular separation rate is zero can be found by a refinement process, for example, using a binary search. Note that the optimal choice of step size depends on the lengths of the intervals over which the distance function is monotone: the step size should be shorter than the shortest of these intervals (within the confinement window). The optimal step size is *not* necessarily related to the lengths of the intervals comprising the result window. For example, if the shortest monotone interval has length 10 days, and if the shortest result window interval has length 5 minutes, a step size of 9.9 days is still adequate to find all of the intervals in the result window. In situations like this, the technique of using monotone windows yields a dramatic efficiency improvement over a state-based search that simply tests at each step whether the specified constraint is satisfied. The latter type of search can miss solution intervals if the step size is longer than the shortest solution interval. Having some knowledge of the relative geometry of the target and observer can be a valuable aid in picking a reasonable step size. In general, the user can compensate for lack of such knowledge by picking a very short step size; the cost is increased computation time. Note that the step size is not related to the precision with which the endpoints of the intervals of the result window are computed. That precision level is controlled by the convergence tolerance. Convergence Tolerance ===================== As described above, the root-finding process used by this routine involves first bracketing roots and then using a search process to locate them. "Roots" are both times when local extrema are attained and times when the distance function is equal to a reference value. All endpoints of the intervals comprising the result window are either endpoints of intervals of the confinement window or roots. Once a root has been bracketed, a refinement process is used to narrow down the time interval within which the root must lie. This refinement process terminates when the location of the root has been determined to within an error margin called the "convergence tolerance." The convergence tolerance used by this routine is set by the parameter SPICE_GF_CNVTOL. The value of SPICE_GF_CNVTOL is set to a "tight" value so that the tolerance doesn't become the limiting factor in the accuracy of solutions found by this routine. In general the accuracy of input data will be the limiting factor. The user may change the convergence tolerance from the default SPICE_GF_CNVTOL value by calling the routine cspice_gfstol, e.g. cspice_gfstol, tolerance value in seconds Call cspice_gfstol prior to calling this routine. All subsequent searches will use the updated tolerance value. Setting the tolerance tighter than SPICE_GF_CNVTOL is unlikely to be useful, since the results are unlikely to be more accurate. Making the tolerance looser will speed up searches somewhat, since a few convergence steps will be omitted. However, in most cases, the step size is likely to have a much greater affect on processing time than would the convergence tolerance. The Confinement Window ====================== The simplest use of the confinement window is to specify a time interval within which a solution is sought. However, the confinement window can, in some cases, be used to make searches more efficient. Sometimes it's possible to do an efficient search to reduce the size of the time period over which a relatively slow search of interest must be performed. Elongation =========================== The angular separation of two targets as seen from an observer where one of those targets is the sun is known as elongation. ## Required ReadingICY.REQ GF.REQ SPK.REQ CK.REQ TIME.REQ WINDOWS.REQ ## Version-Icy Version 1.0.2, 05-SEP-2012, EDW (JPL) Edit to comments to correct search description. Header updated to describe use of cspice_gfstol. -Icy Version 1.0.1, 29-DEC-2009, EDW (JPL) Edited argument descriptions. Removed mention of "ELLIPSOID" shape from 'shape1' and 'shape2' as that option is not yet implemented. -Icy Version 1.0.0, 15-APR-2009, NJB EDW (JPL) ## Index_EntriesGF angular separation search |

Wed Apr 5 17:58:01 2017