cspice_gfpa |
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## AbstractCSPICE_GFPA determines time intervals for which a specified constraint on the phase angle between an illumination source, a target, and observer body centers is met. ## 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- target name of the target body. Optionally, you may 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. [1,c1] = size(target); char = class(target) or [1,1] = size(target); cell = class(target) Case and leading or trailing blanks are not significant in the string 'target'. illmn name of the illuminating body. This will normally be "SUN" but the algorithm can use any ephemeris object [1,c2] = size(illmn); char = class(illmn) or [1,1] = size(illmn); cell = class(illmn) Case and leading or trailing blanks are not significant in the string 'illmn'. abcorr describes the aberration corrections to apply to the state evaluations to account for one-way light time and stellar aberration. [1,c3] = size(abcorr); char = class(abcorr) or [1,1] = size(abcorr); cell = class(abcorr) This routine accepts only reception mode aberration corrections. See the header of spkezr_c for a detailed description of the aberration correction options. For convenience, the allowed aberration options are listed below: 'NONE' Apply no correction. 'LT' "Reception" case: correct for one-way light time using a Newtonian formulation. 'LT+S' "Reception" case: correct for one-way light time and stellar aberration using a Newtonian formulation. 'CN' "Reception" case: converged Newtonian light time correction. 'CN+S' "Reception" case: converged Newtonian light time and stellar aberration corrections. Case and leading or trailing blanks are not significant in the string 'abcorr'. obsrvr name of the observing body. Optionally, you may supply the ID code of the object as an integer string. For example both "MOON" and "301" are legitimate strings that indicate the Moon is the observer. [1,c4] = size(obsrvr); char = class(obsrvr) or [1,1] = size(obsrvr); cell = class(obsrvr) Case and leading or trailing blanks are not significant in the string 'obsrvr'. relate describes the constraint relational operator on phase angle. The result window found by this routine indicates the time intervals where the constraint is satisfied. [1,c5] = size(relate); char = class(relate) or [1,1] = size(relate); cell = class(relate) Supported values of 'relate' and corresponding meanings are shown below: '>' The phase angle value is greater than the reference value REFVAL. '=' The phase angle value is equal to the reference value REFVAL. '<' The phase angle value is less than the reference value REFVAL. 'ABSMAX' The phase angle value is at an absolute maximum. 'ABSMIN' The phase angle value is at an absolute minimum. 'LOCMAX' The phase angle value is at a local maximum. 'LOCMIN' The phase angle value is at a local minimum. The caller may indicate that the region of interest is the set of time intervals where the quantity is within a specified measure of an absolute extremum. The argument 'adjust' (described below) is used to specify this measure. Local extrema are considered to exist only in the interiors of the intervals comprising the confinement window: a local extremum cannot exist at a boundary point of the confinement window. Case and leading or trailing blanks are not significant in the string 'relate'. refval reference value used together with relate argument to define an equality or inequality to satisfy by the phase angle. See the discussion of relate above for further information. [1,1] = size(refval); double = class(refval) The units of 'refval' are radians. adjust value used to modify searches for absolute extrema: when relate is set to ABSMAX or ABSMIN and adjust is set to a positive value, cspice_gfdist finds times when the observer-target vector coordinate is within 'adjust' radians of the specified extreme value. [1,1] = size(adjust); double = class(adjust) For relate set to ABSMAX, the result window contains time intervals when the observer-target vector coordinate has values between ABSMAX - 'adjust' and ABSMAX. For relate set to ABSMIN, the result window contains time intervals when the phase angle has values between ABSMIN and ABSMIN + 'adjust'. 'adjust' is not used for searches for local extrema, equality or inequality conditions. step time step size to use in the search. 'step' must be short enough for a search using this step size to locate the time intervals where coordinate function of the observer-target vector is monotone increasing or decreasing. However, step must not be *too* short, or the search will take an unreasonable amount of time. [1,1] = size(step); double = class(step) The choice of 'step' affects the completeness but not the precision of solutions found by this routine; the precision is controlled by the convergence tolerance. 'step' has units of seconds. nintvls value specifying the number of intervals in the internal workspace array used by this routine. 'nintvls' should be at least as large as the number of intervals within the search region on which the specified observer-target vector coordinate function is monotone increasing or decreasing. It does no harm to pick a value of 'nintvls' larger than the minimum required to execute the specified search, but if chosen too small, the search will fail. [1,1] = size(nintvls); int32 = class(nintvls) cnfine a SPICE window that confines the time period over which the specified search is conducted. 'cnfine' may consist of a single interval or a collection of intervals. [2m,1] = size(cnfine); double = class(cnfine) In some cases the confinement window can be used to greatly reduce the time period that must be searched for the desired solution. See the Particulars section below for further discussion. See the Examples section below for a code example that shows how to create a confinement window. the call: result = ## 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. Use the meta-kernel shown below to load the required SPICE kernels. KPL/MK File name: standard.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 --------- -------- de421.bsp Planetary ephemeris pck00009.tpc Planet orientation and radii naif0009.tls Leapseconds \begindata KERNELS_TO_LOAD = ( 'naif0009.tls' 'de421.bsp' 'pck00009.tpc' ) \begintext Example: Determine the time windows from December 1, 2006 UTC to January 31, 2007 UTC for which the sun-moon-earth configuration phase angle satisfies the relation conditions with respect to a reference value of .57598845 radians (the phase angle at January 1, 2007 00:00:00.000 UTC, 33.001707 degrees). Also determine the time windows corresponding to the local maximum and minimum phase angles, and the absolute maximum and minimum phase angles during the search interval. The configuration defines the sun as the illuminator, the moon as the target, and the earth as the observer. MAXWIN = 5000; TIMFMT = 'YYYY-MON-DD HR:MN:SC.###'; relate = { '=', '<', '>', ... 'LOCMIN', 'ABSMIN', 'LOCMAX', 'ABSMAX' }; % % Define the location for the phase angle calculation as the % geometric center of the target. % pos = [ 0, 0, 0 ]'; % % Load kernels. % cspice_furnsh( 'standard.tm' ); % % Store the time bounds of our search interval in % the 'cnfine' confinement window. % et = cspice_str2et( { '2006 DEC 01', '2007 JAN 31'} ); % % Search using a step size of 1 day (in units of seconds). % The reference value is 0.57598845 radians. We're not using the % adjustment feature, so we set 'adjust' to zero. % target = 'MOON'; illmn = 'SUN'; abcorr = 'LT+S'; obsrvr = 'EARTH'; refval = 0.57598845; adjust = 0.; step = cspice_spd; nintvls = MAXWIN; cnfine = cspice_wninsd( et(1), et(2) ); for j=1:numel( relate ) fprintf( 'Relation condition: %s\n', char( relate(j) ) ) % % Perform the search. The SPICE window 'result' contains % the set of times when the condition is met. % result = ## ParticularsThis routine provides a simple interface for conducting searches for observer-target-illuminator phase angle geometric events. This routine determines a set of one or more time intervals within the confinement window for which the phase angle satisfies some defined relationship. The resulting set of intervals is returned as a SPICE 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 geometric function is monotone increasing and monotone decreasing. Each of these time periods is represented by a SPICE window. Having found these windows, all of the geometric 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 the geometric function 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 range 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 geometric 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, illumination source, 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 geometric 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 ) Call cspice_gfstol prior to calling this routine. All subsequent searches will use the updated tolerance value. 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. ## Required ReadingFor important details concerning this module's function, please refer to the CSPICE routine gfpa_c. MICE.REQ GF.REQ NAIF_IDS.REQ SPK.REQ CK.REQ TIME.REQ WINDOWS.REQ ## Version-Mice Version 1.0.1, 13-NOV-2014, EDW (JPL) Edited I/O section to conform to NAIF standard for Mice documentation. -Mice Version 1.0.0, 15-JUL-2014, EDW (JPL) ## Index_EntriesGF phase angle search |

Wed Apr 5 18:00:32 2017