cspice_gfilum |
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## AbstractCSPICE_GFILUM determines the time intervals over which a specified constraint on the observed phase, solar incidence, or emission angle at a specified target body surface point is met. For important details concerning this module's function, please refer to the CSPICE routine gfilum_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- method scalar string providing parameters defining the computation method to be used. Parameters include, but are not limited to, the shape model used to represent the surface of the target body. The only choice currently supported is 'Ellipsoid' The illumination angle computation uses a triaxial ellipsoid to model the surface of the target body. The ellipsoid's radii must be available in the kernel pool. Neither case nor white space are significant in 'method'. For example, the string ' eLLipsoid ' is valid. angtyp scalar string specifying the type of illumination angle for which a search is to be performed. The possible values of 'angtyp' are 'PHASE' 'SOLAR INCIDENCE' 'EMISSION' See the Particulars section below for a detailed description of these angles. Neither case nor white space are significant in 'angtyp'. For example, the string ' Solar incidence ' is valid. target scalar string name of a target body. The point at which the illumination angles are defined is located on the surface of this 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. illmn scalar string name of the illumination source. This source may be any ephemeris object. Case, blanks, and numeric values are treated in the same way as for the input 'target'. fixref scalar string name of the body-fixed, body-centered reference frame associated with the target body. The input surface point 'spoint' is expressed relative to this reference frame, and this frame is used to define the orientation of the target body as a function of time. The string 'fixref' is case-insensitive, and leading and trailing blanks in 'fixref' are not significant. abcorr scalar string indicating the aberration corrections to apply to the observer-target position vector to account for one-way light time and stellar aberration. Any 'reception' correction accepted by spkezr_c can be used here. See the header of spkezr_c for a detailed description of the aberration correction options. For convenience, the 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 blanks are not significant in the string 'abcorr'. obsrvr scalar string name of an observing body. Optionally, you may supply the ID code of the object as an integer string. For example, both 'EARTH' and '399' are legitimate strings to supply to indicate that the observer is Earth. spoint is a surface point on the target body, expressed in Cartesian coordinates, relative to the body-fixed target frame designated by 'fixref'. 'spoint' need not be visible from the observer's location in order for the constraint specified by 'relate' and 'refval' (see descriptions below) to be satisfied. The components of 'spoint' have units of km. relate scalar string relational operator used to define a constraint on a specified illumination angle. The result window found by this routine indicates the time intervals where the constraint is satisfied. Supported values of 'relate' and corresponding meanings are shown below: '>' The angle is greater than the reference value 'refval'. '=' The angle is equal to the reference value 'refval'. '<' The angle is less than the reference value 'refval'. 'ABSMAX' The angle is at an absolute maximum. 'ABSMIN' The angle is at an absolute minimum. 'LOCMAX' The angle is at a local maximum. 'LOCMIN' The angle is at a local minimum. The caller may indicate that the region of interest is the set of time intervals where the angle is within a specified separation from an absolute extremum. The argument 'adjust' (described below) is used to specify this separation. 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 is not significant in the string 'relate'. refval is the reference value used together with the argument 'relate' to define an equality or inequality to be satisfied by the specified illumination angle. See the discussion of 'relate' above for further information. The units of 'refval' are radians. adjust is a parameter used to modify searches for absolute extrema: when 'relate' is set to 'ABSMAX' or 'ABSMIN' and 'adjust' is set to a positive value, gfilum_c will find times when the observer-target distance is within 'adjust' km of the specified extreme value. If 'adjust' is non-zero and a search for an absolute minimum 'min' is performed, the result window contains time intervals when the observer-target distance has values between 'min' and min+adjust. If the search is for an absolute maximum 'max', the corresponding range is from max-adjust to 'max'. 'adjust' is not used for searches for local extrema, equality or inequality conditions. step is the step size to be used in the search. 'step' must be short enough for a search using this step size to locate the time intervals where the specified illumination angle is monotone increasing or decreasing. However, 'step' must not be *too* short, or the search will take an unreasonable amount of time. 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. See the discussion of the parameter SPICE_GF_CNVTOL for details. 'step' has units of seconds. nintvls is a parameter specifying the number of intervals that can be accommodated by each of the dynamically allocated workspace windows used internally by this routine. In many cases, it's not necessary to compute an accurate estimate of how many intervals are needed; rather, the user can pick a size considerably larger than what's really required. However, since excessively large arrays can prevent applications from compiling, linking, or running properly, sometimes 'nintvls' must be set according to the actual workspace requirement. A rule of thumb for the number of intervals needed is nintvls = 2*n + ( m / step ) where n is the number of intervals in the confinement window m is the measure of the confinement window, in units of seconds step is the search step size in seconds cnfine is 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. The endpoints of the time intervals comprising 'cnfine' are interpreted as seconds past J2000 TDB. See the Examples section below for a code example that shows how to create a confinement window. the call: ## ExamplesThe 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. Determine time intervals over which the planned Mars Science Laboratory (MSL) Gale Crater landing site satisfies certain constraints on its illumination and visibility as seen from the Mars Reconnaissance Orbiter (MRO) spacecraft. The observation period will range from slightly before the planned landing time to about 10 days later. In this case we require the emission angle to be less than 30 degrees and the solar incidence angle to be less than 40 degrees. Use the meta-kernel shown below to load the required SPICE kernels. KPL/MK File name: gfilum.tm This is the meta-kernel file for the example problem for the subroutine gfilum_c. These kernel files can be found on the NAIF website. 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 pck00010.tpc Planet orientation and radii naif0010.tls Leapseconds spk_psp_110101-130101_081216_3pm.bsp MRO predict SPK \begindata KERNELS_TO_LOAD = ( 'de421.bsp', 'pck00010.tpc', 'naif0010.tls', 'spk_psp_110101-130101+' '_081216_3pm.bsp' ) \begintext End of meta-kernel Example: ;; ;; Output time format: ;; TIMFMT = 'YYYY MON DD HR:MN:SC.###### TDB::TDB' ;; ;; Meta-kernel name: ;; META = 'gfilum.tm' ;; ;; Maximum number of intervals in the windows ;; used in this program: ;; MAXIVL = 1000 MAXWIN = ( 2 * MAXIVL ) ;; ;; Maximum length of time string: ;; TIMLEN = 41 ;; ;; Local variables ;; cnfine = cspice_celld( MAXWIN ) result = cspice_celld( MAXWIN ) wnsolr = cspice_celld( MAXWIN ) r2d = cspice_dpr() ;; ;; Initial values ;; ;; Mars planetodetic coordinates of landing site. ;; Angular units are degrees; distance units are km. ;; gclat = -4.543182D gclon = 137.420000D gcalt = -4.876405D ;; ;; Load kernels: ;; cspice_furnsh, META ;; ;; Convert the landing site location from planetodetic ;; to Cartesian coordinates for use with GFILUM. ;; cspice_bodvrd, 'MARS', 'RADII', 3, radii re = radii[0] rp = radii[2] f = ( re - rp ) / re cspice_georec, gclon * cspice_rpd(), gclat * cspice_rpd(), $ gcalt, re, f, gcpos ;; ;; Set the search interval: ;; utcbeg = '2012 AUG 5 00:00:00 UTC' cspice_str2et, utcbeg, et0 utcend = '2012 SEP 15 00:00:00 UTC' cspice_str2et, utcend, et1 cspice_wninsd, et0, et1, cnfine ;; ;; Set observer, target, aberration correction, and the ;; Mars body-fixed, body-centered reference frame. The ;; lighting source is the sun. ;; ;; Aberration corrections are set for remote observations. ;; illmn = 'sun' obsrvr = 'mro' target = 'mars' abcorr = 'cn+s' fixref = 'iau_mars' ;; ;; Initialize the adjustment value for absolute ;; extremum searches. We're not performing ;; such searches in this example, but this input ;; to GFILUM must still be set. ;; adjust = 0.0 ;; ;; The computation uses an ellipsoidal model for the ;; target body shape. ;; method = 'Ellipsoid' ;; ;; Set the reference value to use for the solar ;; incidence angle search. ;; refval = 45.D0 * cspice_rpd() ;; ;; Since the period of the solar incidence angle ;; is about one Martian day, we can safely use 6 hours ;; as the search step. ;; step = 21600.D0 ;; ;; Search over the confinement window for times ;; when the solar incidence angle is less than ;; the reference value. ;; ## ParticularsThis routine determines a set of one or more time intervals within the confinement window when the specified illumination angle satisfies a caller-specified constraint. The resulting set of intervals is returned as a SPICE window. The term 'illumination angles' refers to the following set of angles: phase angle Angle between the vectors from the surface point to the observer and from the surface point to the illumination source. incidence angle Angle between the surface normal at the specified surface point and the vector from the surface point to the illumination source. emission angle Angle between the surface normal at the specified surface point and the vector from the surface point to the observer. The diagram below illustrates the geometric relationships defining these angles. The labels for the incidence, emission, and phase angles are 'inc.', 'e.', and 'phase'. * illumination source surface normal vector ._ _. |\ /| illumination \ phase / source vector \ . . / . . \ ___ / . \/ \/ _\ inc./ . / \ / . | e. \ / * <--------------- * surface point on viewing vector target body location to viewing (observer) location Note that if the target-observer vector, the target normal vector at the surface point, and the target-illumination source vector are coplanar, then phase is the sum of the incidence and emission angles. This rarely occurs; usually phase angle < incidence angle + emission angle All of the above angles can be computed using light time corrections, light time and stellar aberration corrections, or no aberration corrections. In order to describe apparent geometry as observed by a remote sensing instrument, both light time and stellar aberration corrections should be used. The way aberration corrections are applied by this routine is described below. Light time corrections ====================== Observer-target surface point vector ------------------------------------ Let ET be the epoch at which an observation or remote sensing measurement is made, and let ET - LT ('LT' stands for 'light time') be the epoch at which the photons received at ET were emitted from the surface point 'spoint'. Note that the light time between the surface point and observer will generally differ from the light time between the target body's center and the observer. Target body's orientation ------------------------- Using the definitions of ET and LT above, the target body's orientation at ET - LT is used. The surface normal is dependent on the target body's orientation, so the body's orientation model must be evaluated for the correct epoch. Target body -- illumination source vector ----------------------------------------- The surface features on the target body near 'spoint' will appear in a measurement made at ET as they were at ET-LT. In particular, lighting on the target body is dependent on the apparent location of the illumination source as seen from the target body at ET-LT. So, a second light time correction is used to compute the position of the illumination source relative to the surface point. Stellar aberration corrections ============================== Stellar aberration corrections are applied only if light time corrections are applied as well. Observer-target surface point body vector ----------------------------------------- When stellar aberration correction is performed, the observer-to-surface point direction vector, which we'll call SRFVEC, is adjusted so as to point to the apparent position of 'spoint': considering 'spoint' to be an ephemeris object, SRFVEC points from the observer's position at ET to the light time and stellar aberration corrected position of 'spoint'. Target body-illumination source vector -------------------------------------- The target body-illumination source vector is the apparent position of the illumination source, corrected for light time and stellar aberration, as seen from the surface point 'spoint' at time ET-LT. 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 illumination angle is monotone increasing and monotone decreasing. Each of these time periods is represented by a SPICE window. Having found these windows, all of the illumination angle'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 via 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 illumination angle 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, via binary search. Note that the optimal choice of step size depends on the lengths of the intervals over which the illumination angle 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 illumination angle 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 via 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. ## Required ReadingGF.REQ NAIF_IDS.REQ SPK.REQ TIME.REQ ## Version-Icy Version 1.0.0, 05-SEP-2012 (EDW) ## Index_Entriessolve for illumination_angle constraints solve for phase_angle constraints solve for solar_incidence_angle constraints solve for emission_angle constraints search using illumination_angle constraints |

Wed Apr 5 17:58:01 2017