gfsntc |

Table of contents## ProcedureGFSNTC (GF, surface intercept vector coordinate search) SUBROUTINE GFSNTC ( TARGET, FIXREF, METHOD, . ABCORR, OBSRVR, DREF, . DVEC, CRDSYS, COORD, . RELATE, REFVAL, ADJUST, . STEP, CNFINE, MW, . NW, WORK, RESULT ) ## AbstractDetermine time intervals for which a coordinate of a surface intercept position vector satisfies a numerical constraint. ## Required_ReadingGF SPK CK TIME WINDOWS ## KeywordsCOORDINATE EVENT GEOMETRY SEARCH ## DeclarationsIMPLICIT NONE INCLUDE 'gf.inc' INCLUDE 'zzgf.inc' INCLUDE 'zzholdd.inc' INTEGER LBCELL PARAMETER ( LBCELL = -5 ) CHARACTER*(*) TARGET CHARACTER*(*) FIXREF CHARACTER*(*) METHOD CHARACTER*(*) ABCORR CHARACTER*(*) OBSRVR CHARACTER*(*) DREF DOUBLE PRECISION DVEC (3) CHARACTER*(*) CRDSYS CHARACTER*(*) COORD CHARACTER*(*) RELATE DOUBLE PRECISION REFVAL DOUBLE PRECISION ADJUST DOUBLE PRECISION CNFINE ( LBCELL : * ) DOUBLE PRECISION STEP INTEGER MW INTEGER NW DOUBLE PRECISION WORK ( LBCELL : MW, NW ) DOUBLE PRECISION RESULT ( LBCELL : * ) ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- LBCELL P SPICE Cell lower bound. CNVTOL P Convergence tolerance. ZZGET P ZZHOLDD retrieves a stored DP value. GF_TOL P ZZHOLDD acts on the GF subsystem tolerance. TARGET I Name of the target body. FIXREF I Body fixed frame associated with TARGET. METHOD I Name of method type for surface intercept calculation. ABCORR I Aberration correction flag. OBSRVR I Name of the observing body. DREF I Reference frame of direction vector DVEC. DVEC I Pointing direction vector from OBSRVR. CRDSYS I Name of the coordinate system containing COORD. COORD I Name of the coordinate of interest. RELATE I Relational operator. REFVAL I Reference value. ADJUST I Adjustment value for absolute extrema searches. STEP I Step size used for locating extrema and roots. CNFINE I SPICE window to which the search is confined. MW I Workspace window size. NW I The number of workspace windows needed for the search. WORK O Array of workspace windows RESULT I-O SPICE window containing results. ## Detailed_InputTARGET is the string name of a 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. On calling ## Detailed_OutputWORK is an array used to store workspace windows. This array should be declared by the caller as shown: INCLUDE 'gf.inc' ... DOUBLE PRECISION WORK ( LBCELL : MW, NWMAX ) where MW is a constant declared by the caller and NWMAX is a constant defined in the SPICELIB INCLUDE file gf.inc. See the discussion of MW above. WORK need not be initialized by the caller. WORK is modified by this routine. The caller should re-initialize this array before attempting to use it for any other purpose. RESULT is the SPICE window of intervals, contained within the confinement window CNFINE, on which the specified constraint is satisfied. The endpoints of the time intervals comprising RESULT are interpreted as seconds past J2000 TDB. If the search is for local extrema, or for absolute extrema with ADJUST set to zero, then normally each interval of RESULT will be a singleton: the left and right endpoints of each interval will be identical. If no times within the confinement window satisfy the search criteria, RESULT will be returned with a cardinality of zero. ## ParametersLBCELL is the integer value defining the lower bound for SPICE Cell arrays (a SPICE window is a kind of cell). CNVTOL is the convergence tolerance used for finding endpoints of the intervals comprising the result window. CNVTOL is also used for finding intermediate results; in particular, CNVTOL is used for finding the windows on which the specified coordinate is increasing or decreasing. CNVTOL is used to determine when binary searches for roots should terminate: when a root is bracketed within an interval of length 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. NWMAX is the number of workspace windows required by this routine. See INCLUDE file gf.inc for declarations and descriptions of parameters used throughout the GF system. ## Exceptions1) In order for this routine to produce correct results, the step size must be appropriate for the problem at hand. Step sizes that are too large may cause this routine to miss roots; step sizes that are too small may cause this routine to run unacceptably slowly and in some cases, find spurious roots. This routine does not diagnose invalid step sizes, except that if the step size is non-positive, an error is signaled by a routine in the call tree of this routine. 2) Due to numerical errors, in particular, - truncation error in time values - finite tolerance value - errors in computed geometric quantities it is *normal* for the condition of interest to not always be satisfied near the endpoints of the intervals comprising the RESULT window. One technique to handle such a situation, slightly contract RESULT using the window routine WNCOND. 3) If the window size MW is less than 2 or not an even value, the error SPICE(INVALIDDIMENSION) is signaled. 4) If the window size of RESULT is less than 2, the error SPICE(INVALIDDIMENSION) is signaled. 5) If the output SPICE window RESULT has insufficient capacity to contain the number of intervals on which the specified distance condition is met, an error is signaled by a routine in the call tree of this routine. 6) If an error (typically cell overflow) occurs during window arithmetic, the error is signaled by a routine in the call tree of this routine. 7) If the relational operator RELATE is not recognized, an error is signaled by a routine in the call tree of this routine. 8) If the size of the workspace WORK is too small, an error is signaled by a routine in the call tree of this routine. 9) If the aberration correction specifier contains an unrecognized value, an error is signaled by a routine in the call tree of this routine. 10) If ADJUST is negative, an error is signaled by a routine in the call tree of this routine. 11) If either of the input body names do not map to NAIF ID codes, an error is signaled by a routine in the call tree of this routine. 12) If required ephemerides or other kernel data are not available, an error is signaled by a routine in the call tree of this routine. 13) If the search uses GEODETIC or PLANETOGRAPHIC coordinates, and the center body of the reference frame has unequal equatorial radii, an error is signaled by a routine in the call tree of this routine. ## FilesAppropriate SPK and PCK kernels must be loaded by the calling program before this routine is called. The following data are required: - SPK data: the calling application must load ephemeris data for the targets, observer, and any intermediate objects in a chain connecting the targets and observer that cover the time period specified by the window CNFINE. If aberration corrections are used, the states of target and observer relative to the solar system barycenter must be calculable from the available ephemeris data. Typically ephemeris data are made available by loading one or more SPK files using FURNSH. - PCK data: bodies modeled as triaxial ellipsoids must have semi-axis lengths provided by variables in the kernel pool. Typically these data are made available by loading a text PCK file using FURNSH. - If non-inertial reference frames are used, then PCK files, frame kernels, C-kernels, and SCLK kernels may be needed. - In some cases the observer's state may be computed at times outside of CNFINE by as much as 2 seconds; data required to compute this state must be provided by loaded kernels. See $Particulars for details. Such kernel data are normally loaded once per program run, NOT every time this routine is called. ## ParticularsThis routine provides a simpler, but less flexible interface than does the routine GFEVNT for conducting searches for surface intercept vector coordinate value events. Applications that require support for progress reporting, interrupt handling, non-default step or refinement functions, or non-default convergence tolerance should call GFEVNT rather than this routine. This routine determines a set of one or more time intervals within the confinement window when the selected coordinate of the surface intercept position vector satisfies a caller-specified constraint. 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 coordinate 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 coordinate 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 coordinate 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 time derivative of the coordinate 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 coordinate 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 ===================== 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 default convergence tolerance used by this routine is set by the parameter CNVTOL (defined in gf.inc). The value of 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 CNVTOL value by calling the routine GFSTOL, e.g. CALL GFSTOL( tolerance value ) Call GFSTOL prior to calling this routine. All subsequent searches will use the updated tolerance value. Setting the tolerance tighter than 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 effect 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. Practical use of the coordinate search capability would likely consist of searches over multiple coordinate constraints to find time intervals that satisfies the constraints. An effective technique to accomplish such a search is to use the result window from one search as the confinement window of the next. Certain types of searches require the state of the observer, relative to the solar system barycenter, to be computed at times slightly outside the confinement window CNFINE. The time window that is actually used is the result of "expanding" CNFINE by a specified amount "T": each time interval of CNFINE is expanded by shifting the interval's left endpoint to the left and the right endpoint to the right by T seconds. Any overlapping intervals are merged. (The input argument CNFINE is not modified.) The window expansions listed below are additive: if both conditions apply, the window expansion amount is the sum of the individual amounts. - If a search uses an equality constraint, the time window over which the state of the observer is computed is expanded by 1 second at both ends of all of the time intervals comprising the window over which the search is conducted. - If a search uses stellar aberration corrections, the time window over which the state of the observer is computed is expanded as described above. When light time corrections are used, expansion of the search window also affects the set of times at which the light time- corrected state of the target is computed. In addition to the possible 2 second expansion of the search window that occurs when both an equality constraint and stellar aberration corrections are used, round-off error should be taken into account when the need for data availability is analyzed. Longitude and Right Ascension ============================= The cyclic nature of the longitude and right ascension coordinates produces branch cuts at +/- 180 degrees longitude and 0-360 longitude. Round-off error may cause solutions near these branches to cross the branch. Use of the SPICE routine WNCOND will contract solution windows by some epsilon, reducing the measure of the windows and eliminating the branch crossing. A one millisecond contraction will in most cases eliminate numerical round-off caused branch crossings. ## 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. 1) Find the time during 2007 for which the latitude of the intercept point of the vector pointing from the sun towards the earth in the IAU_EARTH frame equals zero i.e. the intercept point crosses the equator. Use the meta-kernel shown below to load the required SPICE kernels. KPL/MK File name: gfsntc_ex1.tm This meta-kernel is intended to support operation of SPICE example programs. The kernels shown here should not be assumed to contain adequate or correct versions of data required by SPICE-based user applications. In order for an application to use this meta-kernel, the kernels referenced here must be present in the user's current working directory. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents --------- -------- de414.bsp Planetary ephemeris pck00008.tpc Planet orientation and radii naif0008.tls Leapseconds \begindata KERNELS_TO_LOAD = ( 'naif0008.tls' 'de414.bsp' 'pck00008.tpc' ) \begintext End of meta-kernel Use the kernel shown below to define a dynamic frame, Sun-Earth Motion. KPL/FK File name: gfsntc_sem.tf The Sun-Earth Motion frame is defined by the sun-to-earth direction vector as the X axis. The Y axis in the earth orbital plane, and Z completing the right hand system. \begindata FRAME_SEM = 10100000 FRAME_10100000_NAME = 'SEM' FRAME_10100000_CLASS = 5 FRAME_10100000_CLASS_ID = 10100000 FRAME_10100000_CENTER = 10 FRAME_10100000_RELATIVE = 'J2000' FRAME_10100000_DEF_STYLE = 'PARAMETERIZED' FRAME_10100000_FAMILY = 'TWO-VECTOR' FRAME_10100000_PRI_AXIS = 'X' FRAME_10100000_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_10100000_PRI_OBSERVER = 'SUN' FRAME_10100000_PRI_TARGET = 'EARTH' FRAME_10100000_PRI_ABCORR = 'NONE' FRAME_10100000_SEC_AXIS = 'Y' FRAME_10100000_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY' FRAME_10100000_SEC_OBSERVER = 'SUN' FRAME_10100000_SEC_TARGET = 'EARTH' FRAME_10100000_SEC_ABCORR = 'NONE' FRAME_10100000_SEC_FRAME = 'J2000' \begintext End of frames kernel Example code begins here. PROGRAM GFSNTC_EX1 IMPLICIT NONE C C Include GF parameter declarations: C INCLUDE 'gf.inc' C C SPICELIB functions C DOUBLE PRECISION SPD INTEGER WNCARD C C Local parameters C INTEGER LBCELL PARAMETER ( LBCELL = -5 ) C C Create 50 windows. C INTEGER MAXWIN PARAMETER ( MAXWIN = 1000 ) C C One window consists of two intervals. C INTEGER NINTRVL PARAMETER ( NINTRVL = MAXWIN *2 ) INTEGER STRLEN PARAMETER ( STRLEN = 64 ) C C Local variables C CHARACTER*(STRLEN) BEGSTR CHARACTER*(STRLEN) ENDSTR CHARACTER*(STRLEN) TARGET CHARACTER*(STRLEN) OBSRVR CHARACTER*(STRLEN) DREF CHARACTER*(STRLEN) ABCORR CHARACTER*(STRLEN) METHOD CHARACTER*(STRLEN) FIXREF CHARACTER*(STRLEN) CRDSYS CHARACTER*(STRLEN) COORD CHARACTER*(STRLEN) RELATE DOUBLE PRECISION STEP DOUBLE PRECISION DVEC ( 3 ) DOUBLE PRECISION CNFINE ( LBCELL : 2 ) DOUBLE PRECISION RESULT ( LBCELL : NINTRVL ) DOUBLE PRECISION WORK ( LBCELL : NINTRVL, NWMAX ) DOUBLE PRECISION BEGTIM DOUBLE PRECISION ENDTIM DOUBLE PRECISION BEG DOUBLE PRECISION END DOUBLE PRECISION REFVAL DOUBLE PRECISION ADJUST INTEGER COUNT INTEGER I C C Saved variables C C The confinement, workspace and result windows CNFINE, C WORK and RESULT are saved because this practice helps to C prevent stack overflow. C SAVE CNFINE SAVE RESULT SAVE WORK C C The SEM frame defines the X axis as always earth C pointing. C C Define the earth pointing vector in the SEM frame. C DATA DVEC / 1.D0, 0.D0, 0.D0 / C C Load kernels. C CALL FURNSH ('gfsntc_ex1.tm') CALL FURNSH ('gfsntc_sem.tf') C C Initialize windows RESULT and CNFINE. C CALL SSIZED ( NINTRVL, RESULT ) CALL SSIZED ( 2, CNFINE ) C C Store the time bounds of our search interval in C the CNFINE confinement window. C CALL STR2ET ( '2007 JAN 01', BEGTIM ) CALL STR2ET ( '2008 JAN 01', ENDTIM ) CALL WNINSD ( BEGTIM, ENDTIM, CNFINE ) C C Search using a step size of 1 day (in units of seconds). C STEP = SPD() C C Search for a condition where the latitudinal system C coordinate latitude in the IAU_EARTH frame has value C zero. In this case, the pointing vector, 'DVEC', C defines the vector direction pointing at the earth C from the sun. C ADJUST = 0.D0 REFVAL = 0.D0 TARGET = 'EARTH' OBSRVR = 'SUN' DREF = 'SEM' METHOD = 'Ellipsoid' FIXREF = 'IAU_EARTH' CRDSYS = 'LATITUDINAL' COORD = 'LATITUDE' RELATE = '=' C C Use the same aberration correction flag as that in the C SEM frame definition. C ABCORR = 'NONE' CALL ## Restrictions1) The kernel files to be used by this routine must be loaded (normally using the SPICELIB routine FURNSH) before this routine is called. 2) This routine has the side effect of re-initializing the coordinate quantity utility package. Callers may need to re-initialize the package after calling this routine. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) E.D. Wright (JPL) ## VersionSPICELIB Version 1.2.0, 27-OCT-2021 (JDR) (NJB) Added initialization of QCPARS(10) to pacify Valgrind. Edited the header to comply with NAIF standard. Fixed bug in code example #2. Renamed example's meta-kernel. Added SAVE statements for CNFINE, WORK, RESULT, RESULT1, RESULT2, RESULT3 and RESULT4 variables in code examples. Added parameter NWMAX's description. Updated $Files section. Added entries #5 and $9 in $Exceptions section. Updated description of WORK and RESULT arguments in $Brief_I/O, $Detailed_Input and $Detailed_Output. Extended description of COORD argument. Updated header to describe use of expanded confinement window. SPICELIB Version 1.1.0, 05-SEP-2012 (EDW) Edit to comments to correct search description. Implemented use of ZZHOLDD to allow user to alter convergence tolerance. Removed the STEP > 0 error check. The GFSSTP call includes the check. SPICELIB Version 1.0.1, 16-FEB-2010 (NJB) (EDW) Edits to and corrections of argument descriptions and header. SPICELIB Version 1.0.0, 17-FEB-2009 (NJB) (EDW) |

Fri Dec 31 18:36:25 2021