| C-Kernel Required Reading |
Table of ContentsC-Kernel Required Reading Abstract References DAF Run-Time Binary File Format Translation Detection of Non-native Text Files Introduction Preliminaries Specifying Spacecraft and Instruments C-Matrices Angular Velocity Vectors Spacecraft Clock Time Encoded SCLK Ticks and Partitions SCLK and other time systems The SCLK kernel file Basics The CK File Reader CKGP FURNSH SCENCD and SCE2C SCTIKS CKGP The CK File Reader CKGPAV Multiple Files and the C-kernel CK Coverage Summary Routines Details File Structure and Implementation Segment Descriptors Segment Identifiers Comment Area A CK file is a DAF SPICE File Identification Word in CK Files How the CK Readers Work The General Search Algorithm The Difference Between CKGP and CKGPAV Locating the Applicable Segment Looking at Descriptors Evaluating the Records --- the Reader CKPFS Transforming the Results Data Types Data Type 1 Type 1 subroutines Data Type 2 Type 2 subroutines Data Type 3 Linear Interpolation Algorithm Type 3 subroutines Data Type 4 CK Type 4 pointing evaluation algorithm Type 4 subroutines Data Type 5 Type 5 subroutines Type 6: ESOC/DDID Piecewise Interpolation Terminology Mini-segments Type 6 subtypes Restrictions on type 6 data Type 6 segment structure Use of non-zero tolerance Type 6 subroutines Appendix A --- Summary of C-kernel Subroutines Summary of Mnemonics Summary of Calling Sequences Appendix B --- Example Program PLANET_POINT Appendix C --- An Example of Writing a Type 1 CK Segment Appendix D --- An Example of Writing a Type 2 CK Segment Appendix E --- An Example of Writing a Type 3 CK Segment Appendix F --- An Example of Writing a Type 4 CK Segment Appendix G: Document Revision History February 13, 2014 April 1, 2009 November 17, 2005 December 21, 2004 February 2, 2004 September 04, 2002 February 15, 2000 October 14, 1999 C-Kernel Required Reading
Abstract
References
DAF Run-Time Binary File Format Translation
Detection of Non-native Text Files
Introduction
The data contained in C-kernel files can be accessed and manipulated by a collection of FORTRAN 77 subroutines which are part of the SPICELIB library. These subroutines can be integrated into user application programs. The purpose of this document is to describe both the C-kernel file structure and the associated SPICELIB software to the level of detail necessary for the user to program almost any application. With few exceptions, all subroutines and functions appearing in this document are part of SPICELIB. The exceptions are placeholders for user-supplied routines which appear in some of the code examples. Each SPICELIB routine is prefaced with a complete SPICELIB header which describes inputs, outputs, restrictions and context, and provides examples of usage. The authoritative documentation for any subroutine is its header, which should be consulted before using the routine in any program. A summary of the CK subroutines presented in this document is included as Appendix A. Preliminaries
Specifying Spacecraft and Instruments
In order to avoid confusion, NAIF, in cooperation with the science teams from each flight project, will assign instrument codes using the following scheme. If you're familiar with SPICE S- and P-kernels, you know that NAIF codes for spacecraft are negative integers: -31 for Voyager 1, -32 for Voyager 2, -94 for Mars Global Surveyor, and so on. We borrow from this convention in defining instrument codes. For example, the Voyager 2 instruments could have been given these IDs:
SPICE s/c instrument code = (s/c code)*(1000) - instrument numberwhich allows for 999 instruments on board any one spacecraft. The term ``instrument'' is used loosely throughout this document since the concept of orientation is applicable to structures other than just science instruments. For example, some of the Galileo instruments are in a fixed position relative to the scan platform. It might therefore be prudent to have a single file containing the orientation of the scan platform, and then produce the pointing for each of the scan platform science instruments by applying instrument offset angles obtained from the I-kernel. C-Matrices
The C-matrix transforms coordinates as follows: if a vector v has coordinates ( x, y, z ) in some base reference frame (like J2000), then v has coordinates ( x', y', z' ) in instrument-fixed coordinates, where
[ ] [ x ] [ x'] | C-matrix | | y | = | y'| [ ] [ z ] [ z']The transpose of a C-matrix rotates vectors from the instrument-fixed frame to the base frame:
[ ]T [ x'] [ x ] | C-matrix | | y'| = | y | [ ] [ z'] [ z ]Therefore, if the coordinates of an instrument in the instrument fixed frame are known, then the transpose of the C-matrix can be used to determine the corresponding coordinates in a base reference frame. This information can be used to help answer questions such as, ``What is the latitude and longitude of the point on the planet that the camera was pointing at when it shuttered this picture?'' The high-level CK file reader CKGP ( Get Pointing ) returns a C-matrix that specifies the pointing of a spacecraft structure at a particular time. An example program is included in Appendix B, which solves the longitude and latitude problem presented above using CKGP and other SPICELIB subroutines. Angular Velocity Vectors
Angular rate information may be important for certain types of science analysis. For instance, investigators for imaging instruments might use angular rates to determine how much smear to expect in their images. CK files are capable of storing angular velocity data for instruments, although the presence of such data is optional. The CK reader CKGPAV (Get Pointing and Angular Velocity) returns an angular velocity vector in addition to a C-matrix. Spacecraft Clock Time
Within the SPICE system, SCLK is represented as an encoded double precision number. You will need this form when using CK reader routines to read from CK files. SPICELIB includes routines to convert between character SCLK format and the double precision encoding. There are also routines to convert between SCLK and standard time systems such as ET and UTC. The SCLK Required Reading, sclk.req, contains a full description of SCLK including the clock formats for individual spacecraft. You should read that document before writing any C-kernel programs. A brief description of SCLK is included here because many of the subroutines presented require a clock time as an input argument. Encoded SCLK
Discrete encoded SCLK values have units of ``ticks''; ticks represent the least significant counts representable by a clock. Continuous encoded SCLK supports non-integral tick values. This enables translation of other time systems to encoded SCLK without rounding. Throughout this document, encoded SCLK should be assumed to be continuous unless otherwise specified. To convert from a character string representation of SCLK to its double precision encoding, use the routine SCENCD (Encode SCLK):
CALL SCENCD ( SC, SCLKCH, SCLKDP )Use SCDECD (Decode SCLK) to recover the character representation from its double precision encoding.
CALL SCDECD ( SC, SCLKDP, SCLKCH )The first argument to both routines, SC, is the NAIF integer ID for the spacecraft whose clock count is being encoded or decoded (for example, -77 for Galileo). Each spacecraft may have a different format for its clock counts, so the encoding scheme may be different for each. The SCLK Required Reading, sclk.req, indicates the expected clock string formats for each mission. To convert from ET to continuous encoded SCLK, use SCE2C (ET to continuous SCLK):
CALL SCE2C ( SC, SCLKCH, SCLKDP )To convert continuous encoded SCLK to ET, use SCT2E (Ticks to ET):
CALL SCT2E ( SC, SCLKDP, ET ) Ticks and Partitions
The problem of encoding SCLK is complicated by the fact that spacecraft clocks do not always advance continuously. A discontinuity may occur if a clock resets to a different value. This occurs when a clock reaches its maximum value, but it can also happen due to other reasons which will not be discussed here. Anytime this occurs, we say that the clock has entered a new ``partition.'' SCLK strings should normally include a partition number prefixed to the rest of the clock count with a ``/''. The partition number uniquely separates a count from identical counts in other partitions. The presence of the partition number is not required. If it is missing, SCENCD will assume the partition to be the earliest possible one containing the clock string. SCLK and other time systems
The first is ephemeris time (ET), which is specified as some number of ephemeris seconds past a reference epoch. Within the SPICE system, state vectors of spacecraft and target bodies are referenced to ET seconds past the J2000 epoch. The other is Coordinated Universal Time (UTC), which is also called Greenwich Mean Time. Two subroutine calls are necessary to convert between UTC and SCLK. One routine converts from SCLK to ET, and another from ET to UTC. See Appendix A for a list of high level subroutines involved in spacecraft clock time conversions. The SCLK kernel file
The SCLK kernel file contains spacecraft specific parameters needed to perform the conversions. Included are such things as clock format definitions, partition start and stop times, and time interpolation constants. You should make sure that the kernel file you are using contains information for the particular spacecraft you are working with. You also have to load the leapseconds kernel file into the kernel pool if you are going to convert between ET and UTC. Basics
A later chapter will present lower level subroutines that allow the programmer to exert the highest amount of control in reading CK files. Appendix B contains an example showing how some of the routines presented in this chapter fit together in a typical application program. The CK File Reader CKGP
Each of the subroutines used is briefly described below. See the individual subroutine headers for a complete description. A complete description of how CKGP searches for pointing is provided in the ``Details'' chapter of this document.
INTEGER SC
INTEGER INST
DOUBLE PRECISION SCLKDP
DOUBLE PRECISION TOL
DOUBLE PRECISION CLKOUT
DOUBLE PRECISION CMAT ( 3, 3 )
CHARACTER*(10) REF
LOGICAL FOUND
C
C NAIF ID numbers for the
C
C 1. Voyager 2 spacecraft
C 2. Voyager 2 narrow angle camera
C
SC = -32
INST = -32001
C
C The C-matrix should transform from J2000 to camera-fixed
C coordinates.
C
REF = 'J2000'
C
C Load the spacecraft clock partition kernel file into the
C kernel pool, for SCLK encoding and decoding.
C
CALL FURNSH ( 'vgr2_sclk.tsc' )
C
C Load the C-kernel pointing file.
C
CALL FURNSH ( 'vgr2_jup_inbound.bc' )
C
C We want pointing at a spacecraft clock time appearing in
C the third spacecraft clock partition.
C
CALL SCENCD ( SC, '3/20556:17:768', SCLKDP )
C
C The Voyager 2 clock is of the form xxxxx yy www, where
C yy is a modulus 60 counter. Pictures were not shuttered
C at intervals smaller than one mod 60 count. Therefore,
C use this as the tolerance. ( Notice that no partition
C number is used when specifying a tolerance )
C
CALL SCTIKS ( SC, '0:01:000', TOL )
C
C
C Get the pointing for the narrow angle camera.
C
CALL CKGP(INST, SCLKDP, TOL, REF, CMAT, CLKOUT, FOUND)
FURNSH
SCENCD (below) and SCDECD require the contents of the SCLK kernel file in order to properly encode and decode clock values. (See section on Spacecraft Clock Time). FURNSH also loads a CK file for processing by other CK routines. It takes as input the name of the C-kernel file to be used, in this example
'vgr2_jup_inbound.bc'Once loaded, a file is ready for any number of reads, so it needs to be loaded only once, typically in the initialization section of your program. Among other things, the lower level routines called by FURNSH open the file with all the appropriate options, relieving you of that responsibility. SCENCD and SCE2C
'3/20556:17:768'into a double precision number (SCLKDP). The value returned by SCENCD is a discrete tick count. When starting with an ET value, a continuous tick count may be obtained by calling SCE2C. You must use encoded SCLK when calling CK reader routines. SCTIKS
The distinction between SCENCD and SCTIKS is important. The result of calling SCENCD is a relative measurement: ticks since the start of the clock at launch. The result of calling SCTIKS is an absolute measurement: ticks. It's like the difference between the times 3:55 p.m. (a specific time of the day) and 3:55 (three hours and fifty-five minutes - a length of time). CKGP
Inputs are:
The CK File Reader CKGPAV
The calling sequence for CKGPAV is:
CALL CKGPAV ( INST, SCLKDP, TOL, REF, CMAT, AV, CLKOUT, FOUND )The angular velocity vector AV is a double precision array of size three. The components of AV are given relative to the base reference frame REF. All of the other arguments are identical to those of CKGP. And, just as with CKGP, you must load a CK file by calling FURNSH before calling CKGPAV. The behavior of CKGPAV is, however, slightly different from that of CKGP, and these differences will be explained in the ``Details'' chapter of this document. Multiple Files and the C-kernel
In both cases, you would like to be able to get the pointing you want without having to run your application on each file separately. C-kernel software allows you to do this through the file loading and unloading process. The file loading routine FURNSH was introduced in the last section. It was mentioned that you have to load the CK file before you try to access it, that you have to load it only once during program execution, and that in subsequent calls to CKGP, you don't have to refer to the file at all. What was not mentioned was that multiple pointing files may be loaded and that CKGP will automatically search through as many of the files as necessary to satisfy the request. If you have multiple files describing pointing for different time periods or different instruments, you can simply load them all at the beginning of your program, and then forget about which file covered what period or instrument. There is a hierarchy for searching, however, that you need to understand in case you happen to load files that have redundant coverage. A request for pointing is satisfied by searching through the last loaded files first. Thus if we ran
CALL FURNSH ( 'ckfile_1.bc' ) CALL FURNSH ( 'ckfile_2.bc' ) CALL FURNSH ( 'ckfile_3.bc' )and then later made a request for pointing, the software would search through ckfile_3 first, ckfile_2 second, and ckfile_1 last. This scheme is consistent with the fact that within an individual file, the data that were inserted last supersede those before them. In essence, loaded files are treated like one big file. What if you have files representing different versions of the same pointing? This is a likely scenario considering there are tools (such as NAIF's C-smithing program) to update and ``improve'' pointing results. For example, suppose you have one file containing predicted pointing values, and another containing improved, updated values. One approach would be to load the files in the following order:
CALL FURNSH ( 'predict.bc' ) CALL FURNSH ( 'update.bc' )This way, the ``better'' (updated) pointing file always gets searched first. If, on the other hand, you want to be explicit about which file to search, you need a way of telling C-kernel software to stop looking in one file, and start looking in another. FURNSH accomplishes the latter by loading a file for processing. To tell C-kernel software to stop looking through a file, then, you need to unload it, with UNLOAD :
C
C Load the first version.
C
CALL FURNSH ( 'predict.bc' )
.
. process pointing from first file.
.
C
C Unload the first version.
C
CALL UNLOAD ( 'predict.bc' )
C
C Load the second version.
C
CALL FURNSH ( 'update.bc' )
.
. process pointing from the second file.
.
CK Coverage Summary Routines
The CKOBJ routine provides an API via which an application can find the set of instruments for which a specified CK file contains data. The instrument IDs are returned in a SPICE ``set'' data structure (see sets.req). The CKCOV routine provides an API via which an application can find the time periods for which a specified CK file provides data for an instrument of interest. The coverage information is a set of disjoint time intervals returned in a SPICE ``window'' data structure (see windows.req). Refer to the headers of CKOBJ and CKCOV for details on the use of those routines. Details
In this chapter we introduce the concept of a CK file segment, and explain how these segments are organized into CK files. We then show exactly how CKGP and CKGPAV go about searching through files and segments to obtain the data that they need. File Structure and Implementation
Notice that the definition of a segment does not specify what type of record it contains. This vagueness is intentional. One of the primary features of the C-kernel is to provide a framework in which to store pointing data in any form, without users having to worry about that form when reading the data. Thus, different segments may contain different implementations of discrete or continuous data, but the same high-level readers are used to access all types. In fact, there are only a couple of routines that are concerned with the internal data type of a segment. Other routines obtain all the information they need about a segment from two fields which precede each segment: ``descriptors'' and ``identifiers.'' Their formats are identical from segment to segment, and provide important information about the data contained inside. Segment Descriptors
A descriptor tells what instrument's pointing is being described, the interval of time for which the segment is valid, the reference frame of the internally stored data, and the segment data type. Each segment descriptor contains two double precision components (DCD) and six integer components (ICD).
-----------------------------------
DCD(1) | Initial SCLK |
-----------------------------------
DCD(2) | Final SCLK |
-----------------------------------
ICD(1) | Instrument |
------------------
ICD(2) | Reference |
------------------
ICD(3) | Data type |
------------------
ICD(4) | Rates Flag |
------------------
ICD(5) | Begin Address |
------------------
ICD(6) | End Address |
------------------
In the ``Looking at Descriptors'' section, you will be shown how to get a descriptor from a particular segment and ``unpack'' it into its double precision and integer components. You can then view the individual components. Segment Identifiers
For the most part, it will be up to the institution that creates a particular C-kernel segment to determine what goes in this free-format 40 character memory cell. However, it should be possible for users to look at a segment identifier and determine who knows the details about the creation of the segment. For example, if a particular identifier looked like
NAIF CSMITHING RET LOGA151then a user should be able to contact NAIF to locate the right people to give the history of that segment: ephemerides used, source of pointing, assumptions, constraints, and so on. Forty characters is not enough space to store all source information for every segment that might be built. Instead, the idea is to provide a pointer to the people or documents that will have all of the details about the source of the data. Comment Area
SPICELIB provides a family of subroutines for handling this Comment Area. The name of each routine in this family begins with the letters ``SPC'' which stand for ``SPk and Ck'' because this feature is common to both types of files. The SPC software provides the ability to add, extract, and delete comments and convert commented files from binary format to SPICE transfer format and back to binary again. The SPC routines and their functions are described in detail in the SPC Required Reading, spc.req. A CK file is a DAF
DAF routines are used at the lowest level to open, close, read, write and search CK files. As such, they allow for maximum flexibility in, for instance, examining a particular number within a segment, or searching for a particular segment within a file. Therefore, if the CK routines presented in this document do not allow you the control you want in looking through files, the DAF routines certainly will. SPICE File Identification Word in CK Files
How the CK Readers Work
The General Search Algorithm
The search ends when a segment is found that can give pointing for the specified instrument at a time falling within the specified tolerance on either side of the request time. Within that segment, the instance closest to the input time is located and returned. The time for which pointing is being returned is not always the closest to the request time in all of the loaded files. The returned time is actually the closest time within the tolerance of the request time from the first segment that can satisfy the request. The algorithm works like this because it assumes that the last loaded files contain the highest quality pointing. Because segments are prioritized in this way users should not make their tolerance argument larger than the minimum spacing between the data in the files they are reading. The following example illustrates this search procedure. Segments A and B are in the same file, with segment A located closer to the end of the file than segment B. Both segments A and B contain discrete pointing data.
SCLKDP TOL
\ /
| |
|/ \
Request 1 [---+---]
. . .
. . .
Segment A (0-----------------0--------0--0-----0)
. . .
. . .
Segment B (-0--0--0--0--0--0--0--0--0--0--0--0--0)
^
|
CK reader returns this instance
SCLKDP
\ TOL
| /
|/\
Request 2 [--+--]
. . .
. . .
Segment A (0-----------------0--------0--0-----0)
^
|
CK reader returns this instance
Segment B (0-0--0--0--0--0--0--0--0--0--0--0--0-0)
Segments that contain continuous pointing data are searched in the same
manner as discrete segments. For request times that fall within the
bounds of continuous intervals, the CK reader will return pointing at
the request time. When the request time does not fall within an
interval, then a time at an endpoint of an interval may be returned if
it is the closest time in the segment to the user request time and also
within the tolerance.
In the following examples segment A contains discrete pointing data and segment C contains continuous data. Segment A is located closer to the end of the file than segment C.
SCLKDP
\ TOL
| /
|/\
Request 3 [--+--]
. . .
. . .
Segment A (0-----------------0--------0--0-----0)
. . .
. . .
Segment C (--[=============]---[====]------[=]--)
^
|
CK reader returns this instance
In the next example assume that the order of segment A and C in file are
reversed.
SCLKDP
\ TOL
| /
|/\
Request 4 [--+--]
. . .
. . .
Segment C (--[=============]---[====]------[=]--)
^
|
CK reader returns this instance
Segment A (0-----------------0--------0--0-----0)
^
|
"Best" answer
The next example illustrates an unfortunate side effect of using a
non-zero tolerance when reading multi-segment CKs with continuous data.
In all cases when the look-up interval formed using tolerance overlaps a
segment boundary and the request time falls within the coverage of the
lower priority segment, the data at the end of the higher priority
segment will be picked instead of the data from the lower priority
segment.
SCLKDP
/
| TOL
| /
|/\
Your request [--+--]
. . .
. . .
Segment C (===============)
^
|
CK reader returns this instance
Segment A (=====================)
^
|
"Best" answer
In general, because using a non-zero tolerance affects selection of the
segment from which the data is obtained, users are strongly discouraged
from using a non-zero tolerance when reading CKs with continuous data.
Using a non-zero tolerance should be reserved exclusively to reading CKs
with discrete data because in practice obtaining data from such CKs
using a zero tolerance is often not possible due to time round off.
The next few sections will go into greater detail about how CKGP and CKGPAV search through segments. The Difference Between CKGP and CKGPAV
Because of this difference, it is possible that on the exact same set of inputs, CKGP and CKGPAV could return different values for the C-matrix. This could occur if a CK file contained two segments covering the same time period for the same instrument, one with angular rates and one without. CKGP might use the C-matrix only segment, whereas CKGPAV would ignore that segment and use the one containing angular velocity data. To avoid this situation, NAIF advises users not to place segments with and without angular velocity data in the same file. Locating the Applicable Segment
CKBSS and CKSNS are both entry points to the routine CKBSR (Buffer Segments for Readers). CKBSS establishes a search for segments. It records the desired instrument (INST), SCLK time (SCLKDP), and SCLK tolerance (TOL) for the search. It also records the need for angular velocity --- NEEDAV is true if angular velocity data is being requested, false otherwise. CKSNS then uses DAF routines to search through loaded files to find a segment matching the criteria established in the call to CKBSS. Last-loaded files get searched first, and within a single file, segments get checked starting from the end of the file and going backwards. When an applicable segment is found, the descriptor and identifier for that segment, and the handle of the file containing the segment, are returned, and the readers output logical flag FOUND is set to true. If no applicable segment is found, FOUND is false. If a segment is found, but is subsequently found to be inadequate, CKSNS can be called again to find the next applicable segment using the searching order described above. CKSNS can be called any number of times after a search has been started by CKBSS, and will just return a false value for FOUND whenever applicable segments have run out. Because CKSNS is called every time a request is made, an internal buffer of segment descriptors is maintained by CKBSR to keep from performing superfluous file reads. You can adjust the size of the buffer by changing the parameter STSIZE in CKBSR. Looking at Descriptors
Evaluating the Records --- the Reader CKPFS
CKPFS takes as input the handle and descriptor of the applicable file and segment, along with the time specifications and angular velocity flag. CKPFS returns the C-matrix and, if requested, the angular velocity vector for the time in the segment closest to SCLKDP and within TOL ticks of it. If CKPFS can't locate a time close enough in the segment, then FOUND is set to false. (If FOUND is false, then CKGP and CKGPAV will try another segment by calling CKSNS again, then CKPFS again, and so on.) The output data are referenced to the base frame indicated by the descriptor. In other words, at this point, CMAT is a transformation from the base frame specified by ICD(2) to instrument-fixed coordinates, and the coordinates of AV lie in that same base frame. Transforming the Results
First, the routines compare the NAIF ID for the requested frame with that of the stored frame. If the requested frame matches the segment frame, there is nothing to be done. Otherwise, the C-matrix and angular velocity vector have to be transformed. Recall that the C-matrix returned by CKPFS is a rotation matrix from a base frame (call it REFSEG) to instrument-fixed coordinates:
[ ] I-fixed | | | CMAT | | | [ ] REFSEGWhat we want is a rotation matrix from the requested frame (call it REFREQ) to instrument-fixed coordinates:
[ ] I-fixed | | | CMAT | | | [ ] REFREQSo all we have to do is multiply the returned C-matrix by a rotation matrix, call it RMAT, from the requested frame to the one specified in the segment:
[ ] I-fixed [ ] I-fixed [ ] REFSEG | | | | | | | CMAT | = | CMAT | | RMAT | | | | | | | [ ] REFREQ [ ] REFSEG [ ] REFREQOnce you have RMAT, it is a trivial matter to transform the angular velocity vector. Its coordinates, upon return from CKPFS, are in the frame REFSEG. Data Types
Each method of storing and evaluating the data contained in a segment defines a different ``data type.'' The data type of a segment is specified by the third integer component of the segment descriptor. The integer code for a data type is equal to the number of that type. For example, a segment of data type 1 would have the third integer component of its descriptor equal to 1. A data type need not accommodate angular velocity data. If it can't, all segments of that data type would have the value of the fourth integer component of the descriptor set equal to zero, which indicates that the segment does not contain angular velocity data. The CK reader that makes a distinction between segments of different data types is the low level reader CKPFS. The main body of CKPFS consists of a case statement of the form:
IF ( TYPE .EQ. 1 ) THEN
.
.
.
ELSE IF ( TYPE .EQ. 2 ) THEN
.
.
.
ELSE IF ( TYPE .EQ. N ) THEN
.
.
.
ELSE
CALL SETMSG( 'The data type # is not currently supported.')
CALL ERRINT( '#', TYPE )
CALL SIGERR( 'SPICE(CKUNKNOWNDATATYPE)' )
END IF
Once CKPFS determines the data type of a segment, two type-specific
routines are called. The first, CKRxx, reads a segment of type xx and
returns the information from the segment necessary to evaluate pointing
at a particular time. The second routine CKExx evaluates the information
returned by CKRxx, producing a C-matrix, and if requested, an angular
velocity vector.
There are currently four supported CK data types in SPICELIB and they are described in detail in the sections that follow. Data Type 1
Each pointing instance is stored as a four-tuple called a ``quaternion.'' Quaternions are widely used to represent rotation matrices. They require less than half the space of 3x3 matrices and finding the rotation matrix given by a quaternion is faster and easier than finding it from, say, RA, Dec, and Twist. In addition, other computations involving rotations, such as finding the rotation representing two successive rotations, may be performed on the quaternions directly. The four numbers of a quaternion represent a unit vector and an angle. The vector represents the axis of a rotation, and the angle represents the magnitude of that rotation. If the vector is U = (u1, u2, u3), and the angle is T, then the quaternion Q is given by:
Q = ( q0, q1, q2, q3 )
= ( cos(T/2), sin(T/2)*u1, sin(T/2)*u2, sin(T/2)*u3 )
The details of quaternion representations of rotations, and the
derivations of those representations are documented in the SPICELIB
Required Reading file ROTATIONS, rotation.req.
Data type 1 provides the option of including angular velocity data. If such data is included, the angular velocity vector A = (a1, a2, a3 ) corresponding to each pointing instance will be stored as itself. The coordinates of the vector will be in the same base reference frame as that of the C-matrix quaternions. A type 1 pointing record consists of either four or seven double precision numbers; four for the C-matrix quaternion, and, optionally, three for the angular velocity vector.
+--------+--------+--------+--------+--------+--------+--------+ | q | q | q | q | a | a | a | | 0 | 1 | 2 | 3 | 1 | 2 | 3 | +--------+--------+--------+--------+--------+--------+--------+Every type 1 segment has four parts to it:
+----------------------------------------------------------------+ | | | | | Pointing | | | | | +----------------------------------------------------------------+ | | | | | SCLK times | | | | | +------------------+ | | | SCLK directory | | | +------------------+ | NPREC | +------------------+The final component, NPREC, gives the total number of pointing instances described by the segment. Preceding it, starting from the top, are NPREC pointing records, ordered with respect to time, each consisting of the four or seven double precision numbers described above. Following the pointing section are the NPREC encoded spacecraft clock times corresponding to the pointing records. These must be in strictly increasing order. Following the SCLK times is a very simple SCLK directory. The directory contains INT( (NPREC-1) / 100 ) entries. The Ith directory entry contains the midpoint of the (I*100)th and the (I*100 + 1)st SCLK time. Thus,
Directory(1) = ( SCLKDP(100) + SCLKDP(101) ) / 2 Directory(2) = ( SCLKDP(200) + SCLKDP(201) ) / 2and so on. If there are 100 or fewer entries, there is no directory. The directory is used to narrow down searches for pointing records to groups of 100 or less. Midpoints of adjacent times are used so that if an input time falls on one side of the directory time, then the group represented by that side is guaranteed to contain the time closest to the input time. Type 1 subroutines
Data Type 2
A type 2 segment consists of disjoint intervals of time during which the angular velocity of the spacecraft is constant. Thus, throughout an interval, the spacecraft structure rotates from its initial position about a fixed right-handed axis defined by the direction of the angular velocity vector at a constant rate equal to the magnitude of that vector. A type 2 CK segment contains the following information for each interval:
Every type 2 segment is organized into four parts.
+----------------------------------------------------------------+ | | | | | Pointing | | | | | +----------------------------------------------------------------+ | | | | | SCLK start times | | | | | +--------------------+ | | | | | SCLK stop times | | | | | +--------------------+ | | | SCLK directory | | | +--------------------+The first part of a segment contains pointing records which are ordered with respect to their corresponding interval start times. A type 2 pointing record contains eight double precision numbers in the following form:
+-------+-------+-------+-------+-------+-------+-------+------+ | | | | | | | | | | q0 | q1 | q2 | q3 | a1 | a2 | a3 | rate | | | | | | | | | | +-------+-------+-------+-------+-------+-------+-------+------+The first four elements are the components of the quaternion Q = (q0,q1,q2,q3) that is used to represent the C-matrix associated with the start time of the interval. Next are the three components of the angular velocity vector A = (a1,a2,a3) which are given with respect to the base reference frame specified in the segment descriptor. The last element is a rate which converts the difference between the requested and interval start time from encoded SCLK ticks to seconds. For segments containing predict data, this factor will be equal to the nominal amount of time represented by one tick of the particular spacecraft's clock. The nominal rate is given here for several spacecraft.
spacecraft seconds / tick ( sec ) --------------------- ---------------------- Galileo 1 / 120 Mars Global Surveyor 1 / 256 Voyager I and II 0.06For segments based on real rather than predicted pointing, the rate at which the spacecraft clock runs relative to ephemeris time will deviate from the nominal rate. The creator of the segment will need to determine an average value for this rate over the time period of the interval. Located after the pointing data are the interval START times followed by the STOP times. The START and STOP times should be ordered and in encoded SCLK form. The intervals should be disjoint except for possibly at the endpoints. If an input request time falls on an overlapping endpoint then the interval used will be the one corresponding to the start time. Degenerate intervals in which the STOP time equals the START time are not allowed. Following the STOP times is a very simple directory of spacecraft clock times containing INT( (NPREC-1)/100 ) entries, where NPREC is the number of pointing intervals. The Ith directory entry contains the midpoint of the (I*100)th STOP and the (I*100 + 1)st START SCLK time.
Thus, Directory(1) = ( STOP(100) + START(101) ) / 2 Directory(2) = ( STOP(200) + START(201) ) / 2 . . .If there are 100 or fewer entries then there is no directory. The directory is used to narrow down searches for pointing records to groups of 100 or less. Type 2 subroutines
Data Type 3
A type 3 segment consists of discrete pointing instances that are partitioned into groups within which linear interpolation between adjacent pointing instances is valid. Since the pointing instances in a segment are ordered with respect to time, these groups can be thought of as representing intervals of time over which the pointing of a spacecraft structure is given continuously. Therefore, in the description that follows, these groups of pointing instances will be referred to as interpolation intervals. All of the pointing instances in the segment must be ordered by encoded spacecraft clock time and must belong to one and only one interpolation interval. The intervals must begin and end at times for which there are pointing instances in the segment. The CK software that evaluates the data in the segment does not extrapolate pointing past the bounds of the intervals. A user's view of the time coverage provided by a type 3 segment can be viewed pictorially as follows:
pointing instances: 0-0-0-0-0----0-0-0-0-0-----0------0-0-0-0
| | | | | | |
interval bounds: BEG | BEG | BEG BEG |
END END END END
In the above picture, the zeros indicate the times associated with the
discrete pointing instances and the vertical bars show the bounds of the
interpolation intervals that they are partitioned into. Note that the
intervals begin and end at times associated with pointing instances.
Also note that intervals consisting of just a single pointing instance
are allowed.
When pointing is desired for a time that is within the bounds of one of the intervals, the CK reader routines return interpolated pointing at the request time. In the example below, the pointing request time is indicated by SCLKDP and the user-supplied tolerance is given by TOL. In this example the tolerance argument of the CK readers could be set to zero and pointing would still be returned.
SCLKDP TOL
\ /
| |
|/ \
[---+---]
. . .
. . .
pointing instances: 0-0-0-0-0----0-0-0-0-0-----0------0-0-0-0
| | | ^ | | | |
interval bounds: BEG | BEG | | BEG BEG |
END | END END END
|
CK reader returns interpolated pointing at this time.
When a request time falls in a gap between intervals, no extrapolation
is performed. Instead, pointing is returned for the interval endpoint
closest to the request time, provided that time is within the user
supplied tolerance. In this example if the tolerance were set to zero no
pointing would be returned.
SCLKDP
\ TOL
| /
|/\
[---+---]
. . .
. . .
pointing instances: 0-0-0-0-0----0-0-0-0-0-----0------0-0-0-0
| | | | | | |
interval bounds: BEG | BEG | BEG BEG |
END END END END
^
|
CK reader returns this instance.
The physical structure of the data stored in a type 3 segment is as
follows:
+-----------------------------------------------------------------+ | | | | | Pointing | | | | | +-----------------------------------------------------------------+ | | | SCLK times | | | +------------------------+ | | | SCLK directory | | | +------------------------+ | | | Interval start times | | | +------------------------+ | | | Start times directory | | | +------------------------+ | | | Number of intervals | | | +------------------------+ | | | Number of pointing | | instances | | | +------------------------+In the discussion that follows let NPREC be the number of pointing instances in the segment and let NUMINT be the number of intervals into which the pointing instances are partitioned. The first part of a segment contains NPREC pointing records which are ordered with respect to increasing time. Depending on whether or not the segment contains angular velocity data, a type 3 pointing record contains either four or seven double precision numbers in the following form:
+--------+--------+--------+--------+--------+--------+--------+ | | | | | | | | | q0 | q1 | q2 | q3 | a1 | a2 | a3 | | | | | | | | | +--------+--------+--------+--------+--------+--------+--------+The first four elements are the components of the quaternion Q = (q0,q1,q2,q3) that is used to represent the pointing of the instrument or spacecraft structure to which the segment applies. Next are the three components of the angular velocity vector AV = (a1,a2,a3) which are given with respect to the base reference frame specified in the segment descriptor. These components are optional and are present only if the segment contains angular velocity data as specified by the fourth integer component of the segment descriptor. Following the pointing data are the NPREC times associated with the pointing instances. These times are in encoded SCLK form and should be strictly increasing. Immediately following the last time is a very simple directory of the SCLK times. The directory contains INT( (NPREC-1) / 100 ) entries. The Ith directory entry contains the (I*100)th SCLK time. Thus,
Directory(1) = SCLKDP(100) Directory(2) = SCLKDP(200) . . .If there are 100 or fewer entries, there is no directory. The directory is used to narrow down searches for pointing records to groups of 100 or less. Next are the NUMINT start times of the intervals that the pointing instances are partitioned into. These times are given in encoded spacecraft clock and must be strictly increasing. They must also be equal to times for which there are pointing instances in the segment. Note that the interval stop times are not stored in the segment. They are not needed because the stop time of the Ith interval is simply the time associated with the pointing instance that precedes the start time of the (I+1)th interval. Following the interval start times is a directory of these times. This directory is constructed in a form similar to the directory for the times associated with the pointing instances. The start times directory contains INT ( (NUMINT-1) / 100 ) entries and contains every 100th start time. Thus:
Directory(1) = START(100) Directory(2) = START(200) . . .Finally, the last two words in the segment give the total number of interpolation intervals (NUMINT) and the total number of pointing instances (NPREC) in the segment. A segment writer routine is provided which calls the low level DAF routines necessary to write a type 3 segment to a C-kernel. However, the creator of the segment is responsible for determining whether or not it is valid to interpolate between adjacent pointing instances, and thus how they should be partitioned into intervals. See the header of the routine CKW03 for a complete description of the inputs required to write a segment. Linear Interpolation Algorithm
t1 <= t <= t2, where t1 < t2.
T T
CMAT2 = ROT12 * CMAT1
or
T
ROT12 = CMAT2 * CMAT1
( t - t1 )
THETA = ANGLE * -----------
( t2 - t1 )
T T
CMAT = ROT1t * CMAT1
T
CMAT = CMAT1 * ROT1t
( t - t1 )
W = -----------
( t2 - t1 )
AV = ( 1 - W ) * AV1 + W * AV2
Type 3 subroutines
Data Type 4
A Type 4 segment contains one or more sets of Chebychev polynomial coefficients that approximate orientation and optionally angular rate of a spacecraft, spacecraft structure or science instrument. Each set of coefficients is valid for a specific interval of time, the bounds of which are attached to the set. A typical Type 4 segment coverage is shown in the picture below:
continuous pointing: 0-------0-------0 00 0-----0
| | | || | |
interval bounds: BEG |BEG | BEG| BEG |
END END END END
In the picture, the zeros indicate the times associated with the bounds
of intervals where pointing is available (between BEG and END) and not
available (between END and BEG). Zero length intervals are not allowed.
When pointing is desired for a time that is within the bounds of one of the intervals, the CK reader routines return pointing and optionally angular rate computed at the request time from Chebychev polynomials for that interval. In the example below, the pointing request time is indicated by SCLKDP and the user supplied tolerance is given by TOL. In this example the tolerance argument could be set to zero and pointing would still be returned.
SCLKDP TOL
\ /
| |
|/ \
[---+---]
. . .
. . .
continuous pointing: 0-------0-------0 00 0-----0
| | ^ | || | |
interval bounds: BEG |BEG . | BEG| BEG |
END . END END END
.
CK reader returns pointing at this time.
When a request time falls in a gap between intervals, pointing is
evaluated for the interval endpoint closest to the request time if there
is an endpoint within the user supplied tolerance of the request time.
In this example if the tolerance were set to zero no pointing would be
returned.
SCLKDP TOL
\ /
| |
|/ \
[---+---]
. . .
. . .
continuous pointing: 0-------0-------0 00 0-----0
| | | || | |
interval bounds: BEG |BEG | BEG| BEG |
END END END END
^
|
CK reader returns this instance.
The CK data Type 4 uses the SPICELIB concept of a generic segment to
store a collection of packets each of which models the pointing of a
spacecraft, spacecraft structure or science instrument during some
interval of time. Each packet contains sets of coefficients for
Chebychev polynomials that approximate the orientation quaternion. The
packets may optionally contain polynomial coefficients for angular
velocity vector components. The time intervals covered by individual
packets in a CK Type 4 segment are non-overlapping and can have variable
length. There can be gaps between intervals; the gaps can also be of
variable length.
The storage, arrangement and retrieval of packets is handled by the SPICELIB generic segment routines. That software is described in the document GENSEG.REQ. We only review the pertinent points about generic segments here. A generic CK segment contains several logical data partitions:
+============================+
| Constants |
+============================+
| Packet 1 |
|----------------------------|
| Packet 2 |
|----------------------------|
| . |
| . |
| . |
|----------------------------|
| Packet N |
+============================+
| Reference Times |
+============================+
| Packet Directory |
+============================+
| Time Directory |
+============================+
| Reserved Area |
+============================+
| Segment Metadata |
+----------------------------+
Only the placement of the metadata at the end of a generic segment is
required. The other data partitions may occur in any order in the
generic segment because the metadata will contain pointers to their
appropriate locations within the generic segment.
In the case of Type 4 CK segments each ``packet'' contains time of the middle of approximation interval SCLKDP, radius of approximation interval RADIUS, numbers of coefficients for each quaternion and angular rate component encoded in a single DP number, and four or seven sets of Chebychev polynomial coefficients which approximate four quaternion components and (optionally) three angular velocity components during the given time interval. In order to provide a more compact data representation the number of coefficients can vary from component to component. To accomodate this generic segments with variable sized data packets are used as the underlying structure holding CK Type 4 data. Each data packet has the following structure:
+----------------------------------------------+
| Midpoint of approx. interval |
+----------------------------------------------+
| Radius of interval |
+----------------------------------------------+
| Number of coefficients for |
| (Q0,Q1,Q2,Q3,AV1,AV2,AV3) |
+----------------------------------------------+
| q0 Cheby coefficients |
+----------------------------------------------+
| q1 Cheby coefficients |
+----------------------------------------------+
| q2 Cheby coefficients |
+----------------------------------------------+
| q3 Cheby coefficients |
+----------------------------------------------+
| av1 Cheby coefficients (optional) |
+----------------------------------------------+
| av2 Cheby coefficients (optional) |
+----------------------------------------------+
| av3 Cheby coefficients (optional) |
+----------------------------------------------+
The maximum Chebychev polynomial degree allowed in CK Type 4 is 18.
Packets within a CK Type 4 segment must be stored in strictly time increasing order. The numbers of coefficients for each quaternion and angular rate component are packed into a single DP number using an encoding subroutine which is a part of the SPICELIB CK4 subroutines family. This DP number occurs as the third entry in a packet. The ``constants'' partition in CK Type 4 does not contain any values. The reference times partition contains an ordered collection of encoded spacecraft clock times. The i'th reference time corresponds to the beginning of the interval for which the i'th packet can be used to determine the pointing of spacecraft. The ``time directory'' contains every 100th reference time. The time directory is used to efficiently locate the reference times that should be associated with a time for which a pointing has been requested. As noted above the exact location of the various partitions must be obtained from the metadata contained at the end of the segment. Access to the Type 4 CK data is made via the SPICELIB generic segment routines. Type 4 CK segments should be created using CK Type 4 writer subroutines CKW04B, CKW04A and CKW04E, provided in the SPICELIB. CK Type 4 pointing evaluation algorithm
Type 4 subroutines
Data Type 5
Because of the possibility of evolution of the mathematical representations of spacecraft attitude used by ESA, CK type 5 is designed to accommodate multiple representations, thereby avoiding a proliferation of CK data types. CK type 5 refers to each supported mathematical representation of attitude data as a ``subtype.'' Currently CK type 5 supports four subtypes. All of these use polynomial interpolation to provide continuous pointing data. However, the creator of a type 5 segment may wish to restrict the intervals over which interpolation is allowed to occur. To support this capability, CK type 5 uses the same interpolation interval scheme as does type 3. This scheme will be explained shortly. The CK type 5 subtypes are as follows:
If the request time coincides with a time tag, the window may be positioned so that either of the central time tags of the window matches the request time. The Lagrange and Hermite interpolation algorithms will produce only round-off level differences between the results obtained from either choice, provided the input data are suitable for interpolation. When the request time is near a segment or interpolation interval boundary, the window is truncated if necessary on the side closest to the boundary. If a segment or interpolation interval contains too few packets to form a window of nominal size, a window will be constructed from the all of the available packets that lie within the nominal window location. In this case the window size may be odd. In any case the window never includes more than WNDSIZ/2 time tags on either side of the request time, where WNDSIZ is the nominal window size. Regarding interpolation intervals: the pointing time tags in a type 5 segment are partitioned into groups within which polynomial interpolation between adjacent groups of WNDSIZ pointing instances is valid. Since the pointing instances in a segment are ordered with respect to time, these groups can be thought of as representing intervals of time over which the pointing of the spacecraft (or a spacecraft instrument or structure) is given continuously. Therefore, in the description that follows, these groups of pointing instances will be referred to as interpolation intervals. All of the pointing instances in the segment must be ordered by encoded spacecraft clock time and must belong to one and only one interpolation interval. The intervals must begin and end at times for which there are pointing instances in the segment. The CK software that evaluates the data in the segment does not extrapolate pointing past the bounds of the intervals. A user's view of the time coverage provided by a type 5 segment can be viewed pictorially as follows:
pointing instances: 0-0-0-0-0----0-0-0-0-0-----0------0-0-0-0
| | | | | | |
interval bounds: BEG | BEG | BEG BEG |
END END END END
In the above picture, the zeros indicate the times associated with the
discrete pointing instances and the vertical bars show the bounds of the
interpolation intervals that they are partitioned into. Note that the
intervals begin and end at times associated with pointing instances.
Also note that intervals consisting of just a single pointing instance
are allowed.
When pointing is desired for a time that is within the bounds of one of the intervals, the CK reader routines return interpolated pointing at the request time. In the example below, the pointing request time is indicated by SCLKDP and the user supplied tolerance is given by TOL. In this example the tolerance argument of the CK readers could be set to zero and pointing would still be returned.
SCLKDP TOL
\ /
| |
|/ \
[---+---]
. . .
. . .
pointing instances: 0-0-0-0-0----0-0-0-0-0-----0------0-0-0-0
| | | ^ | | | |
interval bounds: BEG | BEG | | BEG BEG |
END | END END END
|
CK reader returns interpolated pointing at this time.
When a request time falls in a gap between intervals, no extrapolation
is performed. Instead, pointing is returned for the interval endpoint
closest to the request time, provided that time is within the user
supplied tolerance. In this example if the tolerance were set to zero no
pointing would be returned.
SCLKDP
\ TOL
| /
|/\
[---+---]
. . .
. . .
pointing instances: 0-0-0-0-0----0-0-0-0-0-----0------0-0-0-0
| | | | | | |
interval bounds: BEG | BEG | BEG BEG |
END END END END
^
|
CK reader returns this instance.
The physical structure of the data stored in a type 5 segment is as
follows:
+-----------------------+
| Packet 1 |
+-----------------------+
| Packet 2 |
+-----------------------+
.
.
.
+-----------------------+
| Packet N |
+-----------------------+
| Epoch 1 |
+-----------------------+
| Epoch 2 |
+-----------------------+
.
.
.
+----------------------------+
| Epoch N |
+----------------------------+
| Epoch 100 | (First directory)
+----------------------------+
.
.
.
+----------------------------+
| Epoch ((N-1)/100)*100 | (Last directory)
+----------------------------+
| Start time 1 |
+----------------------------+
| Start time 2 |
+----------------------------+
.
.
.
+----------------------------+
| Start time NUMINT |
+----------------------------+
| Start time 100 | (First interval start
+----------------------------+ time directory)
.
.
.
+----------------------------+
| Start ((NUMINT-1)/100)*100 | (Last interval start
+----------------------------+ time directory)
| Seconds per tick |
+----------------------------+
| Subtype code |
+----------------------------+
| Window size |
+----------------------------+
| Number of interp intervals |
+----------------------------+
| Number of packets |
+----------------------------+
In the discussion that follows let N be the number of pointing instances
in the segment and let NUMINT be the number of intervals into which the
pointing instances are partitioned.
The first part of a segment contains N packets (pointing records) which are ordered with respect to increasing time. Depending the segment subtype, a type 5 packet contains from four to fourteen d.p. numbers. Following the pointing data are the N times associated with the pointing instances. These times are in encoded SCLK form and should be strictly increasing. Immediately following the last time is a very simple directory of the SCLK times. The directory contains INT( (N-1) / 100 ) entries. The Ith directory entry contains the (I*100)th SCLK time. Thus,
Directory(1) = SCLKDP(100) Directory(2) = SCLKDP(200) . . .If there are 100 or fewer entries, there is no directory. The directory is used to narrow down searches for pointing records to groups of 100 or less. Next are the NUMINT start times of the intervals that the pointing instances are partitioned into. These times are given in encoded spacecraft clock and must be strictly increasing. They must also be equal to times for which there are pointing instances in the segment. Note that the interval stop times are not stored in the segment. They are not needed because the stop time of the Ith interval is simply the time associated with the pointing instance that precedes the start time of the (I+1)th interval. Following the interval start times is a directory of these times. This directory is constructed in a form similar to the directory for the times associated with the pointing instances. The start times directory contains INT ( (NUMINT-1) / 100 ) entries and contains every 100th start time. Thus:
Directory(1) = START(100) Directory(2) = START(200) . . .Finally, the last five words in the segment are:
Type 5 subroutines
Type 6: ESOC/DDID Piecewise Interpolation
CK type 6 is an enhanced version of CK type 5. Type 6 enables creation of CK files representing the same attitude data that can be represented using type 5, but containing far fewer segments. Data from multiple type 5 segments can be stored in a single type 6 segment, as long as the type 5 segments satisfy certain restrictions:
Terminology
A ``packet'' is a set of data representing pointing for a given time. Such a set is also referred to as a ``pointing instance.'' Times associated with packets are variously called ``times,'' ``epochs,'' or ``time tags.'' Time tags represent the independent variable of attitude data: they are times at which the associated data are applicable. All times, unless otherwise indicated, are encoded spacecraft clock values, also called ``ticks.'' Mini-segment time coverage bounds are also called ``boundaries.'' Mini-segments
The mini-segments of a type 6 segment need not use the same packet counts, subtypes, clock rates, or interpolation degrees. The time coverage of a mini-segment is called a ``mini-segment interval.'' The mini-segment intervals of a type 6 segment have no intervening gaps (gaps may occur only within mini-segment intervals) and overlap only at single points. The stop time of each mini-segment interval is the start time of the next. The start time of a type 6 segment is greater than (later than) or equal to the start time of the first interval, and the segment's stop time is less than (earlier than) or equal to the stop time of the last interval. Mini-segment intervals must have strictly positive length. An example of the relationship between the time coverage of a type 6 segment and that of its mini-segments is shown below:
mini-segment interval bounds: |----------|----|--------|-|--| segment bounds: [ ]Each mini-segment contains a time ordered, strictly increasing sequence of epochs (no two epochs of the same mini-segment may coincide) and an associated sequence of attitude data sets called ``packets.'' The epoch associated with a packet is also called a ``time tag.'' The composition of a packet depends on the subtype of the mini-segment to which the packet belongs; subtypes are discussed in more detail below. The start time of each mini-segment interval must be greater than or equal to the first member of the corresponding time tag sequence. The stop time of each mini-segment interval must be greater than the interval's start time and is allowed to exceed the last member of the mini-segment's time tag sequence. Thus a mini-segment interval can have a coverage gap between its last time tag and its stop time. There cannot be a gap between a mini-segment interval's stop time and the start time of the next mini-segment interval. The interpolation interval associated with a mini-segment is the time interval over which the mini-segment can satisfy a pointing request. The interpolation interval extends from the start time of the corresponding ``mini-segment interval'' to the minimum of the stop time of the mini-segment interval and the last time tag of the mini-segment's time tag sequence. Mini-segments may contain optional ``padding'' time tags and packets beyond both ends of their coverage intervals. Padding time tags on the left of a mini-segment interval are less than the interval start time; padding time tags on the right exceed the interval stop time. Padding enables control of interpolation behavior at and near mini-segment interval boundaries. Within a mini-segment, padding cannot occur to the right of a gap. Padding does not contribute to a mini-segment's time coverage. The relationships between the time coverage of a mini-segment (the ``mini-segment interval''), the time tags of the pointing instances it contains, and the mini-segment's interpolation interval are shown below. In the following diagrams, zeros represent pointing instances, hyphens represent time periods over which pointing data can be used as inputs for interpolation (this includes padding), and blank areas represent coverage gaps. Mini-segment interval without padding:
pointing instances: 0-0-0--0-0-0-0-0---0-0-0---0-0-0 mini-segment interval bounds: | | interpolation interval bounds: ^ ^Mini-segment interval with padding on both sides:
pointing instances: 0-0-0--0-0-0-0-0---0-0-0---0-0-0 mini-segment interval bounds: | | interpolation interval bounds: ^ ^Note that when padding is present, mini-segment interval bounds need not coincide with time tags of pointing instances. Mini-segment interval with left-side padding and with a gap:
pointing instances: 0-0-0--0-0-0-0-0---0-0 mini-segment interval bounds: | | interpolation interval bounds: ^ ^Padding within or beyond a gap is not supported:
not allowed
v v v
pointing instances: 0-0-0--0-0-0-0-0---0-0 0-0-0
mini-segment interval bounds: | |
interpolation interval bounds: ^ ^
last "usable" time tag -------+
| not allowed
v v v
pointing instances: 0-0-0--0-0-0-0-0-0-0-0
mini-segment interval bounds: | |
interpolation interval bounds: ^ ^
The use of padding is discussed in greater detail below.
When type 6 data are interpolated to produce an attitude instance for a given request time, if the look-up tolerance is zero, only data from a single mini-segment whose interval contains the request time are used. When a request time coincides with the boundary between two mini-segment intervals, there is a choice as to which interval will provide attitude data. The creator of a type 6 segment can control this behavior via a parameter passed to the type 6 segment writer CKW06; this parameter is called the interval selection flag. For a given type 6 segment, depending on the value of this flag, either the earlier interval is always selected, or the later interval is always selected:
Pointing request time: | mini-segment interval n: 0-0-0-0-0-0-0-0-0-0-0 mini-segment interval n+1: @-@-@-@-@-@-@-@-@-@ mini-segment interval bounds: | | |In the case depicted by the above diagram, if the interval selection flag is set to "true," pointing will be selected from interval n+1; if the flag is "false," pointing will be selected from interval n. Type 6 subtypes
Currently CK type 6 supports four subtypes:
If the request time coincides with a time tag, the window may be positioned so that either of the central time tags of the window matches the request time. The Lagrange and Hermite interpolation algorithms will produce only round-off level differences between the results obtained from either choice, provided the input data are suitable for interpolation. In CK type 6, mini-segment interval boundaries affect interpolation in the same way that segment boundaries affect type 5 interpolation. When the request time is near a mini-segment boundary, the window is truncated if necessary on the side closest to the boundary. If mini-segment interval, including padding, contains too few packets to form a window of nominal size, as many packets as are needed and available are used to construct the window. In this case the window size may be odd. In any case the window never includes more than WNDSIZ/2 time tags on either side of the request time, where WNDSIZ is the nominal window size. Restrictions on type 6 data
In addition, quaternion data for subtypes 0 and 2 must have signs chosen so that large variations between successive values of any quaternion element do not occur. For any attitude represented by a quaternion Q, the quaternion -Q represents the same attitude. But only one of these choices can be ``near'' the previous quaternion P in the mini-segment containing Q, in the Euclidean norm sense. Quaternion signs must be selected so that the elements of adjacent quaternions are always ``near'' each other, and quaternion derivatives must be consistent with the selected quaternions. Subtypes 1 and 3 do not have quaternion sign restrictions; the interpolation algorithms for these subtypes adjust quaternion signs at run time if necessary. These subtypes do require that the attitudes represented by adjacent quaternions be ``close'' to each other: if adjacent quaternions are converted to rotation matrices, the matrices must be close to each other. Type 6 segment structure
Type 6 CK segments have the structure shown below:
+---------------------------------------+
| Mini-segment 1 |
+---------------------------------------+
.
.
.
+---------------------------------------+
| Mini-segment N |
+---------------------------------------+
| Mini-segment interval 1 start time |
+---------------------------------------+
.
.
.
+---------------------------------------+
| Mini-segment interval N start time |
+---------------------------------------+
| Mini-segment interval N stop time |
+---------------------------------------+
| Mini-seg. interval start time 100 | (First interval
+---------------------------------------+ directory)
.
.
.
+---------------------------------------+
| Mini-seg. ival. start time (N/100)*100| (Last interval
+---------------------------------------+ directory)
| Mini-segment 1 start pointer |
+---------------------------------------+
.
.
.
+---------------------------------------+
| Mini-segment N start pointer |
+---------------------------------------+
| Mini-segment N stop pointer + 1 |
+---------------------------------------+
| Interval selection flag |
+---------------------------------------+
| Number of intervals |
+---------------------------------------+
In the diagram above, each box labeled as a mini-segment represents a
data structure; the format of these data structures is described below.
The other boxes represent individual double precision numbers.
The mini-segments themselves form the initial portion of the segment. The array of mini-segment interval time bounds contains the start time of each mini-segment interval, plus the stop time of the final interval. The list of mini-segment interval time bounds has its own directory, which has the same structure as the time tag directories of type 5 segments. As with time tag directories, the mini-segment interval boundary directory contains boundary times whose indices are multiples of 100, except that if N+1 is a multiple of 100, the last boundary time is not included. The array of mini-segment pointers contains a pointer to the start of each mini-segment, plus a final ``stop'' pointer for the final mini-segment. The stop pointer points to the location immediately following the last address of the final mini-segment. The mini-segment pointers are offsets relative to the start address of the segment. Each start pointer, when added to the segment's start address, yields the address of the first item in the corresponding mini-segment. Following the mini-segment pointers is the interval selection flag. When this flag has the value 1, the later interpolation interval is used when a request time falls on the common boundary between two interpolation intervals. If the selection flag is 0, the earlier interval is used. The structure of a type 6 CK mini-segment is similar to the structure of a type 5 CK segment, except that a type 6 mini-segment contains no array of interpolation interval start times, and hence no directory for interpolation interval start times. The CK type 6 mini-segment structure is as follows:
+--------------------------+
| Packet 1 |
+--------------------------+
.
.
.
+--------------------------+
| Packet M |
+--------------------------+
| Time tag 1 |
+--------------------------+
.
.
.
+--------------------------+
| Time tag M |
+--------------------------+
| Time tag 100 | (First time tag directory)
+--------------------------+
.
.
.
+--------------------------+
| Time tag ((M-1)/100)*100 | (Last time tag directory)
+--------------------------+
| Clock rate (sec/tick) |
+--------------------------+
| Subtype code |
+--------------------------+
| Window size |
+--------------------------+
| Number of packets |
+--------------------------+
In the mini-segment diagram, each box representing a packet corresponds
to a set of PKTSIZ double precision numbers, where PKTSIZ depends on the
mini-segment's subtype; the other boxes represent individual double
precision numbers.
The window size is related to the polynomial degree as shown:
Subtypes 0,2: WINDOW_SIZE = ( DEGREE + 1 ) / 2 Subtypes 1,3: WINDOW_SIZE = DEGREE + 1Window sizes are required to be even; this imposes the interpolation degree restrictions
Subtypes 0,2: the degree is equivalent to 3 mod 4, i.e.,
the degree is in the set { 3, 7, 11, ... }
Subtypes 1,3: the degree is odd
The number of packets normally should be greater than or equal to the
mini-segment's interpolation window size, but this is not a requirement.
The packet count may not be less than 2.
The set of time tags is augmented by a sequence of directory entries; these entries allow the type 6 reader to search for time tags more efficiently. The directory entries contain time tags whose indices are multiples of 100. The set of indices of time tags stored in the directories ranges from 100 to
( (M-1) / 100 ) * 100where M is the total number of time tags. Note that if M is
Q * 100then only
Q - 1directory entries are stored, and in particular, if there are only 100 packets in the segment, there are no directories. Following the time tag directory are four parameters associated with the mini-segment: the rate of the associated spacecraft clock, in units of seconds/tick, the subtype, the interpolation window size, and the packet count. To facilitate the creation of type 6 segments, a segment writing routine called CKW06 has been provided. This routine takes as input arguments the handle of an CK file that is open for writing, the information needed to construct the segment descriptor, the mini-segments' parameters, and the data to be stored in the segment. The header of the subroutine provides a complete description of the input arguments and an example of its usage. Use of non-zero tolerance
When a non-zero tolerance value is used to look up data from a type 6 segment, the algorithm for selecting data is not exactly the same as it would be for a sequence of type 5 segments corresponding to the type 6 segment's mini-segments. As described in the earlier section titled "The General Search Algorithm," if each mini-segment were replaced with a type 5 segment, it would be possible for a later segment to take precedence over an earlier one, even if the earlier segment had no coverage gap, if a request time were outside of the coverage interval of the higher priority segment but within the tolerance of the higher priority segment's coverage interval. This precedence effect cannot occur between two mini-segments of the same type 6 segment. Specifically, it is not possible for a mini-segment to provide data to satisfy a pointing request when the request time outside of its coverage interval and is in the interpolation interval (and hence not in a gap) of a different mini-segment of the same type 6 segment. This difference is highly unlikely to affect users of type 6 CK segments. Type 6 subroutines
Appendix A --- Summary of C-kernel SubroutinesSummary of Mnemonics
Many of the routines listed below are entry points to another subroutine. If they are, the parent routine's name will be listed inside brackets preceding the mnemonic translation.
Kernel Loading/Unloading Routines
FURNSH ( Load kernel file of any type )
UNLOAD ( Unload kernel file of any type )
C-kernel Routines
CKBSS [CKBSR] ( C-kernel, begin search for segment )
CKCLS ( C-kernel, close a pointing file )
CKCOV ( C-kernel, coverage for an instrument )
CKE01 ( C-kernel, evaluate pointing record, data type 1 )
CKE02 ( C-kernel, evaluate pointing record, data type 2 )
CKE03 ( C-kernel, evaluate pointing record, data type 3 )
CKE04 ( C-kernel, evaluate pointing record, data type 4 )
CKE05 ( C-kernel, evaluate pointing record, data type 5 )
CKE06 ( C-kernel, evaluate pointing record, data type 6 )
CKGP ( C-kernel, get pointing )
CKGPAV ( C-kernel, get pointing and angular velocity )
CKGR01 ( C-kernel, get record, data type 1 )
CKGR02 ( C-kernel, get record, data type 2 )
CKGR03 ( C-kernel, get record, data type 3 )
CKGR04 ( C-kernel, get record, data type 4 )
CKGR05 ( C-kernel, get record, data type 5 )
CKGR06 ( C-kernel, get record, data type 6 )
CKLPF [CKBSR] ( C-kernel, load pointing file )
CKMP06 ( C-kernel, get mini-segment params, data type 6 )
CKNM06 ( C-kernel, get mini-segment count, data type 6 )
CKNR01 ( C-kernel, number of records, data type 1 )
CKNR02 ( C-kernel, number of records, data type 2 )
CKNR03 ( C-kernel, number of records, data type 3 )
CKNR04 ( C-kernel, number of records, data Type 4 )
CKOBJ ( C-kernel, instruments in a file )
CKOPN ( C-kernel, open a new pointing file )
CKPFS ( C-kernel, pointing from segment )
CKR01 ( C-kernel, read pointing record, data type 1 )
CKR02 ( C-kernel, read pointing record, data type 2 )
CKR03 ( C-kernel, read pointing record, data type 3 )
CKR04 ( C-kernel, read pointing record, data type 4 )
CKR05 ( C-kernel, read pointing record, data type 5 )
CKR06 ( C-kernel, read pointing record, data type 6 )
CKSNS [CKBSR] ( C-kernel, select next segment )
CKUPF [CKBSR] ( C-kernel, unload pointing file )
CKW01 ( C-kernel, write segment to C-kernel, data type 1 )
CKW02 ( C-kernel, write segment to C-kernel, data type 2 )
CKW03 ( C-kernel, write segment to C-kernel, data type 3 )
CKW04A ( C-kernel, add to a Type 4 segment )
CKW04B ( C-kernel, begin a Type 4 segment )
CKW04E ( C-kernel, end a Type 4 segment )
CKW05 ( C-kernel, write segment to C-kernel, data type 5 )
CKW06 ( C-kernel, write segment to C-kernel, data type 6 )
SCLK conversion routines
SCDECD ( Decode spacecraft clock )
SCENCD ( Encode spacecraft clock )
SCPART ( Spacecraft clock partitions )
SCFMT ( Spacecraft clock format )
SCTIKS ( Spacecraft clock ticks )
SCT2E ( Convert encoded SCLK Ticks to ET )
SCS2E ( Convert SCLK String to ET )
SCE2C ( Convert ET to continuous SCLK Ticks )
SCE2T ( Convert ET to encoded SCLK Ticks )
SCE2S ( Convert ET to SCLK String )
UTC2ET ( UTC to Ephemeris Time )
ET2UTC ( Ephemeris Time to UTC )
Inertial Reference frame routines
IRFROT [CHGIRF] ( Inertial reference frame, rotate )
IRFNUM [CHGIRF] ( Inertial reference frame number )
IRFNAM [CHGIRF] ( Inertial reference frame name )
IRFDEF [CHGIRF] ( Inertial reference frame, default )
Summary of Calling Sequences
Kernel Loading/Unloading Routines
FURNSH ( FNAME )
UNLOAD ( FNAME )
C-kernel Routines
CKCOV ( FNAME, IDCODE, NEEDAV, LEVEL, TOL, TIMSYS, COVER )
CKOBJ ( FNAME, IDS )
CKLPF ( FNAME, HANDLE )
CKUPF ( HANDLE )
CKBSS ( INST, SCLKDP, TOL, NEEDAV )
CKSNS ( HANDLE, DESCR, SEGID, FOUND )
CKGP ( INST, SCLKDP, TOL, REF, CMAT, CLKOUT, FOUND )
CKGPAV ( INST, SCLKDP, TOL, REF, CMAT, AV, CLKOUT,
FOUND )
CKPFS ( HANDLE, DESCR, SCLKDP, TOL, NEEDAV, CMAT, AV,
CLKOUT, FOUND )
CKOPN ( FNAME, IFNAME, NCOMCH, HANDLE )
CKCLS ( HANDLE )
CKR01 ( HANDLE, DESCR, SCLKDP, TOL, NEEDAV, RECORD, FOUND )
CKE01 ( NEEDAV, RECORD, CMAT, AV, CLKOUT )
CKW01 ( HANDLE, BEGTIM, ENDTIM, INST, REF, AVFLAG, SEGID,
NPREC, SCLKDP, QUATS, AVVS )
CKNR01 ( HANDLE, DESCR, NPREC )
CKGR01 ( HANDLE, DESCR, RECNO, RECORD )
CKR02 ( HANDLE, DESCR, SCLKDP, TOL, RECORD, FOUND )
CKE02 ( NEEDAV, RECORD, CMAT, AV, CLKOUT )
CKW02 ( HANDLE, BEGTIM, ENDTIM, INST, REF, SEGID, NPREC,
START, STOP, QUATS, AVVS, RATES )
CKNR02 ( HANDLE, DESCR, NPREC )
CKGR02 ( HANDLE, DESCR, RECNO, RECORD )
CKR03 ( HANDLE, DESCR, SCLKDP, TOL, NEEDAV, RECORD, FOUND )
CKE03 ( NEEDAV, RECORD, CMAT, AV, CLKOUT )
CKW03 ( HANDLE, BEGTIM, ENDTIM, INST, REF, AVFLAG, SEGID,
NPREC, SCLKDP, QUATS, AVVS, NINTS, STARTS )
CKNR03 ( HANDLE, DESCR, NPREC )
CKGR03 ( HANDLE, DESCR, RECNO, RECORD )
CKE04 ( NEEDAV, RECORD, CMAT, AV, CLKOUT )
CKGR04 ( HANDLE, DESCR, RECNO, RECORD )
CKNR04 ( HANDLE, DESCR, NREC )
CKR04 ( HANDLE, DESCR, SCLKDP, TOL, NEEDAV, RECORD, FOUND )
CKW04A ( HANDLE, NPKTS, PKTSIZ, PKTDAT, SCLKDP )
CKW04B ( HANDLE, BEGTIM, INST, REF, AVFLAG, SEGID )
CKW04E ( HANDLE, ENDTIM )
CKR05 ( HANDLE, DESCR, SCLKDP, TOL, NEEDAV, RECORD, FOUND )
CKE05 ( NEEDAV, RECORD, CMAT, AV, CLKOUT )
CKW05 ( HANDLE, SUBTYP, DEGREE, BEGTIM, ENDTIM, INST, REF,
AVFLAG, SEGID, NPREC, SCLKDP, PACKTS, NINTS, STARTS )
CKNR05 ( HANDLE, DESCR, NPREC )
CKGR05 ( HANDLE, DESCR, RECNO, RECORD )
CKMP06 ( HANDLE, DESCR, MSNO, RATE, SUBTYP, WINSIZ, NREC,
IVLBDS, LSTEPC )
CKNM06 ( HANDLE, DESCR, NMINI )
CKGR06 ( HANDLE, DESCR, MSNO, RECNO, RECORD )
CKE06 ( NEEDAV, RECORD, CMAT, AV, CLKOUT )
CKR06 ( HANDLE, DESCR, SCLKDP, TOL, NEEDAV, RECORD, FOUND )
CKW06 ( HANDLE, INST, REF, AVFLAG, FIRST, LAST, SEGID,
NMINI, NPKTS, SUBTPS, DEGRES, PACKTS, RATES, SCLKDP,
IVLBDS, SELLST )
SCLK conversion routines
SCDECD ( SC, SCLKDP, SCLKCH )
SCENCD ( SC, SCLKCH, SCLKDP )
SCPART ( SC, NPARTS, PSTART, PSTOP )
SCFMT ( SC, TICKS, CLKSTR )
SCTIKS ( SC, CLKSTR, TICKS )
SCT2E ( SC, SCLKDP, ET )
SCS2E ( SC, SCLKCH, ET )
SCE2C ( SC, ET, SCLKDP )
SCE2T ( SC, ET, SCLKDP )
SCE2S ( SC, ET, SCLKCH )
UTC2ET ( UTCSTR, ET )
ET2UTC ( ET, FORMAT, PREC, UTCSTR )
Inertial Reference frame routines
IRFROT ( REFA, REFB, ROTAB )
IRFNUM ( NAME, INDEX )
IRFNAM ( INDEX, NAME )
IRFDEF ( INDEX )
Appendix B --- Example Program PLANET_POINT
All of the subroutines used here are part of SPICELIB.
PROGRAM PLANET_POINT
IMPLICIT NONE
C
C Compute the planetocentric latitude, longitude and radius
C of the point at which the optic axis of an instrument
C intersects the surface of a target planet. Assume that
C the axis of the instrument is along the Z-axis of the
C instrument fixed reference frame.
C
C The following files are required:
C
C 1) Kernel file containing planetary constants.
C 2) Kernel file containing spacecraft clock (SCLK) data.
C 3) SPK file containing planetary and spacecraft
C ephemeris data.
C 4) CK file containing instrument pointing data.
C
C The following quantities are required:
C
C 1) NAIF integer spacecraft ID
C 2) NAIF integer planet ID
C 3) NAIF integer instrument ID
C 4) SCLK time string
C 5) SCLK tolerance.
C
C The following steps are taken to locate the desired point:
C
C 1) The inertial pointing (VPNT) of the instrument at
C the input SCLK time is read from the CK file.
C
C 2) The apparent position (VTARG) is computed for the
C center of the target body as seen from the spacecraft,
C at the ephemeris time (ET) corresponding to SCLK.
C
C The one-way light time (TAU) from the target to the
C spacecraft is also computed.
C
C 3) The transformation (TIBF) from inertial to body-fixed
C coordinates is computed for the epoch ET-TAU, using
C quantities from the planetary constants kernel.
C
C 4) The radii (R) of the tri-axial ellipsoid used to model
C the target body are extracted from the planetary
C constants kernel.
C
C 5) The position of the observer, in body-fixed coordinates
C is computed using VTARG and TIBF.
C
C 6) VPNT is converted to body-fixed coordinates using TIBF.
C
C 7) The routine SURFPT computes the point of intersection,
C given the two body-fixed positions, and tri-axial
C ellipsoid radii.
C
C$ Particulars
C
C 1) The instrument boresight is assumed to define the z-axis
C of the instrument-fixed reference frame. This is reflected
C in the choice of ( 0, 0, 1 ) as the boresight pointing
C vector (VPNT) in instrument-fixed coordinates.
C
C$ Declarations
INTEGER FILEN
PARAMETER ( FILEN = 255 )
INTEGER TIMLEN
PARAMETER ( TIMLEN = 30 )
INTEGER FRMLEN
PARAMETER ( FRMLEN = 20 )
CHARACTER*(FILEN) FILE
CHARACTER*(TIMLEN) SCLKCH
CHARACTER*(TIMLEN) TOLCH
CHARACTER*(FRMLEN) REF
INTEGER SC
INTEGER INST
INTEGER TARG
INTEGER N
DOUBLE PRECISION SCLKDP
DOUBLE PRECISION ET
DOUBLE PRECISION TOL
DOUBLE PRECISION CMAT ( 3, 3 )
DOUBLE PRECISION CLKOUT
DOUBLE PRECISION VTARG ( 6 )
DOUBLE PRECISION TAU
DOUBLE PRECISION TIBF ( 3, 3 )
DOUBLE PRECISION R ( 3 )
DOUBLE PRECISION VPOS ( 3 )
DOUBLE PRECISION VSURF ( 3 )
DOUBLE PRECISION VPNT ( 3 )
DOUBLE PRECISION RADIUS
DOUBLE PRECISION LONG
DOUBLE PRECISION LAT
LOGICAL FOUND
C
C Initial values
C
C
C The inertial reference frame for all output.
C
DATA REF / 'J2000' /
C
C The boresight vector is assumed to define the z-axis of the
C instrument-fixed frame.
C
DATA VPNT / 0.D0, 0.D0, 1.D0 /
C
C Get all of the files, and load them.
C
WRITE (*,*) 'Enter the name of the kernel file containing'//
. ' planetary constants:'
READ (*,FMT='(A)') FILE
CALL FURNSH ( FILE )
WRITE (*,*)
WRITE (*,*) 'Enter the name of the kernel file containing'//
. ' SCLK coefficients:'
READ (*,FMT='(A)') FILE
CALL FURNSH ( FILE )
WRITE (*,*)
WRITE (*,*) 'Enter the name of the SPK file containing' //
. ' planetary and spacecraft ephemerides:'
READ (*,FMT='(A)') FILE
CALL FURNSH ( FILE )
WRITE (*,*)
WRITE (*,*) 'Enter the name of the CK file containing' //
. ' instrument pointing:'
READ (*,FMT='(A)') FILE
CALL FURNSH ( FILE )
C
C Get the ID codes for spacecraft, instrument, and target body.
C
WRITE (*,*)
WRITE (*,*) 'Enter NAIF integer spacecraft ID:'
READ (*,*) SC
WRITE (*,*)
WRITE (*,*) 'Enter NAIF integer instrument ID:'
READ (*,*) INST
WRITE (*,*)
WRITE (*,*) 'Enter NAIF integer ID for the target body:'
READ (*,*) TARG
C
C Determine the input epoch.
C
WRITE (*,*)
WRITE (*,*) 'Enter SCLK string (blank line to quit):'
READ (*,FMT='(A)') SCLKCH
DO WHILE ( SCLKCH .NE. ' ' )
C
C Convert the input clock string to ticks.
C
CALL SCENCD ( SC, SCLKCH, SCLKDP )
C
C Determine the time tolerance.
C
WRITE (*,*) 'Enter the tolerance as a SCLK string'
READ (*,FMT='(A)') TOLCH
C
C Convert the tolerance to ticks.
C
CALL SCTIKS ( SC, TOLCH, TOL )
C
C Search the CK file for pointing data at the time SCLKDP.
C
CALL CKGP ( INST, SCLKDP, TOL, REF, CMAT, CLKOUT, FOUND )
IF ( .NOT. FOUND ) THEN
WRITE (*,*)
WRITE (*,*) 'The C-kernel file does not contain ' //
. 'data for that time.'
STOP
END IF
C
C Compute the inertial pointing vector for the instrument
C boresight.
C
C The C-matrix is a transformation from inertial to
C instrument-fixed coordinates. The transpose rotates
C the other way --- what we want.
C
CALL MTXV ( CMAT, VPNT, VPNT )
C
C For all other computations, use the ET time corresponding
C to the input SCLK.
C
CALL SCT2E ( SC, SCLKDP, ET )
C
C Compute the target state vector (position and velocity).
C
CALL SPKEZ ( TARG, ET, REF, 'LT+S', SC, VTARG, TAU )
C
C Get TIBF matrix and radii of target ellipsoid model.
C
C We need TIBF for the target as it appeared when the
C instrument took its measurement at time ET. The target
C was at its apparent location TAU seconds earlier.
C
C TIPBOD and BODVCD will read constants from the planetary
C constants kernel file.
C
CALL TIPBOD ( 'J2000', TARG, ET-TAU, TIBF )
CALL BODVCD ( TARG, 'RADII', 3, N, R )
C
C The position of the observer is just the negative of the
C position part of the spacecraft-target vector, VTARG.
C Note that this is NOT the same as the apparent position of
C the spacecraft as seen from the target.
C
CALL VMINUS ( VTARG, VPOS )
C
C Put both vectors in body-fixed coordinates.
C
CALL MXV ( TIBF, VPOS, VPOS )
CALL MXV ( TIBF, VPNT, VPNT )
C
C Compute the point of intersection, if any.
C
CALL SURFPT ( VPOS, VPNT, R(1), R(2), R(3), VSURF, FOUND )
IF ( .NOT. FOUND ) THEN
WRITE (*,*)
WRITE (*,*) 'The line-of-sight pointing vector ' //
. 'does not intersect the target '
WRITE (*,*) 'at this epoch.'
ELSE
C
C Convert intersection point from rectangular to lat-lon-
C radius coordinates.
C
CALL RECLAT ( VSURF, RADIUS, LONG, LAT )
WRITE (*,*)
WRITE (*,*) 'Radius: ', RADIUS
WRITE (*,*) 'Longitude: ', LONG
WRITE (*,*) 'Latitude: ', LAT
END IF
C
C Input next epoch.
C
WRITE (*,*)
WRITE (*,*) 'Enter SCLK string (blank line to quit):'
READ (*,FMT='(A)') SCLKCH
END DO
END
Appendix C --- An Example of Writing a Type 1 CK Segment
The program creates a single type 1 segment for the scan platform of the Galileo spacecraft. Assume that C-matrices, angular velocity vectors, and the associated SCLK time strings are contained in time-ordered arrays assumed to have been initialized elsewhere (by the subroutine GET_GLL_PNT --- not part of SPICELIB). The program provides the option of adding the segment to an existing file, or creating a new file.
PROGRAM WRTCK1
IMPLICIT NONE
INTEGER FILEN
PARAMETER ( FILEN = 128 )
INTEGER TIMLEN
PARAMETER ( TIMLEN = 30 )
INTEGER SIDLEN
PARAMETER ( SIDLEN = 40 )
INTEGER FRMLEN
PARAMETER ( FRMLEN = 20 )
INTEGER MAXREC
PARAMETER ( MAXREC = 10000 )
DOUBLE PRECISION CMATS ( 3, 3, MAXREC )
DOUBLE PRECISION QUATS ( 4, MAXREC )
DOUBLE PRECISION AVVS ( 3, MAXREC )
DOUBLE PRECISION SCLKDP ( MAXREC )
DOUBLE PRECISION BEGTIM
DOUBLE PRECISION ENDTIM
CHARACTER*(TIMLEN) SCLKCH ( MAXREC )
CHARACTER*(SIDLEN) SEGID
CHARACTER*(FILEN) FILE
CHARACTER*(1) ANSWR
CHARACTER*(FRMLEN) REF
INTEGER INST
INTEGER NPREC
INTEGER HANDLE
LOGICAL AVFLAG
C
C Can either add to an existing CK file or create a brand
C new one.
C
WRITE (*,*)
WRITE (*,*) 'You may either add to an existing CK file, or'//
. ' create a new one.'
WRITE (*,*) 'Enter the name of the file:'
READ (*,FMT='(A)') FILE
WRITE (*,*)
WRITE (*,*) 'Is this an existing or new file? (Type E or N):'
READ (*,FMT='(A)') ANSWR
C
C To convert SCLK times from clock string to encoded SCLK,
C we need to load the Galileo spacecraft clock kernel file into
C the kernel pool. Assume that the file is called GLL_SCLK.TSC
C
CALL FURNSH ( 'GLL_SCLK.TSC' )
C
C To open a new file use CKOPN, and for an existing file use
C DAFOPW.
C
C For a new file, set the internal file name ( 2nd argument in
C CKOPN ) equal to the file name.
C
IF ( ANSWR .EQ. 'N' ) THEN
CALL CKOPN ( FILE, FILE, 0, HANDLE )
ELSE IF ( ANSWR .EQ. 'E' ) THEN
CALL DAFOPW ( FILE, HANDLE )
END IF
C
C Get the pointing information to go in the C-kernel segment.
C
C 1) Number of pointing instances returned
C 2) Array of SCLK times
C 3) Array of C-matrices
C 4) Array of angular velocity vectors
C
CALL GET_GLL_PNT ( NPREC, SCLKCH, CMATS, AVVS )
C
C Enter the information to go in the segment descriptor.
C
C The NAIF instrument ID code for the Galileo scan platform
C is -77001.
C
INST = -77001
C
C The inertial reference frame is B1950.
C
REF = 'B1950'
C
C This segment will contain angular velocity.
C
AVFLAG = .TRUE.
C
C The segment identifier provides a 40 character label for
C the segment.
C
SEGID = 'GLL SCAN PLT - NAIF - 18-NOV-90'
C
C Now convert the times to encoded SCLK.
C
DO I = 1, NPREC
CALL SCENCD ( -77, SCLKCH(I), SCLKDP(I) )
END DO
C
C Set the segment boundaries equal to the first and last
C time in the segment.
C
BEGTIM = SCLKDP( 1)
ENDTIM = SCLKDP(NPREC)
C
C The C-matrices are represented by quaternions in a type 1 CK
C segment. The SPICELIB routine M2Q converts C-matrices to
C quaternions.
C
DO I = 1, NPREC
CALL M2Q ( CMATS(1,1,I), QUATS(1,I) )
END DO
C
C That is all the information that we need. Write the segment.
C
CALL CKW01 ( HANDLE, BEGTIM, ENDTIM, INST, REF, AVFLAG,
. SEGID, NPREC, SCLKDP, QUATS, AVVS )
C
C Close the file.
C
CALL CKCLS ( HANDLE )
END
Appendix D --- An Example of Writing a Type 2 CK Segment
This program will use data type 2 to store pointing information for time intervals during which the pointing of the scan platform is constant. It is assumed that a routine called GLL_CONST_PNT will provide ordered arrays of C-matrices and interval start and stop times. The Ith C-matrix represents the fixed platform pointing during the Ith interval. Assume that the start and stop times are given in Galileo clock string form so that they must be converted into encoded SCLK for use in the C-kernel.
PROGRAM WRTCK2
IMPLICIT NONE
INTEGER FILEN
PARAMETER ( FILEN = 128 )
INTEGER TIMLEN
PARAMETER ( TIMLEN = 30 )
INTEGER SIDLEN
PARAMETER ( SIDLEN = 40 )
INTEGER FRMLEN
PARAMETER ( FRMLEN = 20 )
INTEGER MAXREC
PARAMETER ( MAXREC = 10000 )
DOUBLE PRECISION CMATS ( 3, 3, MAXREC )
DOUBLE PRECISION QUATS ( 4, MAXREC )
DOUBLE PRECISION AVVS ( 3, MAXREC )
DOUBLE PRECISION START ( MAXREC )
DOUBLE PRECISION STOP ( MAXREC )
DOUBLE PRECISION RATES ( MAXREC )
DOUBLE PRECISION BEGTIM
DOUBLE PRECISION ENDTIM
DOUBLE PRECISION SECTIK
CHARACTER*(SIDLEN) SEGID
CHARACTER*(TIMLEN) BEGCH ( MAXREC )
CHARACTER*(TIMLEN) ENDCH ( MAXREC )
CHARACTER*(FILEN) FILE
CHARACTER*(1) ANSWR
CHARACTER*(FRMLEN) REF
INTEGER INST
INTEGER NPREC
INTEGER HANDLE
C
C Can either add to an existing CK file or create a brand
C new one.
C
WRITE (*,*)
WRITE (*,*) 'You may either add to an existing CK file, or'//
. ' create a new one.'
WRITE (*,*) 'Enter the name of the file:'
READ (*,FMT='(A)') FILE
WRITE (*,*)
WRITE (*,*) 'Is this an existing or new file? (Type E or N):'
READ (*,FMT='(A)') ANSWR
C
C es from clock strings to encoded SCLK,
C we need to load the Galileo spacecraft clock kernel file into
C the kernel pool. Assume that the file is called GLL_SCLK.TSC
C
CALL FURNSH ( 'GLL_SCLK.TSC' )
C
C To open a new file use CKOPN, and for an existing file use
C DAFOPW.
C
C For a new file, set the internal file name ( 2nd argument in
C CKOPN ) equal to the file name.
C
IF ( ANSWR .EQ. 'N' ) THEN
CALL CKOPN ( FILE, FILE, 0, HANDLE )
ELSE IF ( ANSWR .EQ. 'E' ) THEN
CALL DAFOPW ( FILE, HANDLE )
END IF
C
C Get the pointing information to go in the C-kernel segment.
C
C 1) Number of pointing intervals returned
C 2) Interval start times in clock string form
C 3) Interval stop times in clock string form
C 4) Array of C-matrices
C
CALL GLL_CONST_PNT ( NPREC, BEGCH, ENDCH, CMATS )
C
C Need to convert the times to encoded SCLK.
C
DO I = 1, NPREC
CALL SCENCD ( -77, BEGCH(I), START(I) )
CALL SCENCD ( -77, ENDCH(I), STOP (I) )
END DO
C
C Determine the information to go in the segment descriptor.
C
C The NAIF instrument ID code for the Galileo scan platform
C is -77001.
C
INST = -77001
C
C The inertial reference frame is B1950.
C
REF = 'B1950'
C
C Set the segment boundaries equal to the START time of the
C first interval and the STOP time of the last interval.
C
BEGTIM = START( 1)
ENDTIM = STOP (NPREC)
C
C The segment identifier provides a 40 character label for the
C segment.
C
SEGID = 'GLL SCAN PLT - NAIF - TYPE 2 PREDICT '
C
C The C-matrices are represented by quaternions in a type 2 CK
C segment. The SPICELIB routine M2Q converts C-matrices to
C quaternions.
C
DO I = 1, NPREC
CALL M2Q ( CMATS(1,1,I), QUATS(1,I) )
END DO
C
C Since the pointing is constant over each interval the angular
C velocity vector is always zero.
C
DO I = 1, NPREC
CALL CLEARD ( 3, AVVS(1,I) )
END DO
C
C Since this is a predict segment the number of seconds
C represented by one tick during each of the intervals will
C be set equal to the nominal amount of time represented by
C the least significant field of the Galileo clock: 1/120 sec.
C
SECTIK = 1.D0 / 120.D0
DO I = 1, NPREC
RATES(I) = SECTIK
END DO
C
C That is all the information that we need. Write the segment.
C
CALL CKW02 ( HANDLE, BEGTIM, ENDTIM, INST, REF, SEGID,
. NPREC, START, STOP, QUATS, AVVS, RATES )
C
C Close the file.
C
CALL CKCLS ( HANDLE )
END
Appendix E --- An Example of Writing a Type 3 CK Segment
The program creates a single type 3 segment for a two hour time period for the Mars Global Surveyor spacecraft bus. The program calculates the pointing instances directly from the spacecraft and planet ( SPK ) ephemeris file. The names of the input ephemeris, leapseconds, spacecraft clock, and planetary constants kernel files are fictitious.
PROGRAM MGS_TYPE03
IMPLICIT NONE
C
C This program creates a predict type 3 CK segment for the
C Mars Global Surveyor spacecraft when it is in orbit around
C Mars.
C
C
C Assign the NAIF body id codes for the Mars Global Surveyor
C spacecraft and Mars.
C
INTEGER MGS
PARAMETER ( MGS = -94 )
INTEGER MARS
PARAMETER ( MARS = 499 )
C
C The reference frame of the segment is J2000.
C
CHARACTER*(10) REF
PARAMETER ( REF = 'J2000' )
C
C We will need about 2000 pointing instances.
C
INTEGER MAXREC
PARAMETER ( MAXREC = 2000 )
C
C Variables
C
CHARACTER*(30) UTCBEG
CHARACTER*(30) UTCEND
CHARACTER*(60) CKFILE
CHARACTER*(60) INFNAM
CHARACTER*(40) SEGID
CHARACTER*(5) CONT
DOUBLE PRECISION ETBEG
DOUBLE PRECISION ETEND
DOUBLE PRECISION EPOCH
DOUBLE PRECISION BEGTIM
DOUBLE PRECISION ENDTIM
DOUBLE PRECISION SCBEG
DOUBLE PRECISION SCEND
DOUBLE PRECISION SCLK
DOUBLE PRECISION CMAT ( 3, 3 )
DOUBLE PRECISION DCMAT ( 3, 3 )
DOUBLE PRECISION OMEGA ( 3, 3 )
DOUBLE PRECISION SCLKDP ( MAXREC )
DOUBLE PRECISION QUAT ( 4, MAXREC )
DOUBLE PRECISION AV ( 3, MAXREC )
DOUBLE PRECISION START ( MAXREC )
INTEGER HANDLE
INTEGER NREC
INTEGER NINT
INTEGER INST
INTEGER I
LOGICAL AVFLAG
C
C Load the binary SPK file that provides states for MGS with
C respect to Mars for the time period of interest.
C
CALL FURNSH ( 'naf0000c.bsp' )
C
C Load the text leapseconds, spacecraft clock ( sclk ), and
C planetary constants ( pck ) files into the kernel pool.
C
CALL FURNSH ( 'leap.tls' )
CALL FURNSH ( 'mgs.sc' )
CALL FURNSH ( 'mgs.pck' )
C
C The segment begin and end times.
C
UTCBEG = '1994 JAN 21 00:00:00'
UTCEND = '1994 JAN 21 02:00:00'
CALL UTC2ET ( UTCBEG, ETBEG )
CALL UTC2ET ( UTCEND, ETEND )
CALL SCE2C ( MGS, ETBEG, SCBEG )
CALL SCE2C ( MGS, ETEND, SCEND )
C
C Calculate the quaternions and angular velocity vectors at
C roughly four second intervals from the segment start time
C until the end.
C
I = 1
SCLK = SCBEG
DO WHILE ( ( SCLK .LE. SCEND ) .AND. ( I .LE. MAXREC ) )
C
C The times stored in the C-kernel are always in encoded
C spacecraft clock form. SPK takes ET as the input time.
C
SCLKDP(I) = SCLK
CALL SCT2E ( MGS, SCLK, EPOCH )
C
C Find the C-matrix using the MGSSPICE routine LOCVRT_M.
C LOCVRT_M returns the 3x3 matrix that transforms vectors
C from a specified inertial reference frame to the `Local
C Vertical Frame' for a specified observer and target body.
C For Mars Global Surveyor, this frame is also known as the
C "A-frame" and the "Orbital Reference Coordinate System".
C
CALL LOCVRT_M ( MARS, MGS, EPOCH, REF, 'NONE', CMAT )
CALL M2Q ( CMAT, QUAT(1,I) )
C
C Calculate the angular velocity vector using the following
C formula:
C
C Let the angular velocity vector be AV = ( a1, a2, a3 )
C and let the matrix OMEGA be:
C
C +-- --+
C | 0 -a3 a2 |
C | |
C OMEGA = | a3 0 -a1 |
C | |
C | -a2 a1 0 |
C +-- --+
C
C Then the derivative of a C-matrix C is given by
C
C t
C t d [ C ]
C OMEGA * C = -------
C dt
C
C Thus, given a C-matrix and its derivative, the angular
C velocity can be calculated from
C
C t
C dC
C OMEGA = { -- } * C
C dt
C
C
C
C GET_DERVRT is a non SPICELIB routine that will calculate
C the derivative of the C-matrix calculated by LOCVRT_M.
C
CALL GET_DERVRT ( EPOCH, DCMAT )
CALL MTXM ( DCMAT, CMAT, OMEGA )
AV(1,I) = OMEGA (3,2)
AV(2,I) = OMEGA (1,3)
AV(3,I) = OMEGA (2,1)
C
C Increase the counter and encoded SCLK time for the next
C pointing instance.
C
I = I + 1
SCLK = SCLK + 1024.D0
END DO
NREC = I - 1
C
C Unload the SPK file.
C
CALL UNLOAD ( 'naf0000c.bsp' )
C
C The process of determining how to partition the pointing
C instances into interpolation intervals varies with respect
C to the means by which the pointing instances are obtained.
C
C For this example program it is acceptable to interpolate
C between all of the adjacent pointing instances because:
C
C 1) The pointing was calculated at every 4 seconds so there
C are no gaps in the data.
C
C 2) The pointing was calculated directly from the spacecraft
C and planetary ephemeris so that the functions for the
C spacecraft axis and angular velocity vectors will change
C "slowly" and continuously.
C
C Therefore there is only one interpolation interval for the
C entire segment.
C
NINT = 1
START ( 1 ) = SCLKDP (1)
C
C Now that the pointing instances have been calculated the
C segment can be written to a C-kernel file.
C
C Open a new file.
C
CKFILE = 'mgs_predict_ck.bc'
INFNAM = 'mgs_predict_ck.bc'
CALL DAFONW ( CKFILE, 'CK', 2, 6, INFNAM, 0, HANDLE )
C
C Set the values of the components of the segment descriptor.
C
C The NAIF id code for the MGS spacecraft bus is:
C
INST = -94000
C
C This segment contains angular velocity data.
C
AVFLAG = .TRUE.
C
C The segment begins and ends with the first and last
C pointing instances.
C
BEGTIM = SCLKDP ( 1 )
ENDTIM = SCLKDP ( NREC )
C
C The reference frame was specified above as J2000.
C
C The segment identifier is:
C
SEGID = 'MGS PREDICT TYPE 3 SEGMENT'
C
C Write the segment to the file attached to HANDLE.
C
CALL CKW03 ( HANDLE, BEGTIM, ENDTIM, INST, REF, AVFLAG,
. SEGID, NREC, SCLKDP, QUAT, AV, NINT,
. START )
C
C Close the file.
C
CALL DAFCLS ( HANDLE )
END
Appendix F --- An Example of Writing a Type 4 CK Segment
It is assumed that a routine called GETCHB will provide time ordered records containing Chebychev polynomials coefficients for N intervals, the interval start times and total segment coverage start and stop times. The Ith record represents data blocks with a structure described above in the header of the CKW04A subroutine. Assume that the total coverage start and stop times and individual interval midpoint and radius times contained in the data packets are given as encoded SCLK times for use in the C-kernel.
INTEGER DBUFSZ
PARAMETER ( DBUFSZ = 100000 )
INTEGER IBUFSZ
PARAMETER ( IBUFSZ = 1000 )
CHARACTER*(10) REF
CHARACTER*(40) OUTFIL
CHARACTER*(40) SEGID
CHARACTER*(60) IRFNAM
DOUBLE PRECISION BEGTIM
DOUBLE PRECISION ENDTIM
DOUBLE PRECISION RECRDS ( DBUFSZ )
DOUBLE PRECISION SCSTRT ( IBUFSZ )
INTEGER HANDLE
INTEGER INST
INTEGER N
INTEGER NPKTS ( IBUFSZ )
LOGICAL AVFLAG
C
C Open CK-file for write access.
C
OUTFIL = 'galileo1.bc'
IRFNAM = 'GLL S/C CHEBY ORIENTATION CK FILE'
CALL CKOPN ( OUTFIL, IRFNAM, 0, HANDLE )
C
C Call GLLCHB to get data to be written to the output CK file.
C Assume that CHEBPL returns:
C
C BEGTIM is the starting encoded SCLK time for which the
C segment is valid.
C
C ENDTIM is the ending encoded SCLK time for which the
C segment is valid.
C
C N is the number of Type 4 data packets that we
C want to put into a segment in an CK file.
C
C NPKTS is integer array which contains the lengths of
C variable size data packets
C
C RECRDS contains N Type 4 data packets packaged for the
C CK file. Each packet has the following structure:
C
C ---------------------------------------------
C | The midpoint of the approximation interval|
C ---------------------------------------------
C | The radius of the approximation interval |
C ---------------------------------------------
C | Number of coefficients for q0 |
C ---------------------------------------------
C | Number of coefficients for q1 |
C ---------------------------------------------
C | Number of coefficients for q2 |
C ---------------------------------------------
C | Number of coefficients for q3 |
C ---------------------------------------------
C | Number of coefficients for AV1 |
C ---------------------------------------------
C | Number of coefficients for AV2 |
C ---------------------------------------------
C | Number of coefficients for AV3 |
C ---------------------------------------------
C | q0 Cheby coefficients |
C ---------------------------------------------
C | q1 Cheby coefficients |
C ---------------------------------------------
C | q2 Cheby coefficients |
C ---------------------------------------------
C | q3 Cheby coefficients |
C ---------------------------------------------
C | AV1 Cheby coefficients (optional) |
C ---------------------------------------------
C | AV2 Cheby coefficients (optional) |
C ---------------------------------------------
C | AV3 Cheby coefficients (optional) |
C ---------------------------------------------
C
C SCSTRT contains the initial encoded SC time for each of
C the packets contained in RECRDS, where
C
C SCSTRT(I) < SCSTRT(I+1), I = 1, N-1
C
C SCSTRT(1) <= FIRST, SCSTRT(N) < LAST
C
CALL GLLCHB ( BEGTIM, ENDTIM, N, NPKTS, RECRDS, SCSTRT )
C
C Begin CK type 4 segment.
C
INST = -77000
REF = 'J2000'
AVFLAG = 'YES'
SEGID = 'ACTUAL GLL S/C ATT FIT BY CHEBYS'
CALL CKW04B ( HANDLE, BEGTIM, INST, REF, AVFLAG, SEGID )
C
C Add the data to the segment all at once.
C
CALL CKW04A ( HANDLE, N, NPKTS, RECRDS, SCSTRT )
C
C End the segment, making the segment a permanent addition to
C the CK file.
C
CALL CKW04E ( HANDLE, ENDTIM )
C
C Close CK file
C
CALL CKCLS ( HANDLE )
END
Appendix G: Document Revision HistoryFebruary 13, 2014
April 1, 2009
November 17, 2005
Calls/references to the deprecated routine BODVAR were replaced with calls/referenes to BODVCD. BODVRD is mentioned as another routine superseding BODVAR. C examples showing incorrect calling sequences for prompt_c were corrected. December 21, 2004
February 2, 2004
September 04, 2002
Added a brief discussion of the DAF run-time binary file format translation capability now present in the SPICE Toolkit. February 15, 2000
The section describing new Chebyshev polynomial based data type--CK Type 4--was added to the document. October 14, 1999
Code examples showing calls to the routine DAFONW now show calls to CKOPN in its place, and code examples showing calls to the routine SCE2T now show calls to SCE2C instead. All statements referring to the base frame of a C-matrix or quaternion have been modified so as not to indicate that the base frame is inertial. The source-code-level discussion of the implementation of the high level CK readers has been removed. The implementation is not part of the C-kernel software interface and is not guaranteed to remain unchanged. The data selection algorithms used by the readers ARE part of the interface, and the descriptions of the algorithms have been retained. In addition, some minor changes have been made to simplify maintenance of both the Fortran and C versions of this document.
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