C-Kernel Required Reading
This required reading document is reproduced from the original NAIF document available at https://naif.jpl.nasa.gov/pub/naif/misc/toolkit_docs_N0067/C/req/ck.html
Note
These required readings documents were translated from documentation for N67 CSPICE. These pages may not be updated as frequently as the CSPICE version, and so may be out of date. Please consult the changelog for more information.
Abstract
References
- [167] Double Precision Array Files Required Reading
(daf.req)
- [349] FRAMES Required Reading
(frames.req).
- [222] Spacecraft Clock Time Required Reading
(sclk.req)
- [214] Rotations Required Reading
- [211] SPC Required Reading: Comments in SPK and CK Files
(spc.req)
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 ANSI C functions which are part of the CSPICE library. These functions can be integrated into user application programs. The purpose of this document is to describe both the C-kernel file structure and the associated CSPICE software to the level of detail necessary for the user to program almost any application.
With few exceptions, all functions appearing in this document are part of CSPICE or the standard ANSI C library. The exceptions are placeholders for user-supplied functions which appear in some of the code examples. Each CSPICE function is prefaced with a complete CSPICE header which describes inputs, outputs, restrictions and context, and provides examples of usage. The authoritative documentation for any function is its header, which should be consulted before using the function in any program. A summary of the CK functions 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:
- -32000
Instrument Scan Platform
- -32001
ISSNA (Imaging science narrow angle camera)
- -32002
ISSWA (Imaging science wide angle camera)
- -32003
PPS (Photopolarimeter)
- -32004
UVSAG (Ultraviolet Spectrometer, Airglow port)
- -32005
UVSOCC (Ultraviolet Spectrometer, Occultation port)
- -32006
IRIS (Infrared Interferometer Spectrometer and Radiometer)
The simple coding formula is
SPICE s/c instrument code = (s/c code)*(1000) - instrument number
which 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 CSPICE functions.
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 functions to read from CK files.
CSPICE includes functions to convert between character SCLK format and the double precision encoding. There are also functions 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 functions 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 function
scencd() (Encode SCLK):
sclkdp = scencd( sc, sclkch )
Use scdecd() (Decode SCLK) to recover
the character representation from its double precision encoding.
sclkch = scdecd( sc, sclkdp )
The first argument to both functions, "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):
sclkdp =sce2c( sc, sclkch )
To convert continuous encoded SCLK to ET, use
sct2e() (Ticks to ET):
et = sct2e( sc, sclkdp )
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 function calls are necessary to convert between UTC and SCLK. One function converts from SCLK to ET, and another from ET to UTC.
See Appendix A for a list of high level functions involved in spacecraft clock time conversions.
The SCLK kernel file
furnsh().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 functions 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 functions presented in this chapter fit together in a typical application program.
The CK File Reader ckgp()
ckgp() (Get Pointing). The
example finds the C-matrix for the Voyager 2 narrow angle camera at
a particular epoch during the Jupiter encounter. The C-matrix
returned is a transformation from the J2000 frame to
instrument-fixed coordinates.Each of the functions used is briefly described below. See the individual function headers for a complete description.
A complete description of how ckgp()
searches for pointing is provided in the "Details" chapter of this
document.
from spiceypy import *
#NAIF ID numbers for the
# 1. Voyager 2 spacecraft
# 2. Voyager 2 narrow angle camera
sc = -32
inst = -32001
#The C-matrix should transform from J2000 to camera-fixed
#coordinates.
ref = "J2000"
# Load the spacecraft clock partition kernel file into the
# kernel pool, for SCLK encoding and decoding.
furnsh( "vgr2_sclk.tsc" )
# Load the C-kernel pointing file.
furnsh( "vgr2_jup_inbound.bc" )
#We want pointing at a spacecraft clock time appearing in
#the third spacecraft clock partition.
sclkdp = scencd( sc, "3/20556:17:768" )
#The Voyager 2 clock is of the form xxxxx yy www, where
#yy is a modulus 60 counter. Pictures were not shuttered
#at intervals smaller than one mod 60 count. Therefore,
#use this as the tolerance. ( Notice that no partition
#number is used when specifying a tolerance )
tol = sctiks( sc, "0:01:000")
#Get the pointing for the narrow angle camera.
cmat, clkout = ckgp( inst, sclkdp, tol, ref )
furnsh()
furnsh() loads the kernel pool with
the contents of the specified text kernel file, which, in this case
is the SCLK kernel file.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 functions. 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()
scencd() encodes a character
representation of spacecraft clock time such as"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 functions.
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:
- inst
The NAIF instrument ID. In this example, we want pointing for the Voyager 2 narrow angle camera (NAIF code -32001).
- sclkdp
Encoded SCLK time. Units are ticks since clock start at launch May be discrete or continuous.
- tol
SCLK time tolerance. tol is measured in units of "ticks."
The pointing returned by
ckgp()will be for a time within tol ticks of sclkdp. In general, tol should be smaller than the typical spacecraft clock time interval between instrument observations.- ref
The NAIF mnemonic for the base reference frame. The output C-matrix, if found, will be a transformation from ref to instrument-fixed coordinates.
See the FRAMES Required Reading, frames.req, for a list of those frames supported by the SPICE system, along with the accepted mnemonics for those frames.
Outputs are:
- cmat
The C-matrix. cmat is a transformation matrix from the base frame ref to the instrument-fixed frame at the time clkout.
- clkout
Continuous encoded spacecraft clock time for which cmat is valid. This will be within tol ticks of sclkdp.
The CK File Reader ckgpav()
The calling sequence for ckgpav() is:
cmat, av, clkout = ckgpav( inst, sclkdp, tol, ref )
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 function 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
furnsh( "ckfile_1.bc" )
furnsh( "ckfile_2.bc" )
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:
furnsh( "predict.bc" )
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() :
from spiceypy import *
# Load the first version.
furnsh( "predict.bc" )
#
# process pointing from first file.
#
# Unload the first version.
unload( "predict.bc" )
# Load the second version.
furnsh( "update.bc" )
#
# process pointing from the second file.
#
CK Coverage Summary Routines
The ckobj() function 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() function 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 other stuff tutorial and
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 functions that are concerned with the internal data type of a segment. Other functions 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 |
------------------
- DCD(1),DCD(2)
The initial and final encoded spacecraft clock times for the segment.
- ICD(1)
The integer code of the instrument whose pointing is being described.
- ICD(2)
The NAIF integer ID of the base reference frame for the segment data. (For example, J2000, B1950, and so on --- to see which ID represents which coordinate system, see the Frames Required Reading, frames.req.)
- ICD(3)
The data type of the segment. This indicates how the data is stored internally. The reader functions will use it to evaluate the data records. Typically, users will not have to know this code.
- ICD(4)
The angular rates flag. This indicates whether or not the segment is capable of producing angular velocity data. If ICD(4) = 0, then the segment contains pointing data only. If ICD(4) = 1, then the segment contains angular velocity data as well.
- ICD(5),ICD(6)
Initial and final addresses of the segment data within the file. Users will typically not want or need to know about these addresses. They tell the readers where to go within a file to get the records needed to satisfy a particular request.
The descriptor is stored as a double precision array, with pairs of integer components equivalenced to double precision numbers. We say that the descriptor is "packed" into a double precision array. The size of a packed descriptor is five double precision numbers. 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 LOGA151
then 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.
A CK file is a DAF
DAF functions 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 functions presented in this document do not allow you the control you want in looking through files, the DAF functions certainly will.
SPICE File Identification Word in CK Files
How the CK Readers Work
ckgp() and
ckgpav().The General Search Algorithm
furnsh() to satisfy a pointing
request. The files are searched in the reverse order from which
they were loaded. Thus the last-loaded file is searched first, then
the second to last, and so forth. The contents of individual files
are also searched in backwards order, giving priority to segments
that were added to a file later than the others.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()
ckgp() and
ckgpav() is in which segments they
search through to satisfy a request for pointing data. Recall that
segments in a CK file only optionally contain angular velocity
data. Since ckgp() does not return an
angular velocity vector, it is free to consider all segments when
satisfying a request, because all segments will contain the data
for constructing C-matrices.
ckgpav(), on the other hand, will
consider only those segments which also contain angular velocity
data.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
The SPICELIB Fortran routines from which ckbss_ and cksns_ are derived are both entry points to the SPICELIB Fortran 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 functions 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 Boolean 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
dafus() (Unpack Summary).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[1] to instrument-fixed coordinates, and the coordinates of av lie in that same base frame.
Transforming the Results
First, the functions 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_c is a rotation matrix from a base frame (call it 'refseg') to instrument-fixed coordinates:
[ ] I-fixed
| |
| CMAT |
| |
[ ] REFSEG
What we want is a rotation matrix from the requested frame (call it refreq) to instrument-fixed coordinates:
[ ] I-fixed
| |
| CMAT |
| |
[ ] REFREQ
So 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 [ ] REFREQ
Once 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 == 1 )
{
.
.
.
}
else if ( type == 2 )
{
.
.
.
}
else if ( type == n )
{
}
else
{
setmsg_c ( "The data type # is not currently supported." );
errint_c ( "#", type );
sigerr_c ( "SPICE(CKUNKNOWNDATATYPE)" );
}
Once ckpfs_ determines the data type of a segment, two type-specific functions 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 function 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 CSPICE 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 CSPICE 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) ) / 2
and 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 functions
ckw01()writes a type 1 segment to a file.
- ckr01_
reads a pointing record from a type 1 segment that satisfies a request for pointing at a given time.
- cke01_
evaluates the record supplied by CKR01.
- cknr01_
gives the number of pointing instances in a type 1 segment.
- ckgr01_
gets the Ith pointing instance from a type 1 segment.
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:
- The encoded spacecraft clock START and STOP times for the
interval.
- The quaternion representing the C-matrix associated with the
start time of the interval.
- The constant angular velocity vector, in radians per second,
for the interval.
- A factor which relates seconds and encoded SCLK ticks. This
is necessary to convert the difference between the requested and interval start times from SCLK to seconds.
The orientation of a spacecraft structure may be determined from the above information at any time that is within the bounds of one of the intervals. 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 0.06
For 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 functions
ckw02()writes a type 2 segment to a file.
- ckr02_
reads a pointing record from a type 2 segment that satisfies a request for pointing at a given time.
- cke02_
evaluates the record supplied by CKR02.
- cknr02_
gives the number of pointing records in a type 2 segment.
- ckgr02_
gets the Ith pointing record from a type 2 segment.
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 functions 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 function is provided which calls the low level DAF
functions 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 function ckw03() for a
complete description of the inputs required to write a segment.
Linear Interpolation Algorithm
Let t be the time for which pointing is desired and let CMAT1 and CMAT2 be C-matrices associated with times t1 and t2 such that:
t1 <= t <= t2, where t1 < t2.
Assume that the spacecraft frame rotates about a fixed axis at a constant angular rate from time t1 to time t2. Then the rotation axis and angle can be derived from the rotation matrix ROT12 where:
T T
CMAT2 = ROT12 * CMAT1
or
T
ROT12 = CMAT2 * CMAT1
Obtain the axis and angle of the rotation from the matrix ROT12. Let the axis vector of the rotation be AXIS and the rotation angle be ANGLE.
To obtain pointing information at time t, rotate the spacecraft frame about the vector AXIS from its orientation at time t1 by the angle THETA where:
( t - t1 )
THETA = ANGLE * -----------
( t2 - t1 )
Thus if ROT1t is the matrix that rotates vectors by the angle THETA about the vector AXIS, then the desired C-matrix is given by:
T T
CMAT = ROT1t * CMAT1
T
CMAT = CMAT1 * ROT1t
The angular velocity is treated independently of the C-matrix. If it is requested, then the AV at time t is the weighted average of the angular velocity vectors at time t1 and time t2:
( t - t1 )
W = -----------
( t2 - t1 )
AV = ( 1 - W ) * AV1 + W * AV2
Type 3 functions
ckw03()writes a type 3 segment to a file.
- ckr03_
reads a pointing record from a type 3 segment that satisfies a request for pointing at a given time.
- cke03_
evaluates the record supplied by CKR03.
- cknr03_
gives the number of pointing instances in a type 3 segment.
- ckgr03_
gets the Ith pointing instance from a type 3 segment.
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 functions 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 CSPICE 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 CSPICE generic segment functions. 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:
A partition for constant values to be associated with each data packet in the segment.
A partition for the data packets.
A partition for packet coverage begin times.
A partition for a packet directory, if the segment contains variable sized packets.
A partition for a packet coverage begin time directory.
A reserved partition that is not currently used. This partition is only for the use of the NAIF group at the Jet Propulsion Laboratory (JPL).
A partition for the metadata which describes the locations and sizes of other partitions as well as providing some additional descriptive information about the generic segment.
+============================+
| 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 function which is a part of the CSPICE CK4 functions 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 CSPICE generic segment functions.
Type 4 CK segments should be created using CK Type 4 writer functions ckw04b_, ckw04a_ and ckw04e_, provided in the CSPICE.
CK Type 4 pointing evaluation algorithm
Type 4 functions
- ckr04_
reads a record from a Type 4 segment that satisfies a request for pointing at a given time.
- cke04_
evaluates the record supplied by ckr04_.
- cknr04_
gives the total number of data packets in a Type 4 segment.
- ckgr04_
gets the I'th record from a Type 4 segment.
- ckw04b_
begins a Type 4 CK data segment
- ckw04a_
adds data to a Type 4 CK segment
- ckw04e_
ends a Type 4 CK data segment
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:
Subtype 0:
Sliding-window Hermite interpolation of quaternions and quaternion derivatives. Attitude and angular velocity are represented by a series of 8-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components followed by four quaternion time derivative components. A quaternion representing attitude at a request time is derived by using Hermite interpolation on each quaternion component and the corresponding derivative, where the values to be interpolated are obtained for a consecutive series of epochs centered at the request time. The interpolated quaternion is then unitized. The same interpolation degree is used for each quaternion component.
Subtype 1:
Sliding-window Lagrange interpolation of quaternions. Attitude is represented by a series of 4-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components. A quaternion representing attitude at a request time is derived by using Lagrange interpolation on each quaternion component, where the values to be interpolated are obtained for a consecutive series of epochs centered at the request time. The interpolated quaternion is then unitized. The same interpolation degree is used for each quaternion component.
Angular velocity is obtained by first forming the time derivative of the quaternion using the derivatives of the interpolating polynomials, then combining the quaternion and its derivative to obtain angular velocity.
Subtype 2:
Sliding-window Hermite interpolation of quaternions and angular velocity. Attitude and angular velocity are represented by a series of 14-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components, four quaternion derivative components, three angular velocity components, and three angular acceleration components. A quaternion representing attitude at a request time is derived by using Hermite interpolation on each quaternion component and the corresponding derivative, where the values to be interpolated are obtained for a consecutive series of epochs centered at the request time. The interpolated quaternion is then unitized. Angular velocity is obtained by using Hermite interpolation on each angular velocity component and the corresponding derivative. The attitude and angular velocity resulting from this interpolation method are in principle independent. The same interpolation degree is used for each quaternion and angular velocity component.
Subtype 3:
Sliding-window Lagrange interpolation of quaternions and angular velocity. Attitude and angular velocity are represented by a series of 7-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components and three angular velocity components. A quaternion representing attitude at a request time is derived by using Lagrange interpolation on each quaternion component, where the values to be interpolated are obtained for a consecutive series of epochs centered at the request time. The interpolated quaternion is then unitized. Angular velocity is obtained by using Lagrange interpolation on each angular velocity component. The attitude and angular velocity resulting from this interpolation method are in principle independent. The same interpolation degree is used for each quaternion and angular velocity component.
The sliding-window interpolation technique used by this data type works as follows: for any request epoch, the data type defines a component of a quaternion or angular velocity by interpolating a set of values of that component defined on a set of consecutive time tags---a "window"---centered as closely as possible to the request epoch. The nominal window size is dictated by the degree and type (Hermite vs Lagrange) of the interpolating polynomials. Normally the window of time tags has even size, and the window is selected so that the request time is located on or between the two central time tags in the window. 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 functions 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:
The nominal rate for the spacecraft clock associated with this kernel, given in seconds/tick.
The CK type 5 subtype code.
The interpolation window size
the total number of interpolation intervals (NUMINT)
The total number of packets (pointing instances) (N) in the segment.
A segment writer function is provided which calls the low level DAF
functions necessary to write a type 5 segment to a C-kernel. However,
the creator of the segment is responsible for determining whether or
not it is valid to interpolate between contiguous ranges of pointing
instances, and thus how they should be partitioned into intervals.
See the header of the function ckw05()
for a complete description of the inputs required to write a segment.
|
Type 5 functions
ckw05()writes a type 5 segment to a file.
- ckr05_
reads a pointing record from a type 5 segment that satisfies a request for pointing at a given time.
- cke05_
evaluates the record supplied by CKR05.
- cknr05_
gives the number of pointing instances in a type 5 segment.
- ckgr05_
gets the Ith pointing instance from a type 5 segment.
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:
The type 5 segments are for the same reference frame (for an instrument or spacecraft structure) and have the same base frame.
All of the type 5 segments contain angular velocity data, or none do.
The type 5 segments' descriptor coverage intervals, when arranged in increasing time order, overlap at, and only at, their endpoints.
Each type 5 segment contains no gaps, or has a single gap to the right of its last pointing instance.
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 minisegment 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:
Subtype 0:
Sliding-window Hermite interpolation of quaternions and quaternion derivatives. Attitude and angular velocity are represented by a sequence of 8-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components followed by four quaternion time derivative components. A quaternion representing attitude at a request time is derived by using Hermite interpolation on each quaternion component and the corresponding derivative, where the values to be interpolated are obtained for a consecutive sequence of time tags centered at the request time, and converting the result to unit length. Angular velocity is derived from the unit quaternion and its derivative with respect to time. The same interpolation degree is used for each quaternion component.
Subtype 1:
Sliding-window Lagrange interpolation of quaternions. Attitude is represented by a sequence of 4-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components. A quaternion representing attitude at a request time is derived by using Lagrange interpolation on each quaternion component, where the values to be interpolated are obtained for a consecutive sequence of time tags centered at the request time. The interpolated quaternion is then unitized. The same interpolation degree is used for each quaternion component.
Angular velocity is computed from the unit-length quaternion and its time derivative. The derivative is computed using the derivatives of the interpolating polynomials.
Subtype 2:
Sliding-window Hermite interpolation of quaternions and angular velocity. Attitude and angular velocity are represented by a sequence of 14-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components, four quaternion derivative components, three angular velocity components, and three angular acceleration components. A quaternion representing attitude at a request time is derived by using Hermite interpolation on each quaternion component and the corresponding derivative, where the values to be interpolated are obtained for a consecutive sequence of time tags centered at the request time. The interpolated quaternion is then unitized. Angular velocity is obtained by using Hermite interpolation on each angular velocity component and the corresponding derivative. The attitude and angular velocity resulting from this interpolation method are in principle independent. The same interpolation degree is used for each quaternion and angular velocity component.
Subtype 3:
Sliding-window Lagrange interpolation of quaternions and angular velocity. Attitude and angular velocity are represented by a sequence of 7-element "packets" and associated time tags. The time tags may be unequally spaced. Each packet contains four quaternion components and three angular velocity components. A quaternion representing attitude at a request time is derived by using Lagrange interpolation on each quaternion component, where the values to be interpolated are obtained for a consecutive sequence of time tags centered at the request time. The interpolated quaternion is then unitized. Angular velocity is obtained by using Lagrange interpolation on each angular velocity component. The attitude and angular velocity resulting from this interpolation method are in principle independent. The same interpolation degree is used for each quaternion and angular velocity component.
The sliding-window interpolation techniques used by data type 6 work as follows: for any request epoch, the interpolation algorithm computes a component of a quaternion or angular velocity by interpolating a set of values of that component defined on a set of consecutive time tags---a "window"---centered as closely as possible to the request epoch. The nominal window size is dictated by the degree and type (Hermite vs Lagrange) of the interpolating polynomials. Normally the window of time tags has even size, and the window is selected so that the request time is located between the two central time tags in the window. 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 + 1
Window 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 ) * 100
where M is the total number of time tags. Note that if M is
Q * 100
then only
Q - 1
directory 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 function called ckw06_c has been provided. This function 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 function 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 functions
- ckw06_c
writes a type 6 segment to a file.
- ckr06_
reads a pointing record from a type 6 segment that satisfies a request for pointing at a given time.
- cke06_
evaluates the record supplied by CKR06.
- cknm06_
gives the number of mini-segments in a specified type 6 segment.
- ckmp06_
returns mini-segment parameters, including packet count, for specified mini-segment in a type 6 segment.
- ckgr06_
gets the Ith pointing instance from a specified mini-segment in a type 6 segment.
Appendix A --- Summary of C-kernel Functions
Summary of Mnemonics
Kernel Loading/Unloading Routines
furnsh_c ( Load kernel file of any type )
unload_c ( Unload kernel file of any type )
C-kernel Routines
Wrappers
ckcls_c ( C-kernel, close a pointing file )
ckcov_c ( C-kernel, coverage for an instrument )
ckgp_c ( C-kernel, get pointing )
ckgpav_c ( C-kernel, get pointing and angular velocity )
cklpf_c ( C-kernel, load pointing file )
ckobj_c ( C-kernel, instruments in a file )
ckopn_c ( C-kernel, open a new pointing file )
ckupf_c ( C-kernel, unload pointing file )
ckw01_c ( C-kernel, write segment to C-kernel, data type 1 )
ckw02_c ( C-kernel, write segment to C-kernel, data type 2 )
ckw03_c ( C-kernel, write segment to C-kernel, data type 3 )
ckw05_c ( C-kernel, write segment to C-kernel, data type 5 )
Lower-level functions
ckbss_ ( C-kernel, begin search for segment )
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 )
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 )
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 )
cknr05_ ( C-kernel, number of records, data type 5 )
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 )
ckr04_ ( C-kernel, read pointing record, data type 5 )
cksns_ ( C-kernel, select next segment )
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 )
ckw06_ ( C-kernel, write segment to C-kernel, data type 6 )
SCLK conversion functions
scdecd_c ( Decode spacecraft clock )
scencd_c ( Encode spacecraft clock )
scpart_c ( Spacecraft clock partitions )
scfmt_c ( Spacecraft clock format )
sctiks_c ( Spacecraft clock ticks )
sct2e_c ( Convert encoded SCLK Ticks to ET )
scs2e_c ( Convert SCLK String to ET )
sce2c_c ( Convert ET to continuous SCLK Ticks )
sce2t_c ( Convert ET to encoded SCLK Ticks )
sce2s_c ( Convert ET to SCLK String )
utc2et_c ( UTC to Ephemeris Time )
et2utc_c ( Ephemeris Time to UTC )
Inertial Reference frame functions
irfrot_ ( Inertial reference frame, rotate )
irfnum_ ( Inertial reference frame number )
irfnam_ ( Inertial reference frame name )
irfdef_ ( Inertial reference frame, default )
Appendix B --- Example Program PLANET_POINT
All of the functions used here are part of CSPICE or the ANSI C library.
1 #!/usr/bin/env python3
2 """
3 /*
4 PROGRAM PLANET_POINT
5
6
7 Compute the planetocentric latitude, longitude and radius of
8
9 the point at which the optic axis of an instrument intersects
10 the surface of a target planet. Assume that the axis of the
11 instrument is along the Z-axis of the instrument fixed
12 reference frame.
13
14 The following files are required:
15
16 1) Kernel file containing planetary constants.
17 2) Kernel file containing spacecraft clock (SCLK) data.
18 3) SPK file containing planetary and spacecraft
19 ephemeris data.
20 4) CK file containing instrument pointing data.
21
22 The following quantities are required:
23
24 5) NAIF integer spacecraft ID
25 6) NAIF integer planet ID
26 7) NAIF integer instrument ID
27 8) SCLK time string
28 9) SCLK tolerance.
29
30 The following steps are taken to locate the desired point:
31
32 10) The inertial pointing (VPNT) of the instrument at
33 the input SCLK time is read from the CK file.
34
35 11) The apparent position (VTARG) is computed for the
36 center of the target body as seen from the spacecraft,
37 at the ephemeris time (ET) corresponding to SCLK.
38
39 The one-way light time (TAU) from the target to the
40 spacecraft is also computed.
41
42 12) The transformation (TIBF) from inertial to body-fixed
43 coordinates is computed for the epoch ET-TAU, using
44 quantities from the planetary constants kernel.
45
46 13) The radii (R) of the tri-axial ellipsoid used to model
47 the target body are extracted from the planetary
48 constants kernel.
49
50
51 1) The position of the observer, in body-fixed coordinates
52 is computed using VTARG and TIBF.
53
54
55 2) VPNT is converted to body-fixed coordinates using TIBF.
56
57 3) The routine SURFPT computes the point of intersection,
58 given the two body-fixed positions, and tri-axial
59 ellipsoid radii.
60
61 -Particulars
62
63 1) The instrument boresight is assumed to define the z-axis
64
65 of the instrument-fixed reference frame. This is reflected
66 in the choice of ( 0, 0, 1 ) as the boresight pointing
67 vector (VPNT) in instrument-fixed coordinates.
68 */
69 """
70
71 # #include <stdio.h>
72 # #include <string.h>
73 # #include "SpiceUsr.h"
74
75 import spiceypy as spice
76 import numpy as np
77 import sys
78
79 def main():
80 # /*
81 # Constants
82 # The inertial reference frame for all output.
83 # */
84 REF = "J2000"
85
86 # /*
87 # File name length.
88 # */
89 FILSIZ = 256
90
91 # /*
92 # Body name length.
93 # */
94 BDNMLN = 37
95
96 # /*
97 # SCLK string length.
98 # */
99 TIMLEN = 35
100
101 # /*
102 # Instrument name length.
103 # */
104 INNMLN = 32
105
106 # /*
107 # Local variables
108 # */
109 # (In Python, variables are created as needed.)
110
111 # /*
112 # Get all of the files and load them.
113 # */
114 file = input("Enter the name of the kernel file\n"
115 "containing planetary constants > ")
116 spice.furnsh(file)
117
118 file = input("\nEnter the name of the kernel file\n"
119 "containing SCLK coefficients > ")
120 spice.furnsh(file)
121
122 file = input("\nEnter the name of the SPK file\n"
123 "containing planetary and spacecraft\n"
124 "ephemerides > ")
125 spice.furnsh(file)
126
127 file = input("\nEnter the name of the CK file\n"
128 "containing instrument pointing > ")
129 spice.furnsh(file)
130
131 # /*
132 # Get the names of the spacecraft and target body; get the ID
133 # code of the instrument. Convert the instrument ID from
134 # character to integer. Translate the spacecraft and target
135 # names to the corresponding integer codes.
136 # */
137 scname = input("\nEnter spacecraft name > ")
138 targname = input("\nEnter target name > ")
139 instch = input("Enter NAIF integer instrument ID > ")
140
141 try:
142 inst = int(instch) # Equivalent to prsint_c
143 except ValueError:
144 print("Invalid instrument ID.")
145 sys.exit(1)
146
147 sc, found = spice.bodn2c(scname)
148 if not found:
149 msg = "Spacecraft name # was not recognized."
150 msg = msg.replace("#", scname)
151 raise Exception(msg)
152
153 targ, found = spice.bodn2c(targname)
154 if not found:
155 msg = "Target body name # was not recognized."
156 msg = msg.replace("#", targname)
157 raise Exception(msg)
158
159 # /*
160 # Determine the input epoch.
161 # */
162 sclkch = input("\nEnter SCLK string (blank line to quit) > ")
163
164 while sclkch.strip() != "":
165 # /*
166 # Convert the input clock string to ticks.
167 # */
168 sclkdp = spice.scencd(sc, sclkch)
169
170 # /*
171 # Determine the time tolerance.
172 # */
173 tolch = input("Enter the tolerance as an SCLK string > ")
174
175 # /*
176 # Convert the tolerance to ticks.
177 # */
178 tol = spice.sctiks(sc, tolch)
179
180 # /*
181 # Search the CK file for pointing data at the time sclkdp.
182 # */
183 cmat, clkout, found = spice.ckgp(inst, sclkdp, tol, REF)
184
185 if not found:
186 print("\n"
187 "The C-kernel file does not contain "
188 "data for time {} SCLK {}.\n".format(scname, sclkch))
189
190 # /*
191 # Compute the inertial pointing vector for the instrument
192 # boresight.
193 #
194 # The boresight vector is assumed to define the z-axis of the
195 # instrument-fixed frame. This axis vector can be picked off
196 # from the third row of the C-matrix.
197 # */
198 vpnt = np.array(cmat[2])
199
200 # /*
201 # For all other computations, use the ET time corresponding
202 # to the input SCLK.
203 # */
204 et = spice.sct2e(sc, sclkdp)
205
206 # /*
207 # Compute the target state vector (position and velocity).
208 # */
209 vtarg, tau = spice.spkez(targ, et, REF, "lt+s", sc)
210
211 # /*
212 # Get the tibf matrix and radii of target ellipsoid model.
213 #
214 # We need tibf for the target as it appeared when the
215 # instrument took its measurement at time et. The target
216 # was at its apparent location tau seconds earlier.
217 #
218 # tipbod_c and bodvcd_c will read constants from the planetary
219 # constants kernel file.
220 # */
221 tibf = spice.tipbod(REF, targ, et - tau)
222 r, n = spice.bodvcd(targ, "RADII", 3)
223
224 # /*
225 # The position of the observer is just the negative of the
226 # position part of the spacecraft-target vector, vtarg.
227 #
228 # Note that this is NOT the same as the apparent position of
229 # the spacecraft as seen from the target.
230 # */
231 vpos = -np.array(vtarg[0:3])
232
233 # /*
234 # Put both vectors in body-fixed coordinates.
235 # */
236 vpos = np.dot(tibf, vpos)
237 vpnt = np.dot(tibf, vpnt)
238
239 # /*
240 # Compute the point of intersection, if any.
241 # */
242 vsurf, found = spice.surfpt(vpos, vpnt, r[0], r[1], r[2])
243
244 if not found:
245 print("\nThe line-of-sight pointing vector "
246 "does not intersect the target "
247 "at the epoch {} SCLK {}.\n".format(scname, sclkch))
248 else:
249 # /*
250 # Convert intersection point from rectangular to lat-lon-
251 # radius coordinates.
252 # */
253 radius, lon, lat = spice.reclat(vsurf)
254
255 print("\n"
256 "Radius (km) {}\n"
257 "Longitude (deg) {}\n"
258 "Latitude (deg) {}\n".format(radius,
259 lon * spice.dpr(),
260 lat * spice.dpr()))
261
262 # /*
263 # Input next epoch.
264 # */
265 sclkch = input("\nEnter SCLK string (blank line to quit) > ")
266
267 if __name__ == "__main__":
268 main()
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 function get_gll_pnt --- not part of CSPICE). The program provides the option of adding the segment to an existing file, or creating a new file.
1 import os
2 import spiceypy as spice
3
4 def get_gll_pnt(clklen):
5 """
6 Placeholder for get_gll_pnt function.
7 This function should return a tuple:
8 (nprec, sclkch, cmats, avvs)
9 where:
10 - nprec is the number of pointing instances (an int)
11 - sclkch is a list of SCLK time strings (each string length ≤ clklen)
12 - cmats is a list of 3x3 matrices (each represented as a list of three lists of three floats)
13 - avvs is a list of angular velocity vectors (each a list of 3 floats)
14 For demonstration purposes, dummy values are returned.
15 """
16 # Example dummy data
17 nprec = 2
18 sclkch = [
19 "1/2:34:56.789",
20 "1/2:34:57.789"
21 ]
22 cmats = [
23 [[1.0, 0.0, 0.0],
24 [0.0, 1.0, 0.0],
25 [0.0, 0.0, 1.0]],
26 [[0.0, 1.0, 0.0],
27 [1.0, 0.0, 0.0],
28 [0.0, 0.0, 1.0]]
29 ]
30 avvs = [
31 [0.1, 0.2, 0.3],
32 [0.4, 0.5, 0.6]
33 ]
34 return nprec, sclkch, cmats, avvs
35
36 def main():
37 # Local variables
38 # In Python, we do not need to predeclare array sizes; we use lists.
39 #
40 # Define constants (values should be set appropriately)
41 FILSIZ = 256 # Maximum filename size (not used explicitly in Python)
42 MAXREC = 1000 # Maximum number of records (example placeholder)
43 CLKLEN = 80 # Maximum length of clock string (for get_gll_pnt)
44 SCLKKER = "gll_sclk.tsc" # Galileo spacecraft clock kernel file name
45 GLL = "GLL" # Spacecraft clock descriptor (example placeholder)
46 INST = -77001 # NAIF Instrument ID code
47 REF = "B1950" # Inertial reference frame name
48 AVFLAG = True # Angular velocity flag (SPICETRUE equivalent)
49 SEGID = "GLL SCAN PLT - NAIF - 18-NOV-90" # Segment identifier
50
51 # Can either add to an existing CK file, or create a brand
52 # new one.
53 print("You may either add to an existing CK file, or create a new one.")
54 ck = input("Enter the name of the CK file to create > ")
55
56 # To convert SCLK times from clock strings to encoded SCLK,
57 # we need to load the Galileo spacecraft clock kernel file into
58 # the kernel pool. Assume that the file is called gll_sclk.tsc.
59 spice.furnsh(SCLKKER)
60
61 # To open a new CK file use ckopn_c, and for an existing
62 # file use dafopw_c.
63 if os.path.exists(ck):
64 handle = spice.dafopw(ck)
65 else:
66 handle = spice.ckopn(ck, ck, 0)
67
68 # Get the pointing information to go in the C-kernel segment.
69 #
70 # 1) Number of pointing instances returned
71 # 2) Array of SCLK times
72 # 3) Array of C-matrices, dimension [][3][3]
73 # 4) Array of angular velocity vectors, dimension [][3]
74 #
75 nprec, sclkch, cmats, avvs = get_gll_pnt(CLKLEN)
76
77 # Prepare list for encoded SCLK times
78 sclkdp = [0.0] * nprec
79 # Now convert the times to encoded SCLK.
80 for i in range(nprec):
81 sclkdp[i] = spice.scencd(GLL, sclkch[i])
82
83 # Set the segment boundaries equal to the first and last
84 # time in the segment.
85 begtim = sclkdp[0]
86 endtim = sclkdp[nprec - 1]
87
88 # The C-matrices are represented by quaternions in a type 1 CK
89 # segment. The CSPICE routine m2q_c converts C-matrices to
90 # quaternions.
91 quats = [None] * nprec
92 for i in range(nprec):
93 quats[i] = spice.m2q(cmats[i])
94
95 # The constants that will go into the segment descriptor are
96 #
97 # AVFLAG ... Angular velocity flag. Set to SPICETRUE.
98 # INST ... NAIF Instrument ID code. Set to -77001.
99 #
100 # REF ... Name of inertial reference frame. Set to "B1950".
101 # SEGID ... Segment identifer. Set to
102 #
103 # "GLL SCAN PLT - NAIF - 18-NOV-90"
104 # That is all the information that we need. Write the segment.
105 spice.ckw01(handle, begtim, endtim, INST, REF, AVFLAG, SEGID, nprec, sclkdp, quats, avvs)
106
107 # Close the file.
108 spice.ckcls(handle)
109
110 if __name__ == "__main__":
111 main()
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 function 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.
1 #!/usr/bin/env python3
2 """
3
4 PROGRAM WRTCK2
5
6 Write a type 2 CK segment to a new or existing C-kernel.
7 This example assumes the existence of a user-supplied
8 function to return time-tagged pointing values.
9
10 """
11
12 import os
13 import numpy as np
14 import spiceypy as spice
15
16
17 def gll_const_pnt(clklen):
18 # This is a stub implementation of the user-supplied function.
19 # It returns sample pointing data.
20 #
21 # For a realistic application, replace this stub with code that
22 # obtains the actual number of pointing instances, interval start
23 # and stop times in clock string form, and the corresponding
24 # 3x3 C-matrices.
25 #
26 # In this example, we use one record with a dummy clock interval
27 # and an identity matrix for the orientation.
28 n_prec = 1
29 begch = ["0.0"] # Interval start time in clock string form.
30 endch = ["10.0"] # Interval stop time in clock string form.
31 cmats = [np.eye(3)] # 3x3 identity matrix as a dummy orientation.
32 return n_prec, begch, endch, cmats
33
34
35 def main():
36 # Local constants
37 CLKLEN = 30
38 FILSIZ = 256
39 GLL = -77
40 IFNAME = "Test CK created by wrtck.c"
41 INST = -77001
42 MAXREC = 10000
43 NCOMCH = 1000
44 REF = "B1950"
45 REFLEN = 10
46 SCLKKER = "gll_sclk.tsc"
47 SECPERTICK = 1.0 / 120.0
48
49 # Note: SEGID is defined with the full descriptive string.
50 SEGID = "GLL SCAN PLT - NAIF - TYPE 2 PREDICT"
51 SIDLEN = 40
52
53 # Can either add to an existing CK file, or create a new one.
54 print("You may either add to an existing CK file, or create a new one.\n")
55 ck_file = input("Enter the name of the CK file to create > ")
56
57 # To convert SCLK times from clock string to encoded SCLK,
58 # we need to load the Galileo spacecraft clock kernel file into
59 # the kernel pool. Assume that the file is called gll_sclk.tsc.
60 spice.furnsh(SCLKKER)
61
62 # To open a new CK file use ckopn_c, and for an existing
63 # file use dafopw_c.
64 if os.path.exists(ck_file):
65 handle = spice.dafopw(ck_file)
66 else:
67 handle = spice.ckopn(ck_file, ck_file, 0)
68
69 # Get the pointing information to go in the C-kernel segment.
70 #
71 # 1) Number of pointing instances returned
72 # 2) Interval start times in clock string form
73 # 3) Interval stop times in clock string form
74 # 3) Array of C-matrices, dimension [][3][3]
75 n_prec, begch, endch, cmats = gll_const_pnt(CLKLEN)
76
77 # Allocate arrays for the encoded times, quaternions, angular
78 # velocities, and rates. The angular velocity vectors are 3-element
79 # arrays; the quaternions are 4-element arrays.
80 start = np.zeros(n_prec, dtype=np.float64)
81 stop = np.zeros(n_prec, dtype=np.float64)
82 quats = np.zeros((n_prec, 4), dtype=np.float64)
83 # Since the pointing is constant over each interval, each angular
84 # velocity vector is zero.
85 avvs = np.zeros((n_prec, 3), dtype=np.float64)
86 # Since this is a predict segment the number of seconds
87 # represented by one tick during each of the intervals will
88 # be set equal to the nominal amount of time represented by
89 # the least significant field of the Galileo clock: 1/120 sec.
90 rates = np.full(n_prec, SECPERTICK, dtype=np.float64)
91
92 # Now convert the times to encoded SCLK.
93 for i in range(n_prec):
94 start[i] = spice.scencd(GLL, begch[i])
95 stop[i] = spice.scencd(GLL, endch[i])
96
97 # Set the segment boundaries equal to the first and last
98 # time in the segment.
99 begtim = start[0]
100 endtim = stop[n_prec - 1]
101
102 # The C-matrices are represented by quaternions in a type 1 CK
103 # segment. The CSPICE routine m2q_c converts C-matrices to
104 # quaternions.
105 for i in range(n_prec):
106 quats[i, :] = spice.m2q(cmats[i])
107
108 # The constants that will go into the segment descriptor are
109 #
110 # INST ... NAIF Instrument ID code. Set to -77001.
111 #
112 # REF ... Name of inertial reference frame. Set to
113 # "B1950".
114 #
115 # SEGID ... Segment identifer. Set to
116 #
117 # "GLL SCAN PLT - NAIF - TYPE 2 PREDICT"
118 #
119 # That is all the information that we need. Write the segment.
120 spice.ckw02(handle, begtim, endtim, INST, REF, SEGID,
121 n_prec, start, stop, quats, avvs, rates)
122
123
124 # Close the file.
125 spice.ckcls(handle)
126
127
128 if __name__ == "__main__":
129 main()
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.
1"""
2 PROGRAM WRTCK3
3
4 This program creates a predict type 3 CK segment for the
5 Mars Global Surveyor spacecraft.
6"""
7
8import spiceypy as spice
9import numpy as np
10
11
12def locvrt_m__(center, sc, epoch, ref, abcorr="NONE"):
13 """
14 locvrt_m__ returns the 3x3 matrix that transforms vectors
15 from a specified inertial reference frame to the `Local
16 Vertical Frame' for a specified observer and target body.
17 This frame is defined as follows:
18
19
20 Z-axis: The unit vector pointing from the orbiter to
21 the sub-orbiter point on the extended body. This
22 point is the closest point on the body to the
23 orbiter; thus the unit outward normal vector on
24 the body's surface is the negative of the
25 Z-vector.
26
27
28 Y-axis: The unitized cross product
29
30 Z x V
31
32 where V is the orbiter's inertially referenced
33 velocity vector.
34
35
36 X-axis: The cross product
37
38 Y x Z
39
40 (Z and Y are already orthonormal, so X is a unit
41 vector.)
42 """
43 ...
44
45
46def get_dervrt(epoch, center, sc, ref, abcorr="NONE", dt=1e-3):
47 """
48 Calculate the angular velocity vector using the following
49 formula:
50
51 Let the angular velocity vector be AV = ( a1, a2, a3 )
52 and let the matrix OMEGA be:
53
54 +-- --+
55 | 0 -a3 a2 |
56 | |
57 OMEGA = | a3 0 -a1 |
58 | |
59 | -a2 a1 0 |
60 +-- --+
61
62 Then the derivative of a C-matrix C is given by
63
64 t
65 t d [ C ]
66 OMEGA * C = -------
67 dt
68
69 Thus, given a C-matrix and its derivative, the angular
70 velocity can be calculated from
71
72 t
73 d[ C ]
74 OMEGA = ------- * C
75 dt
76
77
78
79 get_dervrt is a non-SPICE routine that will calculate
80 the derivative of the C-matrix calculated by locvrt_m__.
81 """
82 ...
83
84def main():
85 # Functions
86 #
87 # The functions get_dervrt and locvrt_m__ are left as stubs above.
88 # Local constants
89 #
90 # Names of kernels: LSK, SCLK, PCK, SPK, CK.
91 LSK = "leap.tls"
92 SCLKKER = "mgs.tsc"
93 PCK = "mgs.tpc"
94 SPK = "mgs.bsp"
95 CK = "mgs_predict_ck.bc"
96
97 # Internal file name: just set this equal to the CK name.
98 IFNAME = CK
99
100 # Segment identifier.
101 SEGID = "MGS PREDICT TYPE 3 SEGMENT"
102
103 # The number of characters to reserve in the comment area when creating the file.
104 NCOMCH = 0
105
106 # The reference frame of the segment is J2000.
107 REF = "J2000"
108
109 # NAIF body ID codes for the Mars Global Surveyor spacecraft and Mars.
110 CENTERNAME = "Mars"
111 SCNAME = "MGS"
112
113 # The ID code for the MGS spacecraft bus.
114 INST = -94000
115
116 # The angular velocity flag indicates that angular velocity data are available.
117 AVFLAG = True # SPICETRUE
118
119 # We will need about 2000 pointing instances.
120 MAXREC = 2000
121
122 # The segment begin and end times.
123 UTCBEG = "1994 JAN 21 00:00:00"
124 UTCEND = "1994 JAN 21 02:00:00"
125
126 # The time step separating the time tags of the pointing instances.
127 # The units are ticks of encoded SCLK.
128 SCLKSTEP = 1024.0
129
130 # Local variables
131 # Pre-allocate arrays for the pointing data.
132 avvs = np.zeros((MAXREC, 3))
133 quats = np.zeros((MAXREC, 4))
134 sclkdp = np.zeros(MAXREC)
135 starts = np.zeros(MAXREC)
136
137 # Translate the spacecraft and central body names to NAIF ID codes.
138 scid = spice.bodn2c(SCNAME)
139 centerID = spice.bodn2c(CENTERNAME)
140
141 # Load the binary SPK file that provides states for MGS with respect
142 # to Mars for the time period of interest.
143 spice.furnsh(SPK)
144
145 # Load the text leapseconds, spacecraft clock (sclk), and planetary
146 # constants (pck) files into the kernel pool.
147 spice.furnsh(LSK)
148 spice.furnsh(SCLKKER)
149 spice.furnsh(PCK)
150
151 # Convert the segment begin and end times first to ET then to MGS
152 # spacecraft clock.
153 etBeg = spice.str2et(UTCBEG)
154 etEnd = spice.str2et(UTCEND)
155 scBeg = spice.sce2c(scid, etBeg)
156 scEnd = spice.sce2c(scid, etEnd)
157
158 # Calculate the quaternions and angular velocity vectors at roughly
159 # four second intervals from the segment start time until the end.
160 i = 0
161 sclk = scBeg
162 while i < MAXREC and sclk <= scEnd:
163 # The times stored in the CK are always in encoded spacecraft clock form.
164 sclkdp[i] = sclk
165
166 # Convert SCLK to ephemeris time.
167 epoch = spice.sct2e(scid, sclk)
168
169 # Find the C-matrix using the non-SPICE routine locvrt_m__.
170 # In the call below, the argument "NONE" indicates that the
171 # vectors defining the frame are not to be corrected for
172 # light time or stellar aberration.
173 cmat = locvrt_m__(centerID, scid, epoch, REF, "NONE")
174
175 # Convert the C-matrix to a quaternion.
176 quats[i] = spice.m2q(cmat)
177
178 # Calculate the derivative of the C-matrix.
179 dcmat = get_dervrt(epoch, centerID, scid, REF)
180
181 # Multiply the derivative by the C-matrix to obtain the omega matrix.
182 omega = spice.mtxm(dcmat, cmat)
183
184 # Extract the angular velocity vector components.
185 avvs[i, 0] = omega[2, 1]
186 avvs[i, 1] = omega[0, 2]
187 avvs[i, 2] = omega[1, 0]
188
189 i += 1
190 sclk += SCLKSTEP
191
192 # The number of pointing records.
193 nrec = i
194 begtime = sclkdp[0]
195 endtime = sclkdp[nrec - 1]
196
197 # Unload the SPK file.
198 spice.unload(SPK)
199
200 # The process of determining how to partition the pointing
201 # instances into interpolation intervals varies with respect
202 # to the means by which the pointing instances are obtained.
203 #
204 # For this example program it is acceptable to interpolate
205 # between all of the adjacent pointing instances because:
206 #
207 # 1) The pointing was calculated at every 4 seconds so there
208 # are no gaps in the data.
209 #
210 # 2) The pointing was calculated directly from the spacecraft
211 # and planetary ephemeris so that the functions for the
212 # spacecraft axis and angular velocity vectors will change
213 # "slowly" and continuously.
214 #
215 # Therefore there is only one interpolation interval for the
216 # entire segment.
217 #
218 nint = 1
219 starts[0] = sclkdp[0]
220
221 # Now that the pointing instances have been calculated, the segment
222 # can be written to a C-kernel file.
223 #
224 # Open a new file.
225 ckhan = spice.ckopn(CK, IFNAME, NCOMCH)
226
227 # The values that will go in the segment descriptor are
228 # already set. These are:
229 #
230 # 1) The NAIF ID code for the MGS spacecraft bus INST.
231 # 2) The angular velocity flag AVFLAG.
232 # 3) The segment start and stop times scBeg and scEnd.
233 # 4) The reference frame REF.
234 # 5) The segment time bounds begtime and endtime.
235 # The segment identifier SEGID is set as well.
236 # 6) Number of pointing instances returned
237 # 7) Interval start times in clock string form
238 # 8) Interval stop times in clock string form
239 # 9) Array of C-matrices, dimension [][3][3]
240 #
241 # Write the segment to the file attached to HANDLE.
242 spice.ckw03(ckhan, begtime, endtime, INST, REF, AVFLAG, SEGID,
243 nrec, sclkdp, quats, avvs, nint, starts)
244
245 # Close the file.
246 spice.ckcls(ckhan)
247
248if __name__ == "__main__":
249 main()
Comment Area
CSPICE provides a family of functions for handling this Comment Area. The name of each function 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 functions and their purposes are described in detail in the SPC Required Reading, spc.req.