Index Page C-Kernel Required Reading

## Table of Contents

       C-Kernel Required Reading
          Abstract

       References

       DAF Run-Time Binary File Format Translation

       Detection of Non-native Text Files

       Introduction

       Preliminaries
          Specifying Spacecraft and Instruments
          C-Matrices
          Angular Velocity Vectors
          Spacecraft Clock Time
             Encoded SCLK
             Ticks and Partitions
             SCLK and other time systems
             The SCLK kernel file

       Basics
          The CK File Reader ckgp_c
             furnsh_c
             scencd_c and sce2c_c
             sctiks_c
             ckgp_c
          The CK File Reader ckgpav_c
          Multiple Files and the C-kernel
          CK Coverage Summary Routines

       Details
          File Structure and Implementation
             Segment Descriptors
             Segment Identifiers
             Comment Area
             A CK file is a DAF
             SPICE File Identification Word in CK Files
          How the CK Readers Work
             The General Search Algorithm
             The Difference Between ckgp_c and ckgpav_c
             Locating the Applicable Segment
             Looking at Descriptors
             Evaluating the Records --- the Reader ckpfs_
             Transforming the Results

       Data Types
          Data Type 1
             Type 1 functions
          Data Type 2
             Type 2 functions
          Data Type 3
             Linear Interpolation Algorithm
             Type 3 functions
          Data Type 4
             CK Type 4 pointing evaluation algorithm
             Type 4 functions
          Data Type 5
             Type 5 functions
          Type 6: ESOC/DDID Piecewise Interpolation
             Terminology
             Mini-segments
             Type 6 subtypes
             Restrictions on type 6 data
             Type 6 segment structure
             Use of non-zero tolerance
             Type 6 functions

       Appendix A --- Summary of C-kernel Functions
          Summary of Mnemonics
          Summary of Calling Sequences

       Appendix B --- Example Program PLANET_POINT

       Appendix C --- An Example of Writing a Type 1 CK Segment

       Appendix D --- An Example of Writing a Type 2 CK Segment

       Appendix E --- An Example of Writing a Type 3 CK Segment

       Appendix G: Document Revision History
             February 13, 2014
             April 1, 2009
             November 17, 2005
             December 21, 2004
             February 2, 2004
             September 04, 2002
             February 15, 2000
             October 14, 1999
             Overview of the October 14, 1999 revision

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# C-Kernel Required Reading

Last revised on 2014 FEB 13 by N. J. Bachman.

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## Abstract

The C-kernel (CK) system is the component of SPICE concerned with attitude of spacecraft structures or instruments.

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# References

All references are to NAIF documents. The notation [Dn] refers to NAIF document number.

`1.` [167] Double Precision Array Files Required Reading (daf.req)

`2.` [349] FRAMES Required Reading (frames.req).

`3.` [222] Spacecraft Clock Time Required Reading (sclk.req)

`4.` [214] Rotations Required Reading (rotation.req)

`5.` [211] SPC Required Reading: Comments in SPK and CK Files (spc.req)

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# DAF Run-Time Binary File Format Translation

Starting with the N0052 release of the SPICE Toolkit (January, 2002) certain supported platforms are able to read DAF-based binary files (SPK, CK and binary PCK) that were written using a different, or non-native, binary representation. This access is read-only; any operations requiring writing to the file (adding information to the comment area, or appending additional ephemeris data, for example) require prior conversion of the file to the native binary file format. See the Convert User's Guide, convert.ug, for details.

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# Detection of Non-native Text Files

Starting with the N0057 release of the SPICE Toolkit (March, 2004) the SPICE data loading mechanism detects and prohibits loading text kernel files containing lines terminated with EOF character(s) non-native to the platform on which the Toolkit was compiled. If a non-native EOL terminator is detected in the first 132 characters of a text kernel, the execution is stopped and an error message is displayed. This feature does not work with files that are smaller that 132 bytes or have the first line longer that 132 characters.

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# Introduction

In the SPICE system, pointing data for science instruments are stored in the C-kernel, the ``C'' in SPICE. The pointing of an instrument is often expressed in terms of a transformation matrix from some standard base reference frame to a local, instrument-fixed frame. In the past, the instrument was often a camera, and the transformation was thus dubbed the ``C-matrix''; hence the choice of C as the name for the pointing kernel.

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.

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# Preliminaries

In this chapter we discuss four concepts that are essential to using the C-kernel: specification of spacecraft and instruments, C-matrices, angular velocity vectors, and spacecraft clock time.

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## Specifying Spacecraft and Instruments

C-kernel files and software use integer codes to refer to instruments and the spacecraft on which they are mounted. You will use these instrument numbers with C-kernel readers to request pointing data.

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.

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## C-Matrices

A C-matrix is a 3x3 matrix that transforms Cartesian coordinates referenced to a ``base frame'' to coordinates in an instrument-fixed reference frame. In earlier versions of CSPICE, the base frame was required to be inertial; this restriction has been removed.

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_c ( 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_c and other CSPICE functions.

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## Angular Velocity Vectors

In the C-kernel an angular velocity vector is a vector with respect to a base frame whose direction gives the right-handed axis about which an instrument-fixed reference frame is rotating, and whose magnitude is equal to the magnitude of the rotation velocity, in radians per second.

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_c (Get Pointing and Angular Velocity) returns an angular velocity vector in addition to a C-matrix.

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## Spacecraft Clock Time

Each piece of data within the C-kernel is associated with a spacecraft clock time (SCLK). This is because the spacecraft clock time is typically appended to the telemetry data that is the source for pointing information.

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.

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### Encoded SCLK

Encoded SCLK values may be discrete or continuous.

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_c (Encode SCLK):

       scencd_c ( sc, sclkch, &sclkdp );

Use scdecd_c (Decode SCLK) to recover the character representation from its double precision encoding.

       scdecd_c ( sc, sclkdp, lenout, sclkch );

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).

Above, the argument `lenout' is used by the caller to indicate the available space in the output string.

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_c (ET to continuous SCLK):

       sce2c_c ( sc, sclkch, &sclkdp );

To convert continuous encoded SCLK to ET, use sct2e_c (Ticks to ET):

       sct2e_c ( sc, sclkdp, &et );

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### Ticks and Partitions

The units of encoded SCLK are ``ticks since clock start at launch,'' where a ``tick'' is defined to be the shortest time increment expressible by a particular spacecraft clock.

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_c will assume the partition to be the earliest possible one containing the clock string.

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### SCLK and other time systems

CSPICE contains functions that convert between both the encoded and character form of spacecraft clock time and two 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.

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### The SCLK kernel file

Before calling any of the SCLK conversion functions mentioned above, you have to load the contents of the SCLK kernel file into the kernel pool, using the function furnsh_c.

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.

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# Basics

This chapter will present the easiest way to use C-kernel software to obtain pointing data from a CK file for a particular instrument. The mechanism for doing so is a ``reader,'' a function which reads data from the C-kernel. The highest level readers will be discussed here; one that returns the C-matrix, and another that returns the C-matrix and angular velocity vector.

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.

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## The CK File Reader ckgp_c

Below is a code fragment illustrating the use of the C-kernel file reader ckgp_c (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_c searches for pointing is provided in the ``Details'' chapter of this document.

          #include "SpiceUsr.h"

          SpiceBoolean            found;

          SpiceChar             * ref;

          SpiceDouble             clkout;
          SpiceDouble             cmat[3][3];
          SpiceDouble             sclkdp;
          SpiceDouble             tol;

          SpiceInt                inst;
          SpiceInt                sc;

          /*
          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_c ( "vgr2_sclk.tsc" );

          /*
          Load the C-kernel pointing file.
          */
          furnsh_c ( "vgr2_jup_inbound.bc" );

          /*
          We want pointing at a spacecraft clock time appearing in
          the third spacecraft clock partition.
          */
          scencd_c ( sc, "3/20556:17:768", &sclkdp );

          /*
          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 )
          */
          sctiks_c ( sc, "0:01:000", &tol );

          /*
          Get the pointing for the narrow angle camera.
          */
          ckgp_c ( inst, sclkdp, tol, ref, cmat, &clkout, &found );

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### furnsh_c

furnsh_c loads the kernel pool with the contents of the specified text kernel file, which, in this case is the SCLK kernel file.

scencd_c (below) and scdecd_c require the contents of the SCLK kernel file in order to properly encode and decode clock values. (See section on Spacecraft Clock Time).

furnsh_c 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_c open the file with all the appropriate options, relieving you of that responsibility.

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### scencd_c and sce2c_c

scencd_c 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_c is a discrete tick count. When starting with an ET value, a continuous tick count may be obtained by calling sce2c_c.

You must use encoded SCLK when calling CK reader functions.

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### sctiks_c

sctiks_c converts a clock string without partition number to units of ``ticks,'' which are the units of encoded SCLK returned by scencd_c.

The distinction between scencd_c and sctiks_c is important. The result of calling scencd_c is a relative measurement: ticks since the start of the clock at launch. The result of calling sctiks_c 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).

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### ckgp_c

ckgp_c looks through files loaded by furnsh_c to find the data needed to compute the C-matrix for a specified spacecraft instrument at a particular time. It uses the following inputs and outputs.

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_c 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'.

`found'
  Found flag. `found' will be true if it was possible to return a C-matrix for `inst' for a time within `tol' ticks of `sclkdp'. `found' will be false otherwise.

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## The CK File Reader ckgpav_c

ckgpav_c (Get Pointing and Angular Velocity) is almost identical to ckgp_c, except that it returns an angular velocity vector in addition to a C-matrix.

The calling sequence for ckgpav_c is:

       ckgpav_c ( inst, sclkdp, tol, ref, cmat, av, &clkout, &found );

The angular velocity vector `av' is a double precision array of size three. The components of `av' are given relative to the base reference frame `ref'.

All of the other arguments are identical to those of ckgp_c. And, just as with ckgp_c, you must load a CK file by calling furnsh_c before calling ckgpav_c.

The behavior of ckgpav_c is, however, slightly different from that of ckgp_c, and these differences will be explained in the ``Details'' chapter of this document.

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## Multiple Files and the C-kernel

There will probably be occasions when you will want to access pointing that is contained in more than one CK file. For instance, you may have several files describing pointing for several disjoint time periods, or for different instruments. Or you may have one file containing a partially updated version of another file's pointing.

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_c 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_c, 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_c 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_c ( "ckfile_1.bc" );
       furnsh_c ( "ckfile_2.bc" );
       furnsh_c ( "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_c ( "predict.bc" );
       furnsh_c ( "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_c accomplishes the latter by loading a file for processing. To tell C-kernel software to stop looking through a file, then, you need to unload it, with unload_c :

          #include "SpiceUsr.h"

          /*
          Load the first version.
          */
          furnsh_c ( "predict.bc" );

             .
             .  process pointing from first file.
             .

          /*
          Unload the first version.
          */
          unload_c ( "predict.bc" );

          /*
          Load the second version.
          */
          furnsh_c ( "update.bc" );

             .
             .  process pointing from the second file.
             .

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## CK Coverage Summary Routines

The CSPICE includes two functions for obtaining information about the contents of a CK file from within an application.

The ckobj_c 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_c 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 windows.req).

Refer to the headers of ckobj_c and ckcov_c for details on the use of those routines.

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# Details

In the previous chapter, we introduced the two CK readers, ckgp_c and ckgpav_c, which return C-matrices and angular velocity vectors from CK files.

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_c and ckgpav_c go about searching through files and segments to obtain the data that they need.

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## File Structure and Implementation

Each C-kernel file is made up of a number of ``segments.'' A segment is a set of logical records containing double precision numbers. When evaluated, each record gives a C-matrix and optionally, an angular velocity vector, of some spacecraft structure for some time within an interval. The segments in a file are ordered from beginning to end, with new segments added to the end of a file. The C-kernel readers use this ordering to check segments at the end of the file first.

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.

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### Segment Descriptors

The C-kernel reader functions begin addressing the question, ``Can the request for pointing be satisfied by this segment?'' by looking at the descriptor.

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.

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### Segment Identifiers

The idea behind a segment identifier is to provide a character field which allows a user to determine the exact origin of the segment.

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.

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### Comment Area

In addition to segment identifiers, every binary CK file has a ``Comment Area'' for storing free-format textual information about the pointing data in the file. Ideally, each CK file will contain internal documentation that describes all of the details about the source of the data, its recommended use, and any other pertinent information. For example, the beginning and ending epochs for the file, the names and NAIF integer codes of the instruments included, an accuracy estimate, the date the file was produced, the names of the ephemeris files used, and any assumptions or constraints could be included. Comments about a particular segment in the file could refer to the segment by its identifier.

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.

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### A CK file is a DAF

Each CK file is one implementation of a NAIF construct called a Double Precision Array File (DAF). DAFs are described in detail in reference [1]. Each CK segment is an instance of the DAF double precision array. The descriptor is an instance of a DAF ``summary''; the identifier is an instance of a DAF ``name.''

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.

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### SPICE File Identification Word in CK Files

The SPICE file identification word occupying the first eight bytes of a properly created binary CK file is ``DAF/CK ''. For more information on SPICE file identification words refer to the Kernel Required Reading document, kernel.req.

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## How the CK Readers Work

There are basically two steps to reading data from the C-kernel: locating the segment applicable to the request made, and evaluating the data contained inside the segment to return the C-matrix and angular velocity vector. In this section you'll see how these steps are implemented by ckgp_c and ckgpav_c.

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### The General Search Algorithm

The CK readers search through files loaded by furnsh_c 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_c and ckgpav_c search through segments.

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### The Difference Between ckgp_c and ckgpav_c

The only significant difference between the search algorithms of ckgp_c and ckgpav_c 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_c 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_c, 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_c and ckgpav_c 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_c might use the C-matrix only segment, whereas ckgpav_c 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.

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### Locating the Applicable Segment

Within ckgp_c and ckgpav_c, finding the right segment is the job of ckbss_ (Begin a Search for a Segment), and cksns_ (Select the Next 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_.

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### Looking at Descriptors

The descriptor and handle returned by cksns_ are used by other CK functions to locate and evaluate the pointing records. In order to do so, those functions have to unpack a descriptor into its double precision and integer parts, using the DAF function dafus_c (Unpack Summary).

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### Evaluating the Records --- the Reader ckpfs_

After locating an appropriate segment via cksns_, ckgp_c and ckgpav_c evaluate pointing records with a call to ckpfs_ (Pointing From Segment), a low level CK reader.

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_c and ckgpav_c 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.

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### Transforming the Results

The final task performed by ckgp_c and ckgpav_c is to transform the returned data from their stored reference frame to that requested by the calling program.

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'.

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# Data Types

The C-kernel framework for providing pointing data has been designed for flexibility. Different methods of storing and evaluating the data can be implemented independently of the high-level functions used to read the data. The only real restriction is that each segment must be stored as an array of double precision numbers.

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.

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## Data Type 1

The following method of storing and evaluating discrete pointing and angular rate values defines C-kernel 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.

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### Type 1 functions

There are several CK functions that support data type 1. Their names and functions are:

ckw01_c
  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.

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## Data Type 2

The following method of storing and evaluating continuous pointing data for a spacecraft structure defines C-kernel 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:

`1.` The encoded spacecraft clock START and STOP times for the interval.

`2.` The quaternion representing the C-matrix associated with the start time of the interval.

`3.` The constant angular velocity vector, in radians per second, for the interval.

`4.` 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.

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### Type 2 functions

There are several CK functions that support data type 2. Their names and functions are:

ckw02_c
  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.

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## Data Type 3

The following method of storing and evaluating discrete pointing data for a spacecraft structure defines C-kernel 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_c for a complete description of the inputs required to write a segment.

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### Linear Interpolation Algorithm

The linear interpolation performed between adjacent pointing instances by the CK software is defined by the following algorithm:

`1.` 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.

`2.` 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

`3.` 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.

`4.` 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 )

`5.` 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

`6.` 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

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### Type 3 functions

There are several CK functions that support data type 3. Their names and function are:

ckw03_c
  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.

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## Data Type 4

The following method of storing and evaluating continuous pointing data for a spacecraft structure defines C-kernel 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:

`1.` A partition for constant values to be associated with each data packet in the segment.

`2.` A partition for the data packets.

`3.` A partition for packet coverage begin times.

`4.` A partition for a packet directory, if the segment contains variable sized packets.

`5.` A partition for a packet coverage begin time directory.

`6.` 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).

`7.` 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.

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### CK Type 4 pointing evaluation algorithm

The CSPICE function chbval_ is used to evaluate individual quaternion and angular rate components from the corresponding Chebychev polynomial coefficients. Refer to the header of the chbval_ function for more information.

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### Type 4 functions

There are several CK functions that support data Type 4. Their names and functions are:

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

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## Data Type 5

CK type 5 has been provided to support accurate duplication within the CK system of spacecraft attitude data used by the European Space Agency (ESA) on the Mars Express (MEX) and Rosetta missions. However, the algorithms used by CK type 5 are very general; type 5's applicability is by no means limited to these missions.

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:

`1.` 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.

`2.` 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.

`3.` 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.

`4.` 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_c for a complete description of the inputs required to write a segment.

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### Type 5 functions

There are several CK functions that support data type 5. Their names and functions are:

ckw05_c
  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.

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## Type 6: ESOC/DDID Piecewise Interpolation

CK type 6 has been provided to support accurate duplication by the SPICE CK subsystem of spacecraft attitude data used by the European Space Agency (ESA) on the Mars Express, Rosetta, SMART-1 and Venus Express missions.

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.

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### Terminology

In this section of the document, ``pointing'' is a synonym for ``attitude'' or ``orientation.''

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.''

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### Mini-segments

Within a type 6 segment, each set of data corresponding to a type 5 segment is called a ``mini-segment.'' A type 6 segment contains one or more mini-segments.

The mini-segments of a type 6 segment need not use the same packet counts, subtypes, clock rates, or interpolation degrees.

The time coverage of a mini-segment is called a ``mini-segment interval.'' The mini-segment intervals of a type 6 segment have no intervening gaps (gaps may occur only within mini-segment intervals) and overlap only at single points. The stop time of each mini-segment interval is the start time of the next. The start time of a type 6 segment is greater than (later than) or equal to the start time of the first interval, and the segment's stop time is less than (earlier than) or equal to the stop time of the last interval.

Mini-segment intervals must have strictly positive length.

An example of the relationship between the time coverage of a type 6 segment and that of its mini-segments is shown below:

       mini-segment interval bounds:  |----------|----|--------|-|--|
       segment bounds:                  [                           ]

Each mini-segment contains a time ordered, strictly increasing sequence of epochs (no two epochs of the same mini-segment may coincide) and an associated sequence of attitude data sets called ``packets.'' The epoch associated with a packet is also called a ``time tag.'' The composition of a packet depends on the subtype of the mini-segment to which the packet belongs; subtypes are discussed in more detail below.

The start time of each mini-segment interval must be greater than or equal to the first member of the corresponding time tag sequence. The stop time of each mini-segment interval must be greater than the interval's start time and is allowed to exceed the last member of the mini-segment's time tag sequence. Thus a mini-segment interval can have a coverage gap between its last time tag and its stop time. There cannot be a gap between a mini-segment interval's stop time and the start time of the next mini-segment interval.

The interpolation interval associated with a mini-segment is the time interval over which the mini-segment can satisfy a pointing request. The interpolation interval extends from the start time of the corresponding ``mini-segment interval'' to the minimum of the stop time of the mini-segment interval and the last time tag of the mini-segment's time tag sequence.

Mini-segments may contain optional ``padding'' time tags and packets beyond both ends of their coverage intervals. Padding time tags on the left of a mini-segment interval are less than the interval start time; padding time tags on the right exceed the interval stop time. Padding enables control of interpolation behavior at and near mini-segment interval boundaries. Within a mini-segment, padding cannot occur to the right of a gap. Padding does not contribute to a mini-segment's time coverage.

The relationships between the time coverage of a mini-segment (the ``mini-segment interval''), the time tags of the pointing instances it contains, and the mini-segment's interpolation interval are shown below.

In the following diagrams, zeros represent pointing instances, hyphens represent time periods over which pointing data can be used as inputs for interpolation (this includes padding), and blank areas represent coverage gaps.

Mini-segment interval without padding:

       pointing instances:              0-0-0--0-0-0-0-0---0-0-0---0-0-0
       mini-segment interval bounds:    |                              |
       interpolation interval bounds:   ^                              ^

Mini-segment interval with padding on both sides:

       pointing instances:              0-0-0--0-0-0-0-0---0-0-0---0-0-0
       mini-segment interval bounds:          |                    |
       interpolation interval bounds:         ^                    ^

Note that when padding is present, mini-segment interval bounds need not coincide with time tags of pointing instances.

Mini-segment interval with left-side padding and with a gap:

       pointing instances:              0-0-0--0-0-0-0-0---0-0
       mini-segment interval bounds:          |                    |
       interpolation interval bounds:         ^              ^

Padding within or beyond a gap is not supported:

                                                             not allowed
                                                                v v v
       pointing instances:            0-0-0--0-0-0-0-0---0-0    0-0-0
       mini-segment interval bounds:      |                     |
       interpolation interval bounds:     ^                ^

                       last "usable" time tag -------+
                                                     | not allowed
                                                       v v v
       pointing instances:            0-0-0--0-0-0-0-0-0-0-0
       mini-segment interval bounds:      |                     |
       interpolation interval bounds:     ^          ^

The use of padding is discussed in greater detail below.

When type 6 data are interpolated to produce an attitude instance for a given request time, if the look-up tolerance is zero, only data from a single mini-segment whose interval contains the request time are used.

When a request time coincides with the boundary between two mini-segment intervals, there is a choice as to which interval will provide attitude data. The creator of a type 6 segment can control this behavior via a parameter passed to the type 6 segment writer ckw06_; this parameter is called the interval selection flag. For a given type 6 segment, depending on the value of this flag, either the earlier interval is always selected, or the later interval is always selected:

       Pointing request time:                       |

       mini-segment interval n:       0-0-0-0-0-0-0-0-0-0-0
       mini-segment interval n+1:                 @-@-@-@-@-@-@-@-@-@
       mini-segment interval bounds:   |            |             |

In the case depicted by the above diagram, if the interval selection flag is set to "true," pointing will be selected from interval n+1; if the flag is "false," pointing will be selected from interval n.

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### Type 6 subtypes

Because of the possibility of evolution of the mathematical representations of attitude used by ESA, CK type 6 is designed to accommodate multiple representations of attitude data, thereby avoiding a proliferation of CK data types. CK type 6 refers to each supported mathematical representation of attitude data as a ``subtype.''

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.

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### Restrictions on type 6 data

All data used in type 6 segments must be suitable for use by the interpolation algorithms associated with the subtypes selected by the CK creator. In general, adjacent pointing instances must represent attitudes that do not differ greatly; otherwise polynomial interpolation of quaternions will tend to yield invalid results.

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.

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### Type 6 segment structure

Below we first describe the overall type 6 segment structure, then we cover the mini-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.

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### Use of non-zero tolerance

As with other CK types, type 6 segments can provide data for request times outside of their interpolation intervals if a positive tolerance value is used, and if the request time is within the tolerance from the interpolation interval of some mini-segment. If the tolerance permits, a request time that falls into a gap can be satisfied by the closest of the last epoch of the mini-segment whose coverage interval includes the request time, or by the coverage start time of the next mini-segment, if there is one. Requests outside of the segment's coverage interval can be satisfied by data at the nearest endpoint of some mini-segment's interpolation interval, if the tolerance permits it.

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.

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### Type 6 functions

There are several CK functions that support data type 6. Their names and functions are:

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.

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# Appendix A --- Summary of C-kernel Functions

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## Summary of Mnemonics

Each C-kernel function name consists of a mnemonic which translates into a short description of the function's purpose. Those beginning with ```ck''' are names of functions that deal solely with C-kernel files. The other functions provide support that is not necessarily C-kernel specific.

          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     )

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## Summary of Calling Sequences

              Kernel Loading/Unloading Routines

       furnsh_c ( fname                                                  )
       unload_c ( fname                                                  )

              C-kernel Routines

                Wrappers

       ckcls_c  ( handle                                                 )
       ckcov_c  ( fname,  idcode, needav, level,  tol,  timsys,  cover   )
       ckgp_c   ( inst,   sclkdp, tol,    ref,    cmat, &clkout, &found  )
       ckgpav_c ( inst,   sclkdp, tol,    ref,    cmat,   av,    &clkout,
                  &found                                                 )
       cklpf_c  ( fname, &handle                                         )
       ckobj_c  ( fname,  ids                                            )
       ckopn_c  ( fname,  ifname, ncomch, &handle                        )
       ckupf_c  (         handle                                         )
       ckw01_c  ( handle, begtim, endtim, inst,   ref,  avflag, segid,
                  nprec,  sclkdp, quats,  avvs                           )
       ckw02_c  ( handle, begtim, endtim, inst,   ref,   segid,  nprec,
                  start,  stop,   quats,  avvs,   rates                  )
       ckw03_c  ( handle, begtim, endtim, inst,   ref,   avflag, segid,
                  nprec,  sclkdp, quats,  avvs,   nints, starts          )
       ckw05_c  ( handle, subtyp, degree, begtim, endtim, inst,   ref,
                  avflag, segid,  nprec,  sclkdp, packts, nints,  starts )

                Lower-level functions

       ckbss_  ( inst,    sclkdp, tol,    needav                       )
       cksns_  ( handle,  descr,  segid,  &found, SIDLEN               )
       ckpfs_  ( handle,  descr,  sclkdp, tol,    needav, cmat, av,
                 &clkout, &found                                       )
       ckr01_  ( handle,  descr,  sclkdp, tol,    needav, record,
                 &found                                                )
       cke01_  ( needav,  record, cmat,   av,     &clkout              )
       cknr01_ ( handle,  descr,  &nprec                               )
       ckgr01_ ( handle,  descr,  recno,  record                       )
       ckr02_  ( handle,  descr,  sclkdp, tol,    record, &found       )
       cke02_  ( needav,  record, cmat,   av,     &clkout              )
       cknr02_ ( handle,  descr,  &nprec                               )
       ckgr02_ ( handle,  descr,  recno,  record                       )
       ckr03_  ( handle,  descr,  sclkdp, tol,    needav, record,
                 &found                                                )
       cke03_  ( needav,  record, cmat,   av,     &clkout              )
       cknr03_ ( handle,  descr,  &nprec                               )
       ckgr03_ ( handle,  descr,  recno,  record                       )
       cke04_  ( needav,  record, cmat,   av,     &clkout              )
       ckgr04_ ( handle,  descr,  recno,  record                       )
       cknr04_ ( handle,  descr,  &nrec                                )
       ckr04_  ( handle,  descr,  sclkdp, tol,    needav, record,
                 &found                                                )
       ckw04a_ ( handle,  npkts,  pktsiz, pktdat, sclkdp               )
       ckw04b_ ( handle,  begtim, inst,   ref,    avflag, segid,
                 REFLEN,  SIDLEN                                       )
       ckw04e_ ( handle,  endtim                                       )
       ckr05_  ( handle,  descr,  sclkdp, tol,    needav, record,
                 &found                                                )
       cke05_  ( needav,  record, cmat,   av,     &clkout              )
       cknr05_ ( handle,  descr,  &nprec                               )
       ckgr05_ ( handle,  descr,  recno,  record                       )
       ckmp06_ ( handle,  descr,  msno,   &rate,  &subtyp, &winsiz,
                 &nrec,   ivlbds, &lstepc                              )
       cknm06_ ( handle,  descr,  &nmini                               )
       ckgr06_ ( handle,  descr,  msno,   recno,  record               )
       cke06_  ( needav,  record, cmat,   av,     &clkout              )
       ckr06_  ( handle,  descr,  sclkdp, tol,    needav, record,
                 &found                                                )
       ckw06_  ( handle,  inst,   ref,    avflag, first,  last,
                 segid,   nmini,  npkts,  subtps, degres, packts,
                 rates,   sclkdp, ivlbds, sellst, reflen, sidlen       )

              SCLK conversion functions

       scdecd_c ( sc,     sclkdp, lenout, sclkch         )
       scencd_c ( sc,     sclkch, &sclkdp                )
       scpart_c ( sc,     nparts, pstart, pstop          )
       scfmt_c  ( sc,     ticks,  lenout, clkstr         )
       sctiks_c ( sc,     clkstr, &ticks                 )
       sct2e_c  ( sc,     sclkdp, &et                    )
       scs2e_c  ( sc,     sclkch, &et                    )
       sce2c_c  ( sc,     et,     &sclkdp                )
       sce2t_c  ( sc,     et,     &sclkdp                )
       sce2s_c  ( sc,     et,     lenout, sclkch         )

       utc2et_c ( utcstr, &et                            )
       et2utc_c ( et,     format, prec,  lenout, utcstr  )

              Inertial Reference frame functions

       irfrot_ ( refa,   refb,   rotab  )
       irfnum_ ( name,   &index         )
       irfnam_ ( index,  name,   namlen )
       irfdef_ ( index                  )

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# Appendix B --- Example Program PLANET_POINT

The following program shows how C-kernel functions fit together with other CSPICE routines to solve a typical problem requiring pointing data.

All of the functions used here are part of CSPICE or the ANSI C library.

       /*
       PROGRAM PLANET_POINT

          Compute the planetocentric latitude, longitude and radius of
          the point at which the optic axis of an instrument intersects
          the surface of a target planet. Assume that the axis of the
          instrument is along the Z-axis of the instrument fixed
          reference frame.

          The following files are required:

             1) Kernel file containing planetary constants.
             2) Kernel file containing spacecraft clock (SCLK) data.
             3) SPK file containing planetary and spacecraft
                ephemeris data.
             4) CK file containing instrument pointing data.

          The following quantities are required:

             1) NAIF integer spacecraft ID
             2) NAIF integer planet ID
             3) NAIF integer instrument ID
             4) SCLK time string
             5) SCLK tolerance.

          The following steps are taken to locate the desired point:

             1) The inertial pointing (VPNT) of the instrument at
                the input SCLK time is read from the CK file.

             2) The apparent position (VTARG) is computed for the
                center of the target body as seen from the spacecraft,
                at the ephemeris time (ET) corresponding to SCLK.

                The one-way light time (TAU) from the target to the
                spacecraft is also computed.

             3) The transformation (TIBF) from inertial to body-fixed
                coordinates is computed for the epoch ET-TAU, using
                quantities from the planetary constants kernel.

             4) The radii (R) of the tri-axial ellipsoid used to model
                the target body are extracted from the planetary
                constants kernel.

             5) The position of the observer, in body-fixed coordinates
                is computed using VTARG and TIBF.

             6) VPNT is converted to body-fixed coordinates using TIBF.

             7) The routine SURFPT computes the point of intersection,
                given the two body-fixed positions, and tri-axial
                ellipsoid radii.

       -Particulars

           1) The instrument boresight is assumed to define the z-axis
              of the instrument-fixed reference frame. This is reflected
              in the choice of ( 0, 0, 1 ) as the boresight pointing
              vector (VPNT) in instrument-fixed coordinates.

       */

       #include <stdio.h>
       #include <string.h>
       #include "SpiceUsr.h"

       int main()
       {

          /*
          Constants

          The inertial reference frame for all output.
          */
          #define   REF            "J2000"

          /*
          File name length.
          */
          #define   FILSIZ         256

          /*
          Body name length.
          */
          #define   BDNMLN         37

          /*
          SCLK string length.
          */
          #define   TIMLEN         35

          /*
          Instrument name length.
          */
          #define   INNMLN         32
          /*
          Local variables
          */
          SpiceBoolean            found;

          SpiceChar               file      [ FILSIZ ];
          SpiceChar               instch    [ INNMLN ];
          SpiceChar               sclkch    [ TIMLEN ];
          SpiceChar               scname    [ BDNMLN ];
          SpiceChar               targname  [ BDNMLN ];
          SpiceChar               tolch     [ TIMLEN ];

          SpiceInt                inst;
          SpiceInt                n;
          SpiceInt                sc;
          SpiceInt                targ;

          SpiceDouble             clkout;
          SpiceDouble             cmat   [3][3];
          SpiceDouble             et;
          SpiceDouble             lat;
          SpiceDouble             lon;
          SpiceDouble             r      [3];
          SpiceDouble             radius;
          SpiceDouble             sclkdp;
          SpiceDouble             tau;
          SpiceDouble             tibf   [3][3];
          SpiceDouble             tol;
          SpiceDouble             vpnt   [3];
          SpiceDouble             vpos   [3];
          SpiceDouble             vsurf  [3];
          SpiceDouble             vtarg  [6];

          /*
          Get all of the files and load them.
          */
          prompt_c ( "Enter the name of the kernel file\n"
                     "containing planetary constants       > ",
                     FILSIZ,
                     file                                      );

          furnsh_c ( file );

          prompt_c ( "\nEnter the name of the kernel file\n"
                     "containing SCLK coefficients         > ",
                     FILSIZ,
                     file                                      );

          furnsh_c ( file );

          prompt_c ( "\nEnter the name of the SPK file\n"
                     "containing planetary and spacecraft\n"
                     "ephemerides                          > ",
                     FILSIZ,
                     file                                      );

          furnsh_c ( file );

          prompt_c ( "\nEnter the name of the CK file\n"
                     "containing instrument pointing       > ",
                     FILSIZ,
                     file                                      );

          furnsh_c ( file );

          /*
          Get the names of the spacecraft and target body; get the ID
          code of the instrument.  Convert the instrument ID from
          character to integer.  Translate the spacecraft and target
          names to the corresponding integer codes.
          */
          prompt_c ( "\nEnter spacecraft name             > ",
                     BDNMLN,
                     scname                                    );

          prompt_c ( "\nEnter target name                 > ",
                     BDNMLN,
                     targname                                  );

          prompt_c ( "Enter NAIF integer instrument ID    > ",
                     INNMLN,
                     instch                                    );

          prsint_c ( instch, &inst );
          bodn2c_c ( scname, &sc, &found );

          if ( !found )
          {
             setmsg_c ( "Spacecraft name # was not recognized." );
             errch_c  ( "#", scname                             );
             sigerr_c ( "SPICE(NAMENOTRECOGNIZED)"              );
          }

          bodn2c_c ( targname, &targ, &found );

          if ( !found )
          {
             setmsg_c ( "Target body name # was not recognized." );
             errch_c  ( "#", targname                            );
             sigerr_c ( "SPICE(NAMENOTRECOGNIZED)"               );
          }

          /*
          Determine the input epoch.
          */
          prompt_c ( "\nEnter SCLK string (blank line to quit) > ",
                     TIMLEN,
                     sclkch                                        );

          while (  !iswhsp_c ( sclkch )  )
          {
             /*
             Convert the input clock string to ticks.
             */
             scencd_c ( sc, sclkch, &sclkdp );

             /*
             Determine the time tolerance.
             */
             prompt_c ( "Enter the tolerance as an SCLK string  > ",
                        TIMLEN,
                        tolch                                       );

             /*
             Convert the tolerance to ticks.
             */
             sctiks_c ( sc, tolch, &tol );

             /*
             Search the CK file for pointing data at the time sclkdp.
             */
             ckgp_c ( inst, sclkdp, tol, REF, cmat, &clkout, &found );

             if ( !found )
             {
                printf ( "\n"
                         "The C-kernel file does not contain "
                         "data for time %s SCLK %s.\n",
                         scname,
                         sclkch                              );
             }

             /*
             Compute the inertial pointing vector for the instrument
             boresight.

             The boresight vector is assumed to define the z-axis of the
             instrument-fixed frame.  This axis vector can be picked off
             from the third row of the C-matrix.
             */
             vequ_c ( cmat[2], vpnt );

             /*
             For all other computations, use the ET time corresponding
             to the input SCLK.
             */
             sct2e_c ( sc, sclkdp, &et );

             /*
             Compute the target state vector (position and velocity).
             */
             spkez_c ( targ, et, REF, "lt+s", sc, vtarg, &tau );

             /*
             Get the tibf matrix and radii of target ellipsoid model.

             We need tibf for the target as it appeared when the
             instrument took its measurement at time et. The target
             was at its apparent location tau seconds earlier.

             tipbod_c and bodvcd_c will read constants from the planetary
             constants kernel file.
             */
             tipbod_c ( REF,  targ,    et-tau, tibf );
             bodvcd_c ( targ, "RADII", 3,  &n, r    );

             /*
             The position of the observer is just the negative of the
             position part of the spacecraft-target vector, vtarg.
             Note that this is NOT the same as the apparent position of
             the spacecraft as seen from the target.
             */
             vminus_c ( vtarg, vpos );

             /*
             Put both vectors in body-fixed coordinates.
             */
             mxv_c ( tibf, vpos, vpos );
             mxv_c ( tibf, vpnt, vpnt );

             /*
             Compute the point of intersection, if any.
             */
             surfpt_c ( vpos, vpnt, r[0], r[1], r[2], vsurf, &found );

             if ( !found )
             {
                printf ( "\nThe line-of-sight pointing vector "
                         "does not intersect the target "
                         "at the epoch %s SCLK %s.\n",
                         scname,
                         sclkch                                );
             }

             else
             {
                /*
                Convert intersection point from rectangular to lat-lon-
                radius coordinates.
                */
                reclat_c ( vsurf, &radius, &lon, &lat );

                printf ( "\n"
                         "Radius (km)         %f\n"
                         "Longitude (deg)     %f\n"
                         "Latitude (deg)      %f\n"
                         "\n",
                         radius,
                         lon * dpr_c(),
                         lat * dpr_c()             );

             }

             /*
             Input next epoch.
             */
             prompt_c ( "\nEnter SCLK string (blank line to quit) > ",
                        TIMLEN,
                        sclkch                                        );
          }

          return (0);
       }

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# Appendix C --- An Example of Writing a Type 1 CK Segment

The following example shows how one might write a program to create or add to a C-kernel file.

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.

          /*
          Local variables
          */
          SpiceChar                ck      [FILSIZ];
          SpiceChar                sclkch  [MAXREC][CLKLEN];

          SpiceDouble              avvs    [MAXREC][3];
          SpiceDouble              begtim;
          SpiceDouble              cmats   [MAXREC][3][3];
          SpiceDouble              endtim;
          SpiceDouble              quats   [MAXREC][4];
          SpiceDouble              sclkdp  [MAXREC];

          SpiceInt                 handle;
          SpiceInt                 i;
          SpiceInt                 nprec;

          /*
          Can either add to an existing CK file or create a brand
          new one.
          */
          printf ( "You may either add to an existing CK file, or "
                   "create a new one.\n"                            );

          prompt_c ( "Enter the name of the CK file to create > ",
                     FILSIZ,
                     ck                                           );

          /*
          To convert SCLK times from clock strings to encoded SCLK,
          we need to load the Galileo spacecraft clock kernel file into
          the kernel pool.  Assume that the file is called gll_sclk.tsc.
          */
          furnsh_c ( SCLKKER );

          /*
          To open a new CK file use ckopn_c, and for an existing
          file use dafopw_c.
          */
          if (  exists_c ( ck )  )
          {
             dafopw_ ( ck, &handle, strlen(ck) );
          }
          else
          {
             ckopn_c ( ck, ck, 0, &handle );
          }

          /*
          Get the pointing information to go in the C-kernel segment.

             1) Number of pointing instances returned
             2) Array of SCLK times
             3) Array of C-matrices, dimension [][3][3]
             4) Array of angular velocity vectors, dimension [][3]

          */
          get_gll_pnt ( &nprec, CLKLEN, sclkch, cmats, avvs );

          /*
          Now convert the times to encoded SCLK.
          */
          for ( i = 0;  i < nprec;  i++ )
          {
             scencd_c ( GLL, sclkch[i], sclkdp+i );
          }

          /*
          Set the segment boundaries equal to the first and last
          time in the segment.
          */
          begtim = sclkdp[      0];
          endtim = sclkdp[nprec-1];

          /*
          The C-matrices are represented by quaternions in a type 1 CK
          segment.  The CSPICE routine m2q_c converts C-matrices to
          quaternions.
          */

          for ( i = 0;  i < nprec;  i++ )
          {
             m2q_c ( cmats[i], quats[i] );
          }

          /*
          The constants that will go into the segment descriptor are

             AVFLAG ... Angular velocity flag.  Set to SPICETRUE.
             INST   ... NAIF Instrument ID code.  Set to -77001.
             REF    ... Name of inertial reference frame.  Set to "B1950".
             SEGID  ... Segment identifer.  Set to

                          "GLL SCAN PLT - NAIF - 18-NOV-90"

          That is all the information that we need. Write the segment.
          */

          ckw01_c ( handle,
                    begtim,
                    endtim,
                    INST,
                    REF,
                    AVFLAG,
                    SEGID,
                    nprec,
                    sclkdp,
                    quats,
                    avvs    );

          /*
          Close the file.
          */
          ckcls_c ( handle );

          return (0);
       }

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# Appendix D --- An Example of Writing a Type 2 CK Segment

This example program creates a single type 2 segment of predict pointing for the scan platform of the Galileo spacecraft.

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.

       /*

       PROGRAM WRTCK2

          Write a type 2 CK segment to a new or existing C-kernel.
          This example assumes the existence of a user-supplied
          function to return time-tagged pointing values.

       */

       #include <stdio.h>
       #include <string.h>
       #include "SpiceUsr.h"
       #include "SpiceZfc.h"

       int main()
       {

          /*
          Functions
          */
          void gll_const_pnt ( SpiceInt       * nprec,
                               SpiceInt         sclklen,
                               void           * begch,
                               void           * endch,
                               SpiceDouble  ( * cmats  )[3][3] );

          /*
          Local constants
          */
          #define  CLKLEN         30
          #define  FILSIZ         256
          #define  GLL            -77
          #define  IFNAME         "Test CK created by wrtck.c"
          #define  INST           -77001
          #define  MAXREC         10000
          #define  NCOMCH         1000
          #define  REF            "B1950"
          #define  REFLEN         10
          #define  SCLKKER        "gll_sclk.tsc"
          #define  SECPERTICK     ( 1. / 120. )
          #define  SEGID          "GLL SCAN PLT - NAIF - TYPE 2 PREDICT"
          #define  SIDLEN         40

          /*
          Local variables
          */
          SpiceChar                ck      [FILSIZ];
          SpiceChar                begch   [MAXREC][CLKLEN];
          SpiceChar                endch   [MAXREC][CLKLEN];

          SpiceDouble              avvs    [MAXREC][3];
          SpiceDouble              begtim;
          SpiceDouble              cmats   [MAXREC][3][3];
          SpiceDouble              endtim;
          SpiceDouble              quats   [MAXREC][4];
          SpiceDouble              rates   [MAXREC];
          SpiceDouble              start   [MAXREC];
          SpiceDouble              stop    [MAXREC];

          SpiceInt                 handle;
          SpiceInt                 i;
          SpiceInt                 nprec;

          /*
          Can either add to an existing CK file or create a brand
          new one.
          */
          printf ( "You may either add to an existing CK file, or "
                   "create a new one.\n"                            );

          prompt_c ( "Enter the name of the CK file to create > ",
                     FILSIZ,
                     ck                                           );

          /*
          To convert SCLK times from clock string to encoded SCLK,
          we need to load the Galileo spacecraft clock kernel file into
          the kernel pool.  Assume that the file is called gll_sclk.tsc.
          */
          furnsh_c ( SCLKKER );

          /*
          To open a new CK file use ckopn_c, and for an existing
          file use dafopw_c.
          */
          if (  exists_c ( ck )  )
          {
             dafopw_ ( ck, &handle, strlen(ck) );
          }
          else
          {
             ckopn_c ( ck, ck, 0, &handle );
          }

          /*
          Get the pointing information to go in the C-kernel segment.

             1) Number of pointing instances returned
             2) Interval start times in clock string form
             3) Interval stop times in clock string form
             3) Array of C-matrices, dimension [][3][3]

          */
          gll_const_pnt ( &nprec, CLKLEN, begch, endch, cmats );

          /*
          Now convert the times to encoded SCLK.
          */
          for ( i = 0;  i < nprec;  i++ )
          {
             scencd_c ( GLL, begch[i], start+i );
             scencd_c ( GLL, endch[i], stop +i );
          }

          /*
          Set the segment boundaries equal to the first and last
          time in the segment.
          */
          begtim = start[      0];
          endtim = stop [nprec-1];

          /*
          The C-matrices are represented by quaternions in a type 1 CK
          segment.  The CSPICE routine m2q_c converts C-matrices to
          quaternions.
          */
          for ( i = 0;  i < nprec;  i++ )
          {
             m2q_c ( cmats[i], quats[i] );
          }

          /*
          Since the pointing is constant over each interval, each angular
          velocity vector is zero.
          */
          for ( i = 0;  i < (3*nprec);  i++ )
          {
            *( (SpiceDouble *)avvs+i ) = 0.;
          }

          /*
          Since this is a predict segment the number of seconds
          represented by one tick during each of the intervals will
          be set equal to the nominal amount of time represented by
          the least significant field of the Galileo clock: 1/120 sec.
          */
          for ( i = 0;  i < nprec;  i++ )
          {
             rates[i] = SECPERTICK;
          }

          /*
          The constants that will go into the segment descriptor are

             INST   ... NAIF Instrument ID code.  Set to -77001.

             REF    ... Name of inertial reference frame.  Set to
                        "B1950".

             SEGID  ... Segment identifer.  Set to

                          "GLL SCAN PLT - NAIF - TYPE 2 PREDICT"

          That is all the information that we need. Write the segment.
          */
          ckw02_c ( handle,
                    begtim,
                    endtim,
                    INST,
                    REF,
                    SEGID,
                    nprec,
                    start,
                    stop,
                    quats,
                    avvs,
                    rates    );

          /*
          Close the file.
          */
          ckcls_c ( handle );

          return (0);
       }

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# Appendix E --- An Example of Writing a Type 3 CK Segment

The following example program shows how one might write a type 3 C-kernel segment to a new file.

The program creates a single type 3 segment for a two hour time period for the Mars Global Surveyor spacecraft bus. The program calculates the pointing instances directly from the spacecraft and planet ( SPK ) ephemeris file.

The names of the input ephemeris, leapseconds, spacecraft clock, and planetary constants kernel files are fictitious.

       /*

       PROGRAM WRTCK3

          This program creates a predict type 3 CK segment for the
          Mars Global Surveyor spacecraft.

       */

       #include <stdio.h>
       #include "SpiceUsr.h"

       int main()
       {

          /*
          Functions
          */
          void get_dervrt ( SpiceDouble     epoch,
                            SpiceDouble     dcmat[3][3] );

          void locvrt_m__ ( SpiceInt        center,
                            SpiceInt        sc,
                            SpiceDouble     epoch,
                            SpiceChar     * ref,
                            SpiceChar     * abcorr,
                            SpiceDouble     cmat  [3][3] );

          /*
          Local constants
          */

          /*
          Names of kernels:  LSK, SCLK, PCK, SPK, CK.
          */
          #define  LSK            "leap.tls"
          #define  SCLKKER        "mgs.tsc"
          #define  PCK            "mgs.tpc"
          #define  SPK            "mgs.bsp"
          #define  CK             "mgs_predict_ck.bc"

          /*
          The internal file name:  just set this equal to the CK name.
          */
          #define  IFNAME         CK

          /*
          The segment identifier:
          */
          #define  SEGID          "MGS PREDICT TYPE 3 SEGMENT"

          /*
          The number of characters to reserve in the comment area
          when creating the file:
          */
          #define  NCOMCH         0

          /*
          The reference frame of the segment is J2000.
          */
          #define  REF            "J2000"

          /*
          Assign the NAIF body id codes for the Mars Global Surveyor
          spacecraft and Mars.
          */
          #define  CENTERNAME     "Mars"
          #define  SCNAME         "MGS"

          /*
          The ID code for the MGS spacecraft bus:
          */
          #define  INST           -94000

          /*
          The angular velocity flag will indicate that angular velocity
          data are available.
          */
          #define  AVFLAG         SPICETRUE

          /*
          We will need about 2000 pointing instances.
          */
          #define  MAXREC         2000

          /*
          The segment begin and end times.
          */
          #define  UTCBEG         "1994 JAN 21 00:00:00"
          #define  UTCEND         "1994 JAN 21 02:00:00"

          /*
          The time step separating the time tags of the pointing
          instances.  The units are ticks of encoded SCLK.
          */
          #define  SCLKSTEP       1024.0

          /*
          Local variables
          */
          SpiceBoolean            found;

          SpiceDouble             avvs    [MAXREC][3];
          SpiceDouble             begtime;
          SpiceDouble             cmat    [3][3];
          SpiceDouble             dcmat   [3][3];
          SpiceDouble             endtime;
          SpiceDouble             epoch;
          SpiceDouble             etBeg;
          SpiceDouble             etEnd;
          SpiceDouble             omega   [3][3];
          SpiceDouble             quats   [MAXREC][4] ;
          SpiceDouble             scBeg;
          SpiceDouble             scEnd;
          SpiceDouble             sclk;
          SpiceDouble             sclkdp  [MAXREC];
          SpiceDouble             start   [MAXREC];

          SpiceInt                ckhan;
          SpiceInt                i;
          SpiceInt                nint;
          SpiceInt                nrec;
          SpiceInt                SCID;

          SpiceInt                centerID;

          /*
          Translate the spacecraft and central body names to
          NAIF ID codes.
          */
          bodn2c_c ( SCNAME,     &SCID,  &found );

          if ( !found )
          {
             setmsg_c ( "Name # could not be mapped to a NAIF ID code." );
             errch_c  ( "#",  SCNAME                                    );
             sigerr_c ( "SPICE(NAMENOTFOUND)"                           );
          }

          bodn2c_c ( CENTERNAME, &centerID, &found );

          if ( !found )
          {
             setmsg_c ( "Name # could not be mapped to a NAIF ID code." );
             errch_c  ( "#",  CENTERNAME                                );
             sigerr_c ( "SPICE(NAMENOTFOUND)"                           );
          }

          /*
          Load the binary SPK file that provides states for MGS with
          respect to Mars for the time period of interest.
          */
          furnsh_c ( SPK );

          /*
          Load the text leapseconds, spacecraft clock ( sclk ), and
          planetary constants ( pck ) files into the kernel pool.
          */
          furnsh_c ( LSK     );
          furnsh_c ( SCLKKER );
          furnsh_c ( PCK     );

          /*
          Convert the segment begin and end times first to ET then to
          MGS spacecraft clock.
          */
          str2et_c ( UTCBEG, &etBeg );
          str2et_c ( UTCEND, &etEnd );

          sce2c_c  ( SCID, etBeg, &scBeg );
          sce2c_c  ( SCID, etEnd, &scEnd );

          /*
          Calculate the quaternions and angular velocity vectors at
          roughly four second intervals from the segment start time
          until the end.
          */

          for (  ( i = 0,            sclk =  scBeg    );
                 ( i < MAXREC ) && ( sclk <= scEnd    );
                 ( i++,              sclk += SCLKSTEP )   )
          {

             /*
             The times stored in the C-kernel are always in encoded
             spacecraft clock form.  SPK takes ET as the input time.
             */
             sclkdp[i] = sclk;

             sct2e_c ( SCID, sclk, &epoch );

             /*
             Find the C-matrix using the non-CSPICE routine locvrt_m__.
             locvrt_m__ returns the 3x3 matrix that transforms vectors
             from a specified inertial reference frame to the `Local
             Vertical Frame' for a specified observer and target body.
             This frame is defined as follows:

                Z-axis:  The unit vector pointing from the orbiter to
                         the sub-orbiter point on the extended body.  This
                         point is the closest point on the body to the
                         orbiter; thus the unit outward normal vector on
                         the body's surface is the negative of the
                         Z-vector.

                Y-axis:  The unitized cross product

                            Z x V

                         where V is the orbiter's inertially referenced
                         velocity vector.

                X-axis:  The cross product

                            Y x Z

                         (Z and Y are already orthonormal, so X is a unit
                         vector.)

             In the call below, the argument "NONE" indicates that the
             vectors defining the frame are not to be corrected for
             light time or stellar aberration.
             */

             locvrt_m__ ( centerID, SCID,  epoch,       REF,
                          "NONE",   cmat,  strlen(REF), 4   );

             m2q_c ( cmat, quats[i] );

             /*
             Calculate the angular velocity vector using the following
             formula:

             Let the angular velocity vector be  AV = ( a1, a2, a3 )
             and let the matrix OMEGA be:

                         +--              --+
                         |   0   -a3   a2   |
                         |                  |
                OMEGA =  |  a3    0    -a1  |
                         |                  |
                         |  -a2   a1    0   |
                         +--              --+

              Then the derivative of a C-matrix C is given by

                                       t
                          t       d [ C ]
                 OMEGA * C   =    -------
                                     dt

              Thus, given a C-matrix and its derivative, the angular
              velocity can be calculated from

                                  t
                              d[ C  ]
                  OMEGA  =    -------  *  C
                                 dt

             get_dervrt is a non-CSPICE routine that will calculate
             the derivative of the C-matrix calculated by locvrt_m__.
             */
             get_dervrt ( epoch, dcmat );

             mtxm_c ( dcmat, cmat, omega );

             avvs[i][0]  =  omega[2][1];
             avvs[i][1]  =  omega[0][2];
             avvs[i][2]  =  omega[1][0];
          }

          /*
          Set the pointing record count and the segment time bounds.
          */
          nrec    -= i;

          begtime =  sclkdp[0];
          endtime =  sclkdp[nrec-1];

          /*
          Unload the SPK file.
          */
          unload_c ( SPK );

          /*
          The process of determining how to partition the pointing
          instances into interpolation intervals varies with respect
          to the means by which the pointing instances are obtained.

          For this example program it is acceptable to interpolate
          between all of the adjacent pointing instances because:

          1) The pointing was calculated at every 4 seconds so there
             are no gaps in the data.

          2) The pointing was calculated directly from the spacecraft
             and planetary ephemeris so that the functions for the
             spacecraft axis and angular velocity vectors will change
             "slowly" and continuously.

          Therefore there is only one interpolation interval for the
          entire segment.
          */

          nint     =  1;
          start[0] =  sclkdp[0];

          /*
          Now that the pointing instances have been calculated the
          segment can be written to a C-kernel file.

          Open a new file.
          */
          ckopn_c ( CK, IFNAME, NCOMCH, &ckhan );

          /*
          The values that will go in the segment descriptor are
          already set.  These are:

             1) The NAIF ID code for the MGS spacecraft bus INST.
             2) The angular velocity flag AVFLAG.
             3) The segment start and stop times scBeg and scEnd.
             4) The reference frame REF.
             5) The segment time bounds begtime and endtime.

          The segment identifier SEGID is set as well.

             1) Number of pointing instances returned
             2) Interval start times in clock string form
             3) Interval stop times in clock string form
             3) Array of C-matrices, dimension [][3][3]

          */

          /*
          Write the segment to the file attached to HANDLE.
          */
          ckw03_c ( ckhan,  begtime, endtime, INST,   REF,    AVFLAG,
                    SEGID,  nrec,    sclkdp,  quats,  avvs,   nint,
                    start                                           );

          /*
          Close the file.
          */
          ckcls_c ( ckhan );

          return (0);

       }

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# Appendix G: Document Revision History

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### February 13, 2014

Added documentation of CK type 6.

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### April 1, 2009

Added a note about the SPICE file identification word for CK kernels.

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### November 17, 2005

Abstract was added.

Calls/references to the deprecated routine bodvar_c were replaced with calls/referenes to bodvcd_c. bodvrd_c is mentioned as another routine superseding bodvar_c.

C examples showing incorrect calling sequences for prompt_c were corrected.

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### December 21, 2004

Replaced references and examples of lower level CK loading/unloading functions with furnsh_c/unload_c.

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### February 2, 2004

Performed a spell-check on text.

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### September 04, 2002

Added a discussion of CK type 05.

Added a brief discussion of the DAF run-time binary file format translation capability now present in the SPICE Toolkit.

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### February 15, 2000

This February 2000 version of the document differs from the previous version of October 1999 in the following areas:

The section describing new Chebyshev polynomial based data type--CK Type 4--was added to the document.

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### October 14, 1999

This is the initial release of the CSPICE edition of the CK "Required Reading" document.

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### Overview of the October 14, 1999 revision

The SPICE system has been extended to include CSPICE---a version of the NAIF Toolkit software coded in the ANSI C programming language.

The CSPICE library---the C counterpart of SPICELIB---consists of two categories of functions:

`--` Low level functions, translated from Fortran to ANSI C via the automatic translation program f2c.

`--` Application interface-level functions, hand-coded in ANSI C. These hand-coded functions are called ``wrappers'' since they typically serve to encapsulate C code generated by running f2c on Fortran source code.

Wrapper functions are denoted by names ending with the suffix

       _c

Functions created by f2c have names ending with the suffix

       _

In this first version of CSPICE, wrappers are provided for the principal C application interface functions. Hand-coded versions of other, less frequently used interface functions will be supplied in a later version of CSPICE. The remaining, lower-level functions will not be provided with wrappers.

The set of currently available CSPICE CK wrapper functions is:

       ckcls_c
       ckgp_c
       ckgpav_c
       furnsh_c
       ckopn_c
       unload_c
       ckw01_c
       ckw02_c
       ckw03_c

Less frequently used application interface-level functions referenced here but for which wrappers are not yet implemented are:

       Portions of the DAF family of functions
       The SPC family of functions