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Index Page ckw05_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       ckw05_c ( Write CK segment, type 5 )

       void ckw05_c ( SpiceInt            handle,
                      SpiceCK05Subtype    subtyp,
                      SpiceInt            degree,
                      SpiceDouble         begtim,
                      SpiceDouble         endtim,
                      SpiceInt            inst,
                      ConstSpiceChar    * ref,
                      SpiceBoolean        avflag,
                      ConstSpiceChar    * segid,
                      SpiceInt            n,
                      ConstSpiceDouble    sclkdp [],
                      const void        * packts,
                      SpiceDouble         rate,
                      SpiceInt            nints,
                      ConstSpiceDouble    starts []    )

#### Abstract

       Write a type 5 segment to a CK file.

#### Required_Reading

       CK
       NAIF_IDS
       ROTATION
       TIME

#### Keywords

       FILES
       POINTING

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       handle     I   Handle of an open CK file.
       subtyp     I   CK type 5 subtype code.
       degree     I   Degree of interpolating polynomials.
       begtim     I   The beginning encoded SCLK of the segment.
       endtim     I   The ending encoded SCLK of the segment.
       inst       I   The NAIF instrument ID code.
       ref        I   The reference frame of the segment.
       avflag     I   SPICETRUE if the segment will contain angular velocity.
       segid      I   Segment identifier.
       n          I   Number of packets.
       sclkdp     I   Encoded SCLK times.
       packts     I   Array of packets.
       rate       I   Nominal SCLK rate in seconds per tick.
       nints      I   Number of intervals.
       starts     I   Encoded SCLK interval start times.
       MAXDEG     P   Maximum allowed degree of interpolating polynomial.

#### Detailed_Input

       handle      is the handle of the CK file to which the segment will be
                   written. The file must have been opened with write
                   access.

       subtyp      is an integer code indicating the subtype of the
                   segment to be created.

       degree      is the degree of the polynomials used to interpolate the
                   quaternions contained in the input packets. All
                   components of the quaternions are interpolated by
                   polynomials of fixed degree.

       begtim,
       endtim      are the beginning and ending encoded SCLK times
                   for which the segment provides pointing information.
                   begtim must be less than or equal to endtim, and at least
                   one data packet must have a time tag t such that

                             begtim  <  t  <  endtim
                                     -     -

       inst        is the NAIF integer ID code for the instrument.

       ref         is a character string which specifies the
                   reference frame of the segment. This should be one of
                   the frames supported by the SPICELIB routine NAMFRM
                   which is an entry point of FRAMEX.

                   The rotation matrices represented by the quaternions
                   that are to be written to the segment transform the
                   components of vectors from the inertial reference frame
                   specified by ref to components in the instrument fixed
                   frame. Also, the components of the angular velocity
                   vectors to be written to the segment should be given
                   with respect to ref.

                   ref should be the name of one of the frames supported
                   by the SPICELIB routine NAMFRM.

       avflag      is a boolean flag which indicates whether or not the
                   segment will contain angular velocity.

       segid       is the segment identifier.  A CK segment identifier may
                   contain up to 40 characters, excluding the terminating
                   null.

       packts      contains a time-ordered array of data packets
                   representing the orientation of inst relative to the
                   frame ref. Each packet contains a SPICE-style quaternion
                   and optionally, depending on the segment subtype,
                   attitude derivative data, from which a C-matrix and an
                   angular velocity vector may be derived.

                   See the discussion of "Quaternion Styles" in the
                   -Particulars section below.

                   The C-matrix represented by the Ith data packet is a
                   rotation matrix that transforms the components of a
                   vector expressed in the base frame specified by ref to
                   components expressed in the instrument fixed frame at the
                   time sclkdp(I).

                   Thus, if a vector v has components x, y, z in the base
                   frame, then v has components x', y', z' in the instrument
                   fixed frame where:

                      [ x' ]     [          ] [ x ]
                      | y' |  =  |   cmat   | | y |
                      [ z' ]     [          ] [ z ]

                   The attitude derivative information in packts[i] gives
                   the angular velocity of the instrument fixed frame at
                   time sclkdp[i] with respect to the reference frame
                   specified by ref.

                   The direction of an angular velocity vector gives the
                   right-handed axis about which the instrument fixed
                   reference frame is rotating. The magnitude of the vector
                   is the magnitude of the instantaneous velocity of the
                   rotation, in radians per second.

                   Packet contents and the corresponding interpolation
                   methods depend on the segment subtype, and are as
                   follows:

                      Subtype 0:  Hermite interpolation, 8-element packets.
                                  Quaternion and quaternion derivatives
                                  only, no angular velocity vector provided.
                                  Quaternion elements are listed first,
                                  followed by derivatives. Angular velocity
                                  is derived from the quaternions and
                                  quaternion derivatives.

                      Subtype 1:  Lagrange interpolation, 4-element packets.
                                  Quaternion only. Angular velocity is
                                  derived by differentiating the
                                  interpolating polynomials.

                      Subtype 2:  Hermite interpolation, 14-element packets.
                                  Quaternion and angular angular velocity
                                  vector, as well as derivatives of each,
                                  are provided. The quaternion comes first,
                                  then quaternion derivatives, then angular
                                  velocity and its derivatives.

                      Subtype 3:  Lagrange interpolation, 7-element packets.
                                  Quaternion and angular velocity vector
                                  provided. The quaternion comes first.

                   Angular velocity is always specified relative to the base
                   frame.

       rate        is the nominal rate of the spacecraft clock associated
                   with inst. Units are seconds per tick. rate is used to
                   scale angular velocity to radians/second.

       nints       is the number of intervals that the pointing instances
                   are partitioned into.

       starts      are the start times of each of the interpolation
                   intervals. These times must be strictly increasing and
                   must coincide with times for which the segment contains
                   pointing.

#### Detailed_Output

       None. See -Files section.

#### Parameters

       MAXDEG     is the maximum allowed degree of the interpolating
                  polynomial. If the value of MAXDEG is increased, the
                  CSPICE routine ckpfs_ must be changed accordingly. In
                  particular, the size of the record passed to ckrNN_ and
                  ckeNN_ must be increased, and comments describing the
                  record size must be changed.

#### Exceptions

       If any of the following exceptions occur, this routine will
       return without creating a new segment.

       1)  If `handle' is not the handle of a C-kernel opened for writing,
           an error is signaled by a routine in the call tree of this
           routine.

       2)  If the last non-blank character of `segid' occurs past index 40,
           the error SPICE(SEGIDTOOLONG) is signaled by a routine in the
           call tree of this routine.

       3)  If `segid' contains any nonprintable characters, the error
           SPICE(NONPRINTABLECHARS) is signaled by a routine in the call
           tree of this routine.

       4)  If the first encoded SCLK time is negative, the error
           SPICE(INVALIDSCLKTIME) is signaled by a routine in the call
           tree of this routine. If any subsequent times are negative the
           error will be detected in exception (5).

       5)  If the encoded SCLK times are not strictly increasing, the
           error SPICE(TIMESOUTOFORDER) is signaled by a routine in the
           call tree of this routine.

       6)  If the name of the reference frame is not one of those
           supported by the routine FRAMEX, the error
           SPICE(INVALIDREFFRAME) is signaled by a routine in the call
           tree of this routine.

       7)  If the number of packets `n' is not at least 1, the error
           SPICE(TOOFEWPACKETS) is signaled by a routine in the call tree
           of this routine.

       8)  If `nints', the number of interpolation intervals, is less than
           or equal to 0, the error SPICE(INVALIDNUMINTS) is signaled by
           a routine in the call tree of this routine.

       9)  If the encoded SCLK interval start times are not strictly
           increasing, the error SPICE(TIMESOUTOFORDER) is signaled by a
           routine in the call tree of this routine.

       10) If an interval start time does not coincide with a time for
           which there is an actual pointing instance in the segment, the
           error SPICE(INVALIDSTARTTIME) is signaled by a routine in the
           call tree of this routine.

       11) This routine assumes that the rotation between adjacent
           quaternions that are stored in the same interval has a
           rotation angle of `theta' radians, where

              0  <=  theta  <  pi.

           The routines that evaluate the data in the segment produced
           by this routine cannot distinguish between rotations of `theta'
           radians, where `theta' is in the interval [0, pi), and
           rotations of

              theta   +   2 * k * pi

           radians, where k is any integer. These "large" rotations will
           yield invalid results when interpolated. You must ensure that
           the data stored in the segment will not be subject to this
           sort of ambiguity.

       12) If any quaternion has magnitude zero, the error
           SPICE(ZEROQUATERNION) is signaled by a routine in the call
           tree of this routine.

       13) If the interpolation window size implied by `degree' is not
           even, the error SPICE(INVALIDDEGREE) is signaled by a routine
           in the call tree of this routine. The window size is degree+1
           for Lagrange subtypes and is (degree+1)/2 for Hermite
           subtypes.

       14) If an unrecognized subtype code is supplied, the error
           SPICE(NOTSUPPORTED) is signaled by a routine in the call tree
           of this routine.

       15) If `degree' is not at least 1 or is greater than MAXDEG, the
           error SPICE(INVALIDDEGREE) is signaled by a routine in the
           call tree of this routine.

       16) If the segment descriptor bounds are out of order, the error
           SPICE(BADDESCRTIMES) is signaled by a routine in the call tree
           of this routine.

       17) If there is no element of `sclkdp' that lies between `begtim' and
           `endtim' inclusive, the error SPICE(EMPTYSEGMENT) is signaled by
           a routine in the call tree of this routine.

       18) If `rate' is zero, the error SPICE(INVALIDVALUE) is signaled by
           a routine in the call tree of this routine.

       19) If any of the `ref' or `segid' input string pointers is null,
           the error SPICE(NULLPOINTER) is signaled.

       20) If any of the `ref' or `segid' input strings has zero length,
           the error SPICE(EMPTYSTRING) is signaled.

#### Files

       A new type 5 CK segment is written to the CK file attached
       to handle.

#### Particulars

       This routine writes a CK type 5 data segment to the open CK
       file according to the format described in the type 5 section of
       the CK Required Reading. The CK file must have been opened with
       write access.

       Quaternion Styles
       -----------------

       There are different "styles" of quaternions used in
       science and engineering applications. Quaternion styles
       are characterized by

       -  The order of quaternion elements

       -  The quaternion multiplication formula

       -  The convention for associating quaternions
          with rotation matrices

       Two of the commonly used styles are

          - "SPICE"

             > Invented by Sir William Rowan Hamilton
             > Frequently used in mathematics and physics textbooks

          - "Engineering"

             > Widely used in aerospace engineering applications

       CSPICE function interfaces ALWAYS use SPICE quaternions.
       Quaternions of any other style must be converted to SPICE
       quaternions before they are passed to CSPICE functions.

       Relationship between SPICE and Engineering Quaternions
       ------------------------------------------------------

       Let M be a rotation matrix such that for any vector V,

          M*V

       is the result of rotating V by theta radians in the
       counterclockwise direction about unit rotation axis vector A.
       Then the SPICE quaternions representing M are

          (+/-) (  cos(theta/2),
                   sin(theta/2) A(1),
                   sin(theta/2) A(2),
                   sin(theta/2) A(3)  )

       while the engineering quaternions representing M are

          (+/-) ( -sin(theta/2) A(1),
                  -sin(theta/2) A(2),
                  -sin(theta/2) A(3),
                   cos(theta/2)       )

       For both styles of quaternions, if a quaternion q represents
       a rotation matrix M, then -q represents M as well.

       Given an engineering quaternion

          QENG   = ( q0,  q1,  q2,  q3 )

       the equivalent SPICE quaternion is

          QSPICE = ( q3, -q0, -q1, -q2 )

       Associating SPICE Quaternions with Rotation Matrices
       ----------------------------------------------------

       Let FROM and TO be two right-handed reference frames, for
       example, an inertial frame and a spacecraft-fixed frame. Let the
       symbols

          V    ,   V
           FROM     TO

       denote, respectively, an arbitrary vector expressed relative to
       the FROM and TO frames. Let M denote the transformation matrix
       that transforms vectors from frame FROM to frame TO; then

          V   =  M * V
           TO         FROM

       where the expression on the right hand side represents left
       multiplication of the vector by the matrix.

       Then if the unit-length SPICE quaternion q represents M, where

          q = (q0, q1, q2, q3)

       the elements of M are derived from the elements of q as follows:

            +-                                                         -+
            |           2    2                                          |
            | 1 - 2*( q2 + q3 )   2*(q1*q2 - q0*q3)   2*(q1*q3 + q0*q2) |
            |                                                           |
            |                                                           |
            |                               2    2                      |
        M = | 2*(q1*q2 + q0*q3)   1 - 2*( q1 + q3 )   2*(q2*q3 - q0*q1) |
            |                                                           |
            |                                                           |
            |                                                   2    2  |
            | 2*(q1*q3 - q0*q2)   2*(q2*q3 + q0*q1)   1 - 2*( q1 + q2 ) |
            |                                                           |
            +-                                                         -+

       Note that substituting the elements of -q for those of q in the
       right hand side leaves each element of M unchanged; this shows
       that if a quaternion q represents a matrix M, then so does the
       quaternion -q.

       To map the rotation matrix M to a unit quaternion, we start by
       decomposing the rotation matrix as a sum of symmetric
       and skew-symmetric parts:

                                          2
          M = [ I  +  (1-cos(theta)) OMEGA  ] + [ sin(theta) OMEGA ]

                       symmetric                   skew-symmetric

       OMEGA is a skew-symmetric matrix of the form

                     +-             -+
                     |  0   -n3   n2 |
                     |               |
           OMEGA  =  |  n3   0   -n1 |
                     |               |
                     | -n2   n1   0  |
                     +-             -+

       The vector N of matrix entries (n1, n2, n3) is the rotation axis
       of M and theta is M's rotation angle. Note that N and theta
       are not unique.

       Let

          C = cos(theta/2)
          S = sin(theta/2)

       Then the unit quaternions Q corresponding to M are

          Q = +/- ( C, S*n1, S*n2, S*n3 )

       The mappings between quaternions and the corresponding rotations
       are carried out by the CSPICE routines

          q2m_c {quaternion to matrix}
          m2q_c {matrix to quaternion}

       m2q_c always returns a quaternion with scalar part greater than
       or equal to zero.

       SPICE Quaternion Multiplication Formula
       ---------------------------------------

       Given a SPICE quaternion

          Q = ( q0, q1, q2, q3 )

       corresponding to rotation axis A and angle theta as above, we can
       represent Q using "scalar + vector" notation as follows:

          s =   q0           = cos(theta/2)

          v = ( q1, q2, q3 ) = sin(theta/2) * A

          Q = s + v

       Let Q1 and Q2 be SPICE quaternions with respective scalar
       and vector parts s1, s2 and v1, v2:

          Q1 = s1 + v1
          Q2 = s2 + v2

       We represent the dot product of v1 and v2 by

          <v1, v2>

       and the cross product of v1 and v2 by

          v1 x v2

       Then the SPICE quaternion product is

          Q1*Q2 = s1*s2 - <v1,v2>  + s1*v2 + s2*v1 + (v1 x v2)

       If Q1 and Q2 represent the rotation matrices M1 and M2
       respectively, then the quaternion product

          Q1*Q2

       represents the matrix product

          M1*M2

#### Examples

       This example code fragment writes a type 5 C-kernel segment
       for the Mars Express spacecraft bus to a previously opened CK
       file attached to handle.

          /.
          Include CSPICE interface definitions.
          ./
          #include "SpiceUsr.h"
                    .
                    .
                    .
          /.
          Assume arrays of quaternions, angular velocities, and the
          associated SCLK times are produced elsewhere. The software
          that calls ckw05_c must then decide how to partition these
          pointing instances into intervals over which linear
          interpolation between adjacent points is valid.
          ./
                     .
                     .
                     .

          /.
          The subroutine ckw05_c needs the following items for the
          segment descriptor:

             1) SCLK limits of the segment.
             2) Instrument code.
             3) Reference frame.
             4) The angular velocity flag.

          ./

          begtim = SCLK [      0 ];
          endtim = SCLK [ nrec-1 ];

          inst   =  -41000;
          ref    =  "J2000";
          avflag =  SPICETRUE;

          segid  = "MEX spacecraft bus - data type 5";

          /.
          Write the segment.
          ./
          ckw05_c ( handle,  subtyp,  degree,  begtim,  endtim,  inst,
                    ref,     avflag,  segid,   n,       sclkdp,  packts,
                    rate,    nints,   starts                             );
                    .
                    .
                    .
          /.
          After all segments are written, close the C-kernel.
          ./
          ckcls_c ( handle );

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       K.R. Gehringer      (JPL)
       J.M. Lynch          (JPL)
       W.L. Taber          (JPL)

#### Version

       -CSPICE Version 2.0.1, 10-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard.

       -CSPICE Version 2.0.0, 01-JUN-2010 (NJB)

           The check for non-unit quaternions has been replaced
           with a check for zero-length quaternions. (The
           implementation of the check is located in ckw05_.)

       -CSPICE Version 1.0.2, 27-FEB-2008 (NJB)

           Updated header; added information about SPICE
           quaternion conventions.

       -CSPICE Version 1.0.1, 07-JAN-2005 (NJB)

           Description in -Detailed_Input header section of
           constraints on BEGTIM and ENDTIM was corrected

       -CSPICE Version 1.0.0, 30-AUG-2002 (NJB) (WLT) (KRG) (JML)

#### Index_Entries

       write CK type_5 data segment

#### Link to routine ckw05_c source file ckw05_c.c

    Fri Dec 31 18:41:02 2021