Index Page ckw03_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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

       void ckw03_c ( SpiceInt            handle,
                      SpiceDouble         begtim,
                      SpiceDouble         endtim,
                      SpiceInt            inst,
                      ConstSpiceChar    * ref,
                      SpiceBoolean        avflag,
                      ConstSpiceChar    * segid,
                      SpiceInt            nrec,
                      ConstSpiceDouble    sclkdp [],
                      ConstSpiceDouble    quats  [][4],
                      ConstSpiceDouble    avvs   [][3],
                      SpiceInt            nints,
                      ConstSpiceDouble    starts []    )

#### Abstract

       Add a type 3 segment to a C-kernel.

#### Required_Reading

       CK
       DAF
       SCLK

#### Keywords

       POINTING
       UTILITY

#### Brief_I/O

       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       handle     I   Handle of an open CK file.
       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   True if the segment will contain angular velocity.
       segid      I   Segment identifier.
       nrec       I   Number of pointing records.
       sclkdp     I   Encoded SCLK times.
       quats      I   Quaternions representing instrument pointing.
       avvs       I   Angular velocity vectors.
       nints      I   Number of intervals.
       starts     I   Encoded SCLK interval start times.

#### 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.

       begtim     is the beginning encoded SCLK time of the segment. This
                  value should be less than or equal to the first time in
                  the segment.

       endtim     is the encoded SCLK time at which the segment ends.
                  This value should be greater than or equal to the last
                  time in the segment.

       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.

       nrec       is the number of pointing instances in the segment.

       sclkdp     are the encoded spacecraft clock times associated with
                  each pointing instance. These times must be strictly
                  increasing.

       quats      is an array of SPICE-style quaternions representing a
                  sequence of C-matrices. See the discussion of "Quaternion
                  Styles" in the Particulars section below.

                  The C-matrix represented by the ith quaternion in
                  quats is a rotation matrix that transforms the
                  components of a vector expressed in the inertial
                  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
                  inertial frame, then V has components x', y', z' in
                  the instrument fixed frame where:

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

       avvs       are the angular velocity vectors ( optional ).

                  The ith vector in avvs gives the angular velocity of
                  the instrument fixed frame at time sclkdp[i]. The
                  components of the angular velocity vectors should
                  be given with respect to the inertial 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.

                  If avflag is FALSE then this array is ignored by the
                  routine; however it still must be supplied as part of
                  the calling sequence.

       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

       None.

#### Exceptions

       1)  If handle is not the handle of a C-kernel opened for writing
           the error will be diagnosed by routines called by this
           routine.

       2)  If segid is more than 40 characters long, the error
           SPICE(SEGIDTOOLONG) is signaled.

       3)  If segid contains any nonprintable characters, the error
           SPICE(NONPRINTABLECHARS) is signaled.

       4)  If the first encoded SCLK time is negative then the error
           SPICE(INVALIDSCLKTIME) is signaled. If any subsequent times
           are negative the error SPICE(TIMESOUTOFORDER) is signaled.

       5)  If the encoded SCLK times are not strictly increasing,
           the error SPICE(TIMESOUTOFORDER) is signaled.

       6)  If begtim is greater than sclkdp[0] or endtim is less than
           sclkdp[nrec-1], the error SPICE(INVALIDDESCRTIME) is
           signaled.

       7)  If the name of the reference frame is not one of those
           supported by the SPICELIB routine NAMFRM, the error
           SPICE(INVALIDREFFRAME) is signaled.

       8)  If nrec, the number of pointing records, is less than or
           equal to 0, the error SPICE(INVALIDNUMRECS) is signaled.

       9)  If nints, the number of interpolation intervals, is less than
           or equal to 0, the error SPICE(INVALIDNUMINTS) is signaled.

       10) If the encoded SCLK interval start times are not strictly
           increasing, the error SPICE(TIMESOUTOFORDER) is signaled.

       11)  If an interval start time does not coincide with a time for
            which there is an actual pointing instance in the segment,
            then the error SPICE(INVALIDSTARTTIME) is signaled.

       12)  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.

       14)  If the start time of the first interval and the time of the
            first pointing instance are not the same, the error
            SPICE(TIMESDONTMATCH) is signaled.

       15)  If any quaternion has magnitude zero, the error
            SPICE(ZEROQUATERNION) is signaled.

#### Files

       This routine adds a type 3 segment to a C-kernel.  The C-kernel
       may be either a new one or an existing one opened for writing.

#### Particulars

       For a detailed description of a type 3 CK segment please see the
       CK Required Reading.

       This routine relieves the user from performing the repetitive
       calls to the DAF routines necessary to construct a CK segment.

       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 3 C-kernel segment
       for the Mars Global Surveyor 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 ckw03_c must then decide how to partition these
          pointing instances into intervals over which linear
          interpolation between adjacent points is valid.
          ./
                     .
                     .
                     .

          /.
          The subroutine ckw03_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   =  -94000;
          ref    =  "j2000";
          avflag =  SPICETRUE;

          segid  = "MGS spacecraft bus - data type 3";

          /.
          Write the segment.
          ./
          ckw03_c ( handle,  begtim,  endtim,  inst,  ref,  avflag,
                    segid,   nrec,    sclkdp,  quats, avvs, nints,
                    starts                                         );
                    .
                    .
                    .
          /.
          After all segments are written, close the C-kernel.
          ./
          ckcls_c ( handle );

#### Restrictions

       1)  The creator of the segment is given the responsibility for
           determining whether it is reasonable to interpolate between
           two given pointing values.

       2)  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.

       3)  All pointing instances in the segment must belong to one and
           only one of the intervals.

#### Literature_References

       None.

#### Author_and_Institution

       K.R. Gehringer  (JPL)
       N.J. Bachman    (JPL)
       J.M. Lynch      (JPL)
       B.V. Semenov    (JPL)
       E.D. Wright     (JPL)

#### Version

       -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 ckw03_.)

       -CSPICE Version 1.4.2, 27-FEB-2008 (NJB)

          Updated header; added information about SPICE
          quaternion conventions.

       -CSPICE Version 1.4.1, 27-SEP-2005 (BVS)

           Added an item for SPICE(TIMESDONTMATCH) exception to the
           Exceptions section of the header.

       -CSPICE Version 1.3.1, 07-JAN-2004 (EDW)

           Trivial typo correction in index entries section.

       -CSPICE Version 1.3.0, 28-AUG-2001 (NJB)

           Changed prototype:  inputs  sclkdp, quats, avvs, and starts
           are now const-qualified.  Implemented interface macros for
           casting these inputs to const.

       -CSPICE Version 1.2.0, 02-SEP-1999 (NJB)

           Local type logical variable now used for angular velocity
           flag used in interface of ckw03_.

       -CSPICE Version 1.1.0, 08-FEB-1998 (NJB)

           References to C2F_CreateStr_Sig were removed; code was
           cleaned up accordingly.  String checks are now done using
           the macro CHKFSTR.

       -CSPICE Version 1.0.0, 25-OCT-1997 (NJB)

           Based on SPICELIB Version 2.0.0, 28-DEC-1993 (WLT)

#### Index_Entries

       write ck type_3 pointing data segment

#### Link to routine ckw03_c source file ckw03_c.c

    Wed Apr  5 17:54:30 2017