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   void ckw01_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]  )


   Add a type 1 segment to a C-kernel. 






   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. 


   handle     is the handle of the CK file to which the segment will 
              be written. The file must have been opened with write 
   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. 
   avflag     is a logical 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
   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 
   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.
   avvs       are the angular velocity vectors (optional). 
              If avflag is FALSE then this array is ignored by the 
              routine, however it still must be supplied as part of 
              the calling sequence. 


   None.  See Files section. 




   1)  If handle is not the handle of a C-kernel opened for writing 
       the error will be diagnosed by routines called by this 
   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 
   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 any quaternion has magnitude zero, the error
       SPICE(ZEROQUATERNION) is signaled.


   This routine adds a type 1 segment to a C-kernel.  The C-kernel 
   may be either a new one or an existing one opened for writing. 


   For a detailed description of a type 1 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,


   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

      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:

      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.


      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


   represents the matrix product



   This example writes a type 1 C-kernel segment for the 
   Galileo scan platform to a previously opened file attached to 
      Include CSPICE interface definitions.
      #include "SpiceUsr.h"
      Assume arrays of quaternions, angular velocities, and the 
      associated SCLK times are produced elsewhere. 
      The subroutine ckw01_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  = (SpiceChar *) sclk[0]; 
      endtim  = (SpiceChar *) sclk[nrec-1];
      inst    = -77001;
      ref     = "J2000";
      avflag  = SPICETRUE;
      segid   = "GLL SCAN PLT - DATA TYPE 1"; 
      Write the segment. 
      ckw01_c ( handle,  begtim,  endtim,  inst,  ref,  avflag, 
                segid,   nrec,    sclkdp,  quats, avvs         );
      After all segments are written, close the C-kernel.
      ckcls_c ( handle );






   K.R. Gehringer  (JPL) 
   N.J. Bachman    (JPL) 
   J.M. Lynch      (JPL) 


   -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 ckw01_.)

   -CSPICE Version 1.3.2, 27-FEB-2008 (NJB)

      Updated header; added information about SPICE 
      quaternion conventions.

   -CSPICE Version 1.3.1, 12-JUN-2006 (NJB)

      Corrected typo in example, the sclk indexes for the begtim
      and endtim assignments used FORTRAN convention.
   -CSPICE Version 1.3.0, 28-AUG-2001 (NJB)

      Changed prototype:  inputs sclkdp, quats, and avvs 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 ckw01_.
   -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)


   write ck type_1 pointing data segment 
Wed Apr  5 17:54:29 2017