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cspice_ckw03

Table of contents
Abstract
I/O
Parameters
Examples
Particulars
Exceptions
Files
Restrictions
Required_Reading
Literature_References
Author_and_Institution
Version
Index_Entries

Abstract


   CSPICE_CKW03 adds a type 3 segment to a C-kernel.

I/O


   Given:

      handle   file handle for an open CK file, returned from cspice_ckopn.

               [1,1] = size(handle); int32 = class(handle)

      begtim   encoded SCLK segment begin time.

               [1,1] = size(begtim); double = class(begtim)

      endtim   encoded SCLK segment end time.

               [1,1] = size(endtim); double = class(endtim)

      inst     NAIF instrument ID code.

               [1,1] = size(inst); int32 = class(inst)

      ref      name of the reference frame for the segment.

               [1,c1] = size(ref); char = class(ref)

                  or

               [1,1] = size(ref); cell = class(ref)

      avflag   a boolean signifying if the segment will contain
               angular velocity.

               [1,1] = size(avflag); logical = class(avflag)

      segid    name to identify the segment.

               [1,c2] = size(segid); char = class(segid)

                  or

               [1,1] = size(segid); cell = class(segid)

      sclkdp   array containing the encoded SCLK times for the data.

               [n,1] = size(sclkdp); double = class(sclkdp)

      quats    array of SPICE style quaternions representing instrument
               pointing.

               [4,n] = size(quats); double = class(quats)

      avvs     array of angular velocity vectors in units of radians per
               second.

               [3,n] = size(avvs); double = class(avvs)

      starts   array containing the encoded SCLK interval start times of
               each interpolation interval, the times must be strictly
               increasing and coincide with pointing data times.

               [m,1] = size(starts); double = class(starts)

   the call:

      cspice_ckw03( handle, ...
                    begtim, ...
                    endtim, ...
                    inst,   ...
                    ref,    ...
                    avflag, ...
                    segid,  ...
                    sclkdp, ...
                    quats,  ...
                    avvs,   ...
                    starts)

   returns:

      None.

Parameters


   None.

Examples


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

   1) The following example creates a CK file with a type-3 segment.

      Example code begins here.


      function ckw03_ex1()

         INST3      = -77703;
         NCOMCH     = 10;
         REF        = 'J2000';
         SEGID3     = 'Test type 3 test CK';
         SECPERTICK = 0.001;
         SPACING    = 10.0;
         MAXREC     = 50;

         %
         % Note, `sclkdp' is a vector input, not a vectorized scalar.
         %
         sclkdp    = [1:MAXREC]';
         sclkdp    = (sclkdp - 1)*SPACING;

         spinrate  = [1:MAXREC]*1.e-6;

         theta     = [0:MAXREC-1]*SPACING;
         theta     = theta .* spinrate;

         %
         % Create a zero-filled array for the angular velocity
         % vectors. This allocates the needed memory and
         % defines a variable of the correct shape.
         %
         expavvs = zeros( [3 MAXREC] );

         a1 = zeros( [1 MAXREC] );
         a2 = a1;

         r  = cspice_eul2m( theta, a2, a1, 3, 1 ,3 );
         q  = cspice_m2q( r );

         %
         % Fill the z component of the expavvs vectors with the
         % corresponding spinrate element scaled to SECPERTICK.
         %
         expavvs(3,:) = spinrate/SECPERTICK;

         begtim = sclkdp(1);
         endtim = sclkdp(MAXREC);
         avflag = 1;

         starts = [1:(MAXREC/2)]';
         starts = (starts-1)*2*SPACING;

         %
         % Open a new CK, write the data, catch any errors.
         %
         try
            handle = cspice_ckopn( 'ckw03_ex1.ck', 'ck', 0);
            cspice_ckw03( handle,  ...
                          begtim,  ...
                          endtim,  ...
                          INST3,   ...
                          REF,     ...
                          avflag,  ...
                          SEGID3,  ...
                          sclkdp,  ...
                          q,       ...
                          expavvs, ...
                          starts )
         catch

            error( [ 'Failure: ' lasterr] )
         end

         cspice_ckcls(handle)


      When this program is executed, no output is presented on
      screen. After run completion, a new CK file exists in the
      output directory.

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


   Mice routine interfaces ALWAYS use SPICE quaternions.
   Quaternions of any other style must be converted to SPICE
   quaternions before they are passed to Mice routines.


   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 Mice routines

      cspice_q2m {quaternion to matrix}
      cspice_m2q {matrix to quaternion}

   cspice_m2q 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

Exceptions


   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 `segid' is more than 40 characters long, the error
       SPICE(SEGIDTOOLONG) is signaled by a routine in the call tree
       of this routine.

   3)  If `segid' contains any non-printable 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.

   5)  If the second encoded SCLK or any subsequent times, or 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 `begtim' is greater than sclkdp(1) or `endtim' is less than
       sclkdp(nrec), where `nrec' is the number of pointing records,
       the error SPICE(INVALIDDESCRTIME) is signaled by a routine in
       the call tree of this routine.

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

   8)  If `nrec', the number of pointing records, is less than or
       equal to 0, the error SPICE(INVALIDNUMREC) is signaled by a
       routine in the call tree of this routine.

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

   10) 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.

   11) 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.

   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.

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

   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 by a routine in the call
       tree of this routine.

   15) If any of the input arguments, `handle', `begtim', `endtim',
       `inst', `ref', `avflag', `segid', `sclkdp', `quats', `avvs' or
       `starts', is undefined, an error is signaled by the Matlab
       error handling system.

   16) If any of the input arguments, `handle', `begtim', `endtim',
       `inst', `ref', `avflag', `segid', `sclkdp', `quats', `avvs' or
       `starts', is not of the expected type, or it does not have the
       expected dimensions and size, an error is signaled by the Mice
       interface.

   17) If the input vector arguments `sclkdp', `quats' and `avvs' do
       not have the same dimension (N), an error is signaled by the
       Mice interface.

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.

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.

Required_Reading


   MICE.REQ
   CK.REQ
   DAF.REQ
   SCLK.REQ

Literature_References


   None.

Author_and_Institution


   J. Diaz del Rio     (ODC Space)
   E.D. Wright         (JPL)

Version


   -Mice Version 1.1.0, 25-AUG-2021 (EDW) (JDR)

       Changed input argument names "begtime" and "endtime" to "begtim"
       and "endtim".

       Edited the header to comply with NAIF standard. Added example's
       problem statement.

       Added -Parameters, -Particulars, -Exceptions, -Files, -Restrictions,
       -Literature_References and -Author_and_Institution sections.

       Eliminated use of "lasterror" in rethrow.

       Removed reference to the function's corresponding CSPICE header from
       -Required_Reading section.

   -Mice Version 1.0.2, 29-OCT-2014 (EDW)

       Edited -I/O section to conform to NAIF standard for Mice
       documentation.

   -Mice Version 1.0.1, 11-JUL-2012 (EDW)

       Edited -I/O section to conform to NAIF standard for Mice
       documentation.

   -Mice Version 1.0.0, 19-MAY-2006 (EDW)

Index_Entries


   write CK type_3 pointing data segment


Fri Dec 31 18:44:23 2021