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Index Page ckw02_c
Table of contents
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
       ckw02_c ( C-Kernel, write segment to C-kernel, data type 2 )

       void ckw02_c ( SpiceInt            handle,
                      SpiceDouble         begtim,
                      SpiceDouble         endtim,
                      SpiceInt            inst,
                      ConstSpiceChar    * ref,
                      ConstSpiceChar    * segid,
                      SpiceInt            nrec,
                      ConstSpiceDouble    start  [],
                      ConstSpiceDouble    stop   [],
                      ConstSpiceDouble    quats  [][4],
                      ConstSpiceDouble    avvs   [][3],
                      ConstSpiceDouble    rates  []    )
#### Abstract
       Write a type 2 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.
       segid      I   Segment identifier.
       nrec       I   Number of pointing records.
       start      I   Encoded SCLK interval start times.
       stop       I   Encoded SCLK interval stop times.
       quats      I   Quaternions representing instrument pointing.
       avvs       I   Angular velocity vectors.
       rates      I   Number of seconds per tick for each interval.
#### 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 START
                   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
                   STOP time in the segment.

       inst        is the NAIF integer ID code for the instrument.

       ref         is a character string that 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.

       segid       is the segment identifier.  A CK segment identifier may
                   contain up to 40 characters.

       nrec        is the number of pointing intervals that will be
                   written to the segment.

       start       are the start times of each interval in encoded
                   spacecraft clock. These times must be strictly
                   increasing.

       stop        are the stop times of each interval in encoded
                   spacecraft clock. These times must be greater than
                   the START times that they correspond to but less
                   than or equal to the START time of the next interval.

       quats       are the quaternions representing the C-matrices
                   associated with the start times of each interval. See the
                   discussion of "Quaternion Styles" in the -Particulars
                   section below.

       avvs        are the angular velocity vectors for each interval.

       rates       are the number of seconds per encoded spacecraft clock
                   tick for each interval.

                   In most applications this value will be the same for
                   each interval within a segment. For example, when
                   constructing a predict C-kernel for Mars Observer, the
                   rate would be 1/256 for each interval since this is
                   the smallest time unit expressible by the MO clock. The
                   nominal seconds per tick rates for Galileo and Voyager
                   are 1/120 and 0.06 respectively.
#### Detailed_Output
       None. See -Files section.
#### Parameters
       None.
#### 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 nonprintable characters, the error
           SPICE(NONPRINTABLECHARS) is signaled by a routine in the call
           tree of this routine.

       4)  If the first `start' time is negative, the error
           SPICE(INVALIDSCLKTIME) is signaled by a routine in the call
           tree of this routine.

       5)  If the second or any subsequent `start' times are negative, the
           error SPICE(TIMESOUTOFORDER) is signaled by a routine in the
           call tree of this routine.

       6)  If any of the `stop' times are negative, the error
           SPICE(DEGENERATEINTERVAL) is signaled by a routine in the call
           tree of this routine.

       7)  If the `stop' time of any of the intervals is less than or equal
           to the `start' time, the error SPICE(DEGENERATEINTERVAL) is
           signaled by a routine in the call tree of this routine.

       8)  If the `start' times are not strictly increasing, the error
           SPICE(TIMESOUTOFORDER) is signaled by a routine in the call
           tree of this routine.

       9)  If the `stop' time of one interval is greater than the `start'
           time of the next interval, the error SPICE(BADSTOPTIME)
           is signaled by a routine in the call tree of this routine.

       10) If `begtim' is greater than start[0] or `endtim' is less than
           stop[nrec-1], the error SPICE(INVALIDDESCRTIME) is
           signaled by a routine in the call tree of this routine.

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

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

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

       15) If any of the `ref' or `segid' input strings has zero length,
           the error SPICE(EMPTYSTRING) is signaled.
#### Files
       This routine adds a type 2 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 2 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
       The numerical results shown for this example may differ across
       platforms. The results depend on the SPICE kernels used as
       input, the compiler and supporting libraries, and the machine
       specific arithmetic implementation.

       1) The following example creates a CK file with a type-2 segment,
          with data for a simple time dependent rotation and angular
          velocity.

          Example code begins here.

          /.
             Program ckw02_ex1
          ./
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters.
             ./
             #define CK2          "ckw02_ex1.bc"
             #define SPTICK       0.001
             #define INST         -77702
             #define MAXREC       21

             /.
             Local variables.
             ./
             SpiceChar          * ref;
             SpiceChar          * ifname;
             SpiceChar          * segid;

             SpiceDouble          avvs   [MAXREC][3];
             SpiceDouble          begtim;
             SpiceDouble          endtim;
             SpiceDouble          quats  [MAXREC][4];
             SpiceDouble          rate;
             SpiceDouble          rates  [MAXREC];
             SpiceDouble          rwmat  [3][3];
             SpiceDouble          spaces;
             SpiceDouble          starts [MAXREC];
             SpiceDouble          stops  [MAXREC];
             SpiceDouble          sticks;
             SpiceDouble          theta;
             SpiceDouble          wmat   [3][3];
             SpiceDouble          wquat  [4];

             SpiceInt             handle;
             SpiceInt             i;
             SpiceInt             ncomch;

             /.
             `ncomch' is the number of characters to reserve for the
             kernel's comment area. This example doesn't write
             comments, so set to zero.
             ./
             ncomch = 0;

             /.
             The base reference from for the rotation data.
             ./
             ref = "J2000";

             /.
             Time spacing in encoded ticks and in seconds
             ./
             sticks = 10.0;
             spaces = sticks * SPTICK;

             /.
             Declare an angular rate in radians per sec.
             ./
             rate = 1.e-2;

             /.
             Internal file name and segment ID.
             ./
             segid  = "Test type 2 CK segment";
             ifname = "Test CK type 2 segment created by ckw02_c";

             /.
             Open a new kernel.
             ./
             ckopn_c ( CK2, ifname, ncomch, &handle );

             /.
             Create a 3x3 double precision identity matrix.
             ./
             ident_c ( wmat );

             /.
             Convert the matrix to quaternion.
             ./
             m2q_c ( wmat, wquat );

             /.
             Copy the work quaternion to the first row of
             `quats'.
             ./
             moved_c ( wquat, 4, quats[0] );

             /.
             Create an angular velocity vector. This vector is in the
             `ref' reference frame and indicates a constant rotation
             about the Z axis.
             ./
             vpack_c ( 0.0, 0.0, rate, avvs[0] );

             /.
             Set the initial value of the encoded ticks. The interval
             associated with each quaternion will start at the epoch
             of the quaternion and will extend 0.8 * sticks forward in
             time, leaving small gaps between the intervals.

             The clock rates array will have a constant SPTICK value.
             ./
             starts[0] = 1000.0;
             stops[0]  = starts[0] + ( 0.8 * sticks );
             rates[0]  = SPTICK;

             /.
             Fill the rest of the `avvs' and `quats' matrices
             with simple data.
             ./
             for ( i = 1; i < MAXREC; i++ )
             {

                /.
                Create the corresponding encoded tick value in
                increments of `sticks' with an initial value of
                1000.0 ticks.
                ./
                starts[i] = 1000.0 + i * sticks;
                stops[i]  = starts[i] + ( 0.8 * sticks );
                rates[i]  = SPTICK;

                /.
                Create the transformation matrix for a rotation of
                `theta' about the Z axis. Calculate `theta' from the
                constant angular rate `rate' at increments of `spaces'.
                ./
                theta = i * rate * spaces;
                rotmat_c ( wmat, theta, 3, rwmat );

                /.
                Convert the `rwmat' matrix to SPICE type quaternion.
                ./
                m2q_c ( rwmat, wquat );

                /.
                Store the quaternion in the `quats' matrix.
                Store angular velocity in `avvs'.
                ./
                moved_c ( wquat, 4, quats[i] );
                vpack_c ( 0.0, 0.0, rate, avvs[i] );

             }

             /.
             Set the segment boundaries equal to the first and last
             time for the data arrays.
             ./
             begtim = starts[0];
             endtim = stops[MAXREC-1];

             /.
             All information ready to write. Write to a CK type 2
             segment to the file indicated by `handle'.
             ./
             ckw02_c ( handle, begtim, endtim, INST,  ref,  segid,
                       MAXREC, starts, stops,  quats, avvs, rates );

             /.
             SAFELY close the file.
             ./
             ckcls_c ( handle );

             return ( 0 );
          }

          When this program is executed, no output is presented on
          screen. After run completion, a new CK file exists in the
          output directory.
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
#### Version
       -CSPICE Version 2.0.1, 10-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard. Added complete
           code example from existing fragment.

       -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 ckw02_.)

       -CSPICE Version 1.2.1, 27-FEB-2008 (NJB)

           Updated header; added information about SPICE
           quaternion conventions.

       -CSPICE Version 1.2.0, 28-AUG-2001 (NJB)

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

       -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_2 pointing data segment
#### Link to routine ckw02_c source file ckw02_c.c

    Fri Dec 31 18:41:02 2021