Index of Functions: A B C D E F G H I J K L M N O P Q R S T U V W X
Index Page ckw03_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
       ckw03_c ( C-Kernel, write segment to C-kernel, data type 3 )

       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   SPICETRUE 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 SPICEFALSE 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,
           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[0] or `endtim' is less than
           sclkdp[nrec-1], 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 CSPICE routine namfrm_c, 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 `ref' or `segid' input string pointers is null,
           the error SPICE(NULLPOINTER) is signaled.

       16) If any of the `ref' or `segid' input strings has zero length,
           the error SPICE(EMPTYSTRING) 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
       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) Create a CK type 3 segment; fill with data for a simple time
          dependent rotation and angular velocity.

          Example code begins here.

          /.
             Program ckw03_ex1
          ./
          #include "SpiceUsr.h"

          int main( )
          {

             /.
             Local parameters.
             ./
             #define CK3          "ckw03_ex1.bc"
             #define SPTICK       0.001
             #define INST         -77703
             #define MAXREC       201

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

             SpiceDouble          avvs   [MAXREC][3];
             SpiceDouble          begtim;
             SpiceDouble          endtim;
             SpiceDouble          quats  [MAXREC][4];
             SpiceDouble          rate;
             SpiceDouble          rwmat  [3][3];
             SpiceDouble          spaces;
             SpiceDouble          sclkdp [MAXREC];
             SpiceDouble          starts [MAXREC/2];
             SpiceDouble          sticks;
             SpiceDouble          theta;
             SpiceDouble          wmat   [3][3];
             SpiceDouble          wquat  [4];

             SpiceInt             handle;
             SpiceInt             i;
             SpiceInt             ncomch;
             SpiceInt             nints;

             SpiceBoolean         avflag;

             /.
             `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 3 CK segment";
             ifname = "Test CK type 3 segment created by ckw03_c";

             /.
             Open a new kernel.
             ./
             ckopn_c ( CK3, 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.
             ./
             sclkdp[0] = 1000.0;

             /.
             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.
                ./
                sclkdp[i] = 1000.0 + i * sticks;

                /.
                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] );

             }

             /.
             Create an array start times for the interpolation
             intervals. The end time for a particular interval is
             determined as the time of the final data value prior in
              time to the next start time.
             ./
             nints = MAXREC/2;
             for ( i = 0; i < nints; i++ )
             {

                starts[i] = sclkdp[i*2];

             }

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

             /.
             This segment contains angular velocity.
             ./
             avflag = SPICETRUE;

             /.
             All information ready to write. Write to a CK type 3
             segment to the file indicated by `handle'.
             ./
             ckw03_c ( handle, begtim, endtim, INST, ref,   avflag, segid,
                       MAXREC, sclkdp, quats,  avvs, nints, starts       );

             /.
             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
       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
       N.J. Bachman        (JPL)
       J. Diaz del Rio     (ODC Space)
       B.V. Semenov        (JPL)
       E.D. Wright         (JPL)
#### Version
       -CSPICE Version 2.0.1, 10-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard. Created
           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 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

    Fri Dec 31 18:41:02 2021