Index Page ckw01_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 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]  )
#### Abstract
       Add a type 1 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.
#### 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.

       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
                  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.

       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.
#### 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 any quaternion has magnitude zero, the error
           SPICE(ZEROQUATERNION) is signaled.
#### Files
       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.
#### Particulars
       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,

          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 writes a type 1 C-kernel segment for the
       Galileo scan platform to a previously opened 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 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 );
#### Restrictions
       None.
#### Literature_References
       None.
#### Author_and_Institution
       K.R. Gehringer  (JPL)
       N.J. Bachman    (JPL)
       J.M. Lynch      (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 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)
#### Index_Entries
       write ck type_1 pointing data segment
#### Link to routine ckw01_c source file ckw01_c.c

    Wed Jun  9 13:05:19 2010