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.
CK
DAF
SCLK
POINTING
UTILITY
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
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.
None. See Files section.
None.
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.
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,
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
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 );
None.
None.
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
Link to routine ckw01_c source file ckw01_c.c
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