void ckw05_c ( SpiceInt handle,
SpiceCK05Subtype subtyp,
SpiceInt degree,
SpiceDouble begtim,
SpiceDouble endtim,
SpiceInt inst,
ConstSpiceChar * ref,
SpiceBoolean avflag,
ConstSpiceChar * segid,
SpiceInt n,
ConstSpiceDouble sclkdp [],
const void * packts,
SpiceDouble rate,
SpiceInt nints,
ConstSpiceDouble starts [] )
Write a type 5 segment to a CK file.
CK
NAIF_IDS
ROTATION
TIME
POINTING
FILES
Variable I/O Description
-------- --- --------------------------------------------------
handle I Handle of an open CK file.
subtyp I CK type 5 subtype code.
degree I Degree of interpolating polynomials.
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.
n I Number of packets.
sclkdp I Encoded SCLK times.
packts I Array of packets.
rate I Nominal SCLK rate in seconds per tick.
nints I Number of intervals.
starts I Encoded SCLK interval start times.
MAXDEG P Maximum allowed degree of interpolating polynomial.
handle is the handle of the CK file to which the segment will be
written. The file must have been opened with write
access.
subtyp is an integer code indicating the subtype of the
segment to be created.
degree is the degree of the polynomials used to interpolate the
quaternions contained in the input packets. All
components of the quaternions are interpolated by
polynomials of fixed degree.
begtim,
endtim are the beginning and ending encoded SCLK times
for which the segment provides pointing information.
begtim must be less than or equal to endtim, and at least
one data packet must have a time tag t such that
begtim < t < endtim
- -
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.
packts contains a time-ordered array of data packets
representing the orientation of inst relative to the
frame ref. Each packet contains a SPICE-style quaternion
and optionally, depending on the segment subtype,
attitude derivative data, from which a C-matrix and an
angular velocity vector may be derived.
See the discussion of "Quaternion Styles" in the
Particulars section below.
The C-matrix represented by the Ith data packet is a
rotation matrix that transforms the components of a
vector expressed in the base 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 base
frame, then v has components x', y', z' in the instrument
fixed frame where:
[ x' ] [ ] [ x ]
| y' | = | cmat | | y |
[ z' ] [ ] [ z ]
The attitude derivative information in packts[i] gives
the angular velocity of the instrument fixed frame at
time sclkdp[i] with respect to the 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.
Packet contents and the corresponding interpolation
methods depend on the segment subtype, and are as
follows:
Subtype 0: Hermite interpolation, 8-element packets.
Quaternion and quaternion derivatives
only, no angular velocity vector provided.
Quaternion elements are listed first,
followed by derivatives. Angular velocity
is derived from the quaternions and
quaternion derivatives.
Subtype 1: Lagrange interpolation, 4-element packets.
Quaternion only. Angular velocity is
derived by differentiating the
interpolating polynomials.
Subtype 2: Hermite interpolation, 14-element packets.
Quaternion and angular angular velocity
vector, as well as derivatives of each,
are provided. The quaternion comes first,
then quaternion derivatives, then angular
velocity and its derivatives.
Subtype 3: Lagrange interpolation, 7-element packets.
Quaternion and angular velocity vector
provided. The quaternion comes first.
Angular velocity is always specified relative to the base
frame.
rate is the nominal rate of the spacecraft clock associated
with inst. Units are seconds per tick. rate is used to
scale angular velocity to radians/second.
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.
None. See Files section.
MAXDEG is the maximum allowed degree of the interpolating
polynomial. If the value of MAXDEG is increased, the
CSPICE routine ckpfs_ must be changed accordingly. In
particular, the size of the record passed to ckrNN_ and
ckeNN_ must be increased, and comments describing the
record size must be changed.
If any of the following exceptions occur, this routine will return
without creating a new segment.
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 the last non-blank character of segid occurs past index 40,
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 will be detected in exception (5).
5) If the encoded SCLK times are not strictly increasing,
the error SPICE(TIMESOUTOFORDER) is signaled.
6) If the name of the reference frame is not one of those
supported by the routine framex_, the error
SPICE(INVALIDREFFRAME) is signaled.
7) If the number of packets n is not at least 1, the error
SPICE(TOOFEWPACKETS) will be signaled.
8) If nints, the number of interpolation intervals, is less than
or equal to 0, the error SPICE(INVALIDNUMINTS) is signaled.
9) If the encoded SCLK interval start times are not strictly
increasing, the error SPICE(TIMESOUTOFORDER) is signaled.
10) If an interval start time does not coincide with a time for
which there is an actual pointing instance in the segment,
then the error SPICE(INVALIDSTARTTIME) is signaled.
11) 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.
12) If any quaternion is the zero vector, the error
SPICE(ZEROQUATERNION) is signaled.
13) If the interpolation window size implied by degree is not
even, the error SPICE(INVALIDDEGREE) is signaled. The window
size is degree+1 for Lagrange subtypes and is (degree+1)/2
for Hermite subtypes.
14) If an unrecognized subtype code is supplied, the error
SPICE(NOTSUPPORTED) is signaled.
15) If degree is not at least 1 or is greater than MAXDEG, the
error SPICE(INVALIDDEGREE) is signaled.
16) If the segment descriptor bounds are out of order, the
error SPICE(BADDESCRTIMES) is signaled.
17) If there is no element of SCLKDP that lies between BEGTIM and
ENDTIM inclusive, the error SPICE(EMPTYSEGMENT) is signaled.
18) If RATE is zero, the error SPICE(INVALIDVALUE) is signaled.
18) If either the input frame or segment ID have null string
pointers, the error SPICE(NULLPOINTER) is signaled.
19) If either the input frame or segment ID are zero-length
strings, the error SPICE(EMPTYSTRING) is signaled.
A new type 5 CK segment is written to the CK file attached
to handle.
This routine writes a CK type 5 data segment to the open CK
file according to the format described in the type 5 section of
the CK Required Reading. The CK file must have been opened with
write access.
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 code fragment writes a type 5 C-kernel segment
for the Mars Express spacecraft bus to a previously opened CK
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 software
that calls ckw05_c must then decide how to partition these
pointing instances into intervals over which linear
interpolation between adjacent points is valid.
./
.
.
.
/.
The subroutine ckw05_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 = sclk [ 0 ];
endtim = sclk [ nrec-1 ];
inst = -41000;
ref = "J2000";
avflag = SPICETRUE;
segid = "MEX spacecraft bus - data type 5";
/.
Write the segment.
./
ckw05_c ( handle, subtyp, degree, begtim, endtim, inst,
ref, avflag, segid, n, sclkdp, packts,
rate, nints, starts );
.
.
.
/.
After all segments are written, close the C-kernel.
./
ckcls_c ( handle );
None.
None.
N.J. Bachman (JPL)
W.L. Taber (JPL)
K.R. Gehringer (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 ckw05_.)
-CSPICE Version 1.0.2, 27-FEB-2008 (NJB)
Updated header; added information about SPICE
quaternion conventions.
-CSPICE Version 1.0.1, 07-JAN-2005 (NJB)
Description in Detailed_Input header section of
constraints on BEGTIM and ENDTIM was corrected
-CSPICE Version 1.0.0, 30-AUG-2002 (NJB) (WLT) (KRG) (JML)
write ck type_5 data segment
Link to routine ckw05_c source file ckw05_c.c
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