ckw05_c |

Table of contents## Procedureckw05_c ( Write CK segment, type 5 ) 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 [] ) ## AbstractWrite a type 5 segment to a CK file. ## Required_ReadingCK NAIF_IDS ROTATION TIME ## KeywordsFILES POINTING ## Brief_I/OVARIABLE 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 SPICETRUE 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. ## Detailed_Inputhandle 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. ## Detailed_OutputNone. See -Files section. ## ParametersMAXDEG 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. ## ExceptionsIf 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, an error is signaled by a routine in the call tree of this routine. 2) If the last non-blank character of `segid' occurs past index 40, 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 encoded SCLK time is negative, the error SPICE(INVALIDSCLKTIME) is signaled by a routine in the call tree of this routine. 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 by a routine in the call tree of this routine. 6) If the name of the reference frame is not one of those supported by the routine FRAMEX, the error SPICE(INVALIDREFFRAME) is signaled by a routine in the call tree of this routine. 7) If the number of packets `n' is not at least 1, the error SPICE(TOOFEWPACKETS) is signaled by a routine in the call tree of this routine. 8) If `nints', the number of interpolation intervals, is less than or equal to 0, the error SPICE(INVALIDNUMINTS) is signaled by a routine in the call tree of this routine. 9) 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. 10) 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. 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 has magnitude zero, the error SPICE(ZEROQUATERNION) is signaled by a routine in the call tree of this routine. 13) If the interpolation window size implied by `degree' is not even, the error SPICE(INVALIDDEGREE) is signaled by a routine in the call tree of this routine. 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 by a routine in the call tree of this routine. 15) If `degree' is not at least 1 or is greater than MAXDEG, the error SPICE(INVALIDDEGREE) is signaled by a routine in the call tree of this routine. 16) If the segment descriptor bounds are out of order, the error SPICE(BADDESCRTIMES) is signaled by a routine in the call tree of this routine. 17) If there is no element of `sclkdp' that lies between `begtim' and `endtim' inclusive, the error SPICE(EMPTYSEGMENT) is signaled by a routine in the call tree of this routine. 18) If `rate' is zero, the error SPICE(INVALIDVALUE) is signaled by a routine in the call tree of this routine. 19) If any of the `ref' or `segid' input string pointers is null, the error SPICE(NULLPOINTER) is signaled. 20) If any of the `ref' or `segid' input strings has zero length, the error SPICE(EMPTYSTRING) is signaled. ## FilesA new type 5 CK segment is written to the CK file attached to handle. ## ParticularsThis 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 ## ExamplesThis 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 ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) K.R. Gehringer (JPL) J.M. Lynch (JPL) W.L. Taber (JPL) ## Version-CSPICE Version 2.0.1, 10-AUG-2021 (JDR) Edited the header to comply with NAIF standard. -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) ## Index_Entrieswrite CK type_5 data segment |

Fri Dec 31 18:41:02 2021