ckw02_c |

Table of contents## Procedureckw02_c ( C-Kernel, write segment to C-kernel, data type 2 ) void ckw02_c ( SpiceInt handle, SpiceDouble begtim, SpiceDouble endtim, SpiceInt inst, ConstSpiceChar * ref, ConstSpiceChar * segid, SpiceInt nrec, ConstSpiceDouble start [], ConstSpiceDouble stop [], ConstSpiceDouble quats [][4], ConstSpiceDouble avvs [][3], ConstSpiceDouble rates [] ) ## AbstractWrite a type 2 segment to a C-kernel. ## Required_ReadingCK DAF SCLK ## KeywordsPOINTING UTILITY ## Brief_I/OVARIABLE 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. segid I Segment identifier. nrec I Number of pointing records. start I Encoded SCLK interval start times. stop I Encoded SCLK interval stop times. quats I Quaternions representing instrument pointing. avvs I Angular velocity vectors. rates I Number of seconds per tick for each interval. ## 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. begtim is the beginning encoded SCLK time of the segment. This value should be less than or equal to the first START 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 STOP time in the segment. inst is the NAIF integer ID code for the instrument. ref is a character string that 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. segid is the segment identifier. A CK segment identifier may contain up to 40 characters. nrec is the number of pointing intervals that will be written to the segment. start are the start times of each interval in encoded spacecraft clock. These times must be strictly increasing. stop are the stop times of each interval in encoded spacecraft clock. These times must be greater than the START times that they correspond to but less than or equal to the START time of the next interval. quats are the quaternions representing the C-matrices associated with the start times of each interval. See the discussion of "Quaternion Styles" in the -Particulars section below. avvs are the angular velocity vectors for each interval. rates are the number of seconds per encoded spacecraft clock tick for each interval. In most applications this value will be the same for each interval within a segment. For example, when constructing a predict C-kernel for Mars Observer, the rate would be 1/256 for each interval since this is the smallest time unit expressible by the MO clock. The nominal seconds per tick rates for Galileo and Voyager are 1/120 and 0.06 respectively. ## Detailed_OutputNone. See -Files section. ## ParametersNone. ## Exceptions1) 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 nonprintable characters, the error SPICE(NONPRINTABLECHARS) is signaled by a routine in the call tree of this routine. 4) If the first `start' time is negative, the error SPICE(INVALIDSCLKTIME) is signaled by a routine in the call tree of this routine. 5) If the second or any subsequent `start' times are negative, the error SPICE(TIMESOUTOFORDER) is signaled by a routine in the call tree of this routine. 6) If any of the `stop' times are negative, the error SPICE(DEGENERATEINTERVAL) is signaled by a routine in the call tree of this routine. 7) If the `stop' time of any of the intervals is less than or equal to the `start' time, the error SPICE(DEGENERATEINTERVAL) is signaled by a routine in the call tree of this routine. 8) If the `start' times are not strictly increasing, the error SPICE(TIMESOUTOFORDER) is signaled by a routine in the call tree of this routine. 9) If the `stop' time of one interval is greater than the `start' time of the next interval, the error SPICE(BADSTOPTIME) is signaled by a routine in the call tree of this routine. 10) If `begtim' is greater than start[0] or `endtim' is less than stop[nrec-1], the error SPICE(INVALIDDESCRTIME) is signaled by a routine in the call tree of this routine. 11) If the name of the reference frame is not one of those supported by the routine namfrm_c, the error SPICE(INVALIDREFFRAME) is signaled by a routine in the call tree of this routine. 12) If `nrec', the number of pointing records, is less than or equal to 0, the error SPICE(INVALIDNUMRECS) is signaled by a routine in the call tree of this routine. 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 any of the `ref' or `segid' input string pointers is null, the error SPICE(NULLPOINTER) is signaled. 15) If any of the `ref' or `segid' input strings has zero length, the error SPICE(EMPTYSTRING) is signaled. ## FilesThis routine adds a type 2 segment to a C-kernel. The C-kernel may be either a new one or an existing one opened for writing. ## ParticularsFor a detailed description of a type 2 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 ## ExamplesThe 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) The following example creates a CK file with a type-2 segment, with data for a simple time dependent rotation and angular velocity. Example code begins here. /. Program ckw02_ex1 ./ #include "SpiceUsr.h" int main( ) { /. Local parameters. ./ #define CK2 "ckw02_ex1.bc" #define SPTICK 0.001 #define INST -77702 #define MAXREC 21 /. Local variables. ./ SpiceChar * ref; SpiceChar * ifname; SpiceChar * segid; SpiceDouble avvs [MAXREC][3]; SpiceDouble begtim; SpiceDouble endtim; SpiceDouble quats [MAXREC][4]; SpiceDouble rate; SpiceDouble rates [MAXREC]; SpiceDouble rwmat [3][3]; SpiceDouble spaces; SpiceDouble starts [MAXREC]; SpiceDouble stops [MAXREC]; SpiceDouble sticks; SpiceDouble theta; SpiceDouble wmat [3][3]; SpiceDouble wquat [4]; SpiceInt handle; SpiceInt i; SpiceInt ncomch; /. `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 2 CK segment"; ifname = "Test CK type 2 segment created by ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) ## Version-CSPICE Version 2.0.1, 10-AUG-2021 (JDR) Edited the header to comply with NAIF standard. Added 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 ckw02_.) -CSPICE Version 1.2.1, 27-FEB-2008 (NJB) Updated header; added information about SPICE quaternion conventions. -CSPICE Version 1.2.0, 28-AUG-2001 (NJB) Changed prototype: inputs start, stop, sclkdp, quats, and avvs are now const-qualified. Implemented interface macros for casting these inputs to const. -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_Entrieswrite CK type_2 pointing data segment |

Fri Dec 31 18:41:02 2021