Index Page pxfrm2_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 pxfrm2_c ( ConstSpiceChar   * from,
                       ConstSpiceChar   * to,
                       SpiceDouble        etfrom,
                       SpiceDouble        etto,
                       SpiceDouble        rotate[3][3]     )

#### Abstract

       Return the 3x3 matrix that transforms position vectors from one
       specified frame at a specified epoch to another specified
       frame at another specified epoch.

#### Required_Reading

       FRAMES

#### Keywords

       FRAMES
       TRANSFORM

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       from       I   Name of the frame to transform from.
       to         I   Name of the frame to transform to.
       etfrom     I   Evaluation time of `from' frame.
       etto       I   Evaluation time of `to' frame.
       rotate     O   A position transformation matrix from
                      frame `from' to frame `to'.

#### Detailed_Input

       from       is the name of a reference frame recognized by
                  cspice that corresponds to the input `etfrom'.

       to         is the name of a reference frame recognized by
                  cspice that corresponds to the desired output
                  at `etto'.

       etfrom     is the epoch in ephemeris seconds past the epoch
                  of J2000 (TDB) corresponding to the `from' reference
                  frame.

       etto       is the epoch in ephemeris seconds past the epoch
                  of J2000 (TDB) that corresponds to the `to' reference
                  frame.

#### Detailed_Output

       rotate     is the transformation matrix that relates the reference
                  frame `from' at epoch `etfrom' to the frame `to' at epoch
                  `etto'.

                  If (x, y, z) is a position relative to the reference
                  frame `from' at time `etfrom' then the vector ( x', y',
                  z') is the same position relative to the frame `to' at
                  epoch `etto'. Here the vector ( x', y', z' ) is defined
                  by the equation:

                     -   -       -        -     -  -
                    | x'  |     |          |   | x  |
                    | y'  |  =  |  rotate  |   | y  |
                    | z'  |     |          |   | z  |
                     -   -       -        -     -  -

#### Parameters

       None.

#### Exceptions

       1)  If sufficient information has not been supplied via loaded
           SPICE kernels to compute the transformation between the
           two frames, the error will be diagnosed by a routine
           in the call tree to this routine.

       2)  If either frame `from' or `to' is not recognized the error
           'SPICE(UNKNOWNFRAME)' will be signaled.

#### Files

       Appropriate kernels must be loaded by the calling program before
       this routine is called.  Kernels that may be required include
       SPK files, PCK files, frame kernels, C-kernels, and SCLK kernels.

       Such kernel data are normally loaded once per program
       run, NOT every time this routine is called.

#### Particulars

       The routine `pxfrm2_c' is most commonly used to transform a
       position between time-dependant reference frames.

       For more examples of where to use `pxfrm2_c', please see:

             sincpt_c
             surfpt_c
             subslr_c
             ilumin_c

#### Examples

          The numerical results shown for these examples 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) Suppose that MGS has taken a picture of Mars at time `etrec' with
             the MOC narrow angle camera. We want to know the latitude and
             longitude associated with two pixels projected to Mars'
             surface: the boresight and one along the boundary of the
             field of view (FOV). Due to light time, the photons taken in
             the picture left Mars at time `etemit', when Mars was at a
             different state than at time `etrec'.

             In order to solve this problem, we could use the `sincpt_c'
             routine for both pixels, but this would be slow.  Instead, we
             will assume that the light time for each pixel is the same. We
             will call `sincpt_c' once to get the light time and surface point
             associated with the boresight. Then, we will rotate one of the
             FOV boundary vectors from the camera frame at `etrec' to the
             body-fixed Mars frame at `etemit', and call the faster routine
             `surfpt_c' to retrieve the surface point for one of the FOV
             boundary vectors.

             This example problem could be extended to find the latitude
             and longitude associated with every pixel in an instrument's
             field of view, but this example is simplified to only solve
             for two pixels:  the boresight and one along the boundary of
             the field of view.

             Assumptions:

                1)  The light times from the surface points in the camera's
                    field of view to the camera are equal.

                2)  The camera offset from the center of gravity of the
                    spacecraft is zero. If the data are more accurate
                    and precise, this assumption can be easily discarded.

                3)  An ellipsoid shape model for the target body is
                    sufficient.

                4)  The boundary field of view vector returned from `getfov_c'
                    is associated with a boundary field of view pixel. If
                    this example were extended to include a geometric camera
                    model, this assumption would not be needed since the
                    direction vectors associated with each pixel would be
                    calculated from the geometric camera model.

             Use the meta-kernel shown below to load the required SPICE
             kernels.

                KPL/MK

                File name: mgs_ex.tm

                This is the meta-kernel file for the example problem for
                the subroutine PXFRM2. These kernel files can be found in
                the NAIF archives.

                In order for an application to use this meta-kernel, the
                kernels referenced here must be present in the user's
                current working directory.

                The names and contents of the kernels referenced
                by this meta-kernel are as follows:

                   File name                     Contents
                   ---------                     --------
                   de421.bsp                     Planetary ephemeris
                   pck00009.tpc                  Planet orientation and
                                                 radii
                   naif0009.tls                  Leapseconds
                   mgs_ext12_ipng_mgs95j.bsp     MGS ephemeris
                   mgs_moc_v20.ti                MGS MOC instrument
                                                 parameters
                   mgs_sclkscet_00061.tsc        MGS SCLK coefficients
                   mgs_sc_ext12.bc               MGS s/c bus attitude

                \begindata

                KERNELS_TO_LOAD = ( 'de421.bsp',
                                    'pck00009.tpc',
                                    'naif0009.tls',
                                    'mgs_ext12_ipng_mgs95j.bsp',
                                    'mgs_moc_v20.ti',
                                    'mgs_sclkscet_00061.tsc',
                                    'mgs_sc_ext12.bc' )

                \begintext

                End of meta-kernel.

          Example code begins here.

                #include <stdio.h>
                #include <math.h>
                #include "SpiceUsr.h"

                int main()
                {
                    /.
                     Constants

                     ABCORR is the desired light time and stellar
                     aberration correction setting.

                     METAKR is the name of the meta-kernel.
                    ./

                     #define ABCORR "CN+S"
                     #define METAKR "mgs_ex.tm"
                     #define FRMNLN 32
                     #define NCORNR 4
                     #define SHPLEN 80

                     /.
                     Local variables
                     ./
                     SpiceBoolean            found;

                     /.
                     MGS_MOC_NA is the name of the camera that took
                     the picture being analyzed.
                     ./
                     SpiceChar              *camera  = "MGS_MOC_NA";

                     /.
                     The variable `obsref' is the observer reference frame
                     on MGS.
                     ./
                     SpiceChar               obsref [FRMNLN] ;
                     SpiceChar               shape  [SHPLEN] ;

                     SpiceDouble             bounds [NCORNR][3];
                     SpiceDouble             bndvec [3];
                     SpiceDouble             bsight [3];
                     SpiceDouble             dist;

                     /.
                     The variable `etemit' is the time at which the photons were
                     emitted from Mars, and `etrec' is the time at
                     which the picture was taken by MGS.
                     ./
                     SpiceDouble             etemit;
                     SpiceDouble             etrec;

                     /.
                     The variables `lat' and `lon' and the latitude and longitude
                     associated with one of the boundary FOV vectors.
                     ./
                     SpiceDouble             lat;
                     SpiceDouble             lon;

                     /.
                     The variable `pmgsmr' is the opposite of the apparent
                     position of Mars with respect to MGS.
                     ./
                     SpiceDouble             pmgsmr [3];

                     /.
                     The variable `radii' is a vector of the semi-axes of Mars.
                     ./
                     SpiceDouble             radii [3];
                     SpiceDouble             radius;

                     /.
                     The variable `rotate' is a position transformation matrix
                     from the camera frame at `etrec' to the IAU_MARS frame
                     at `etemit'.
                     ./
                     SpiceDouble             rotate [3][3];
                     SpiceDouble             spoint [3];
                     SpiceDouble             srfvec [3];
                     SpiceDouble             tmp [3];

                     SpiceInt                camid;
                     SpiceInt                dim;
                     SpiceInt                n;

                     /.  ------------------ Program Setup ------------------

                     Load kernels.
                     ./
                     furnsh_c ( METAKR );

                     /.
                     Convert the time the picture was taken from a
                     UTC time string to seconds past J2000, TDB.
                     ./
                     str2et_c ( "2003 OCT 13 06:00:00 UTC", &etrec );

                     /.
                     Assume the one-way light times from different
                     surface points on Mars to MGS within the camera's
                     FOV are equal. This means the photons that make
                     up different pixels were all emitted from Mars at
                     `etemit' and received by the MGS MOC camera at `etrec'. It
                     would be slow to process images using `sincpt_c' for every
                     pixel. Instead, we will use `sincpt_c' on the
                     boresight pixel and use `surfpt_c' for one of the FOV
                     boundary pixels. If this example program were extended
                     to include all of the camera's pixels, `surfpt_c' would
                     be used for the remaining pixels.

                     Get the MGS MOC Narrow angle camera (MGS_MOC_NA)
                     ID code. Then look up the field of view (FOV)
                     parameters by calling `getfov_c'.
                     ./

                     bodn2c_c ( camera, &camid, &found );
                     if ( !found  )
                     {
                       setmsg_c ("Could not find ID code for instrument #." );
                       errch_c  ("#", camera );
                       sigerr_c ("SPICE(NOTRANSLATION)");
                     }

                     /.
                     `getfov_c' will return the name of the camera-fixed frame
                     in the string `obsref', the camera boresight vector in
                     the array `bsight', and the FOV corner vectors in the
                     array `bounds'.
                     ./

                     getfov_c ( camid,  NCORNR, SHPLEN, FRMNLN, shape,
                                obsref, bsight, &n,     bounds        );

                     printf( "Observation Reference Frame:  %s\n", obsref );

                     /. ----------- Boresight Surface Intercept -----------

                     Retrieve the time, surface intercept point, and vector
                     from MGS to the boresight surface intercept point
                     in IAU_MARS coordinates.
                     ./
                     sincpt_c ( "Ellipsoid", "Mars", etrec, "IAU_MARS",
                                ABCORR, "MGS",   obsref,
                                bsight,  spoint, &etemit, srfvec, &found );
                     if ( !found  )
                     {
                       setmsg_c("Intercept not found for the boresight vector.");
                       sigerr_c("SPICE(NOINTERCEPT)");
                     }

                     /.
                     Convert the intersection point of the boresight
                     vector and Mars from rectangular into latitudinal
                     coordinates. Convert radians to degrees.
                     ./
                     reclat_c ( spoint, &radius, &lon, &lat );

                     lon *= dpr_c();
                     lat *= dpr_c();

                     printf( "Boresight surface intercept coordinates:\n"
                             "    Radius    (km) :  %f\n"
                             "    Latitude  (deg):  %f\n"
                             "    Longitude (deg):  %f\n",
                             radius, lat, lon );

                     /.---- A Boundary FOV Surface Intercept (`surfpt_c') -----

                     Now we will transform one of the FOV corner vectors into the
                     IAU_MARS frame so the surface intercept point can be
                     calculated using surfpt_c, which is faster than subpnt_c.

                     If this example program were extended to include all
                     of the pixels in the camera's FOV, a few steps, such as
                     finding the rotation matrix from the camera frame to the
                     IAU_MARS frame, looking up the radii values for Mars,
                     and finding the position of MGS with respect to Mars could
                     be done once and used for every pixel.

                     Find the rotation matrix from the ray's reference
                     frame at the time the photons were received (etrec)
                     to IAU_MARS at the time the photons were emitted
                     (etemit).
                     ./
                     pxfrm2_c ( obsref, "IAU_MARS", etrec, etemit, rotate );

                     /.
                     Look up the radii values for Mars.
                     ./
                     bodvrd_c ( "MARS", "RADII", 3, &dim, radii );

                     /.
                     Find the position of the center of Mars with respect
                     to MGS.  The position of the observer with respect
                     to Mars is required for the call to `surfpt_c'.  Note:
                     the apparent position of MGS with respect to Mars is
                     not the same as the negative of Mars with respect to MGS.
                     ./
                     vsub_c ( spoint, srfvec, pmgsmr );

                     /.
                     The selected boundary FOV pixel must be rotated into the
                     IAU_MARS reference frame.
                     ./
                     mxv_c ( rotate, bounds[1], bndvec );

                     /.
                     Calculate the surface point of the boundary FOV
                     vector.
                     ./
                     surfpt_c ( pmgsmr, bndvec, radii[0], radii[1], radii[2],
                                spoint, &found );

                     if ( !found  )
                     {
                       setmsg_c ("Could not calculate surface point.");
                       sigerr_c ("SPICE(NOTFOUND)");
                     }
                     vequ_c ( spoint, tmp );

                     /.
                     Convert the intersection point of the boundary
                     FOV vector and Mars from rectangular into
                     latitudinal coordinates. Convert radians
                     to degrees.
                     ./
                     reclat_c ( spoint, &radius, &lon, &lat );

                     lon *= dpr_c();
                     lat *= dpr_c();

                     printf( "Boundary vector surface intercept coordinates "
                             "using SURFPT:\n"
                             "    Radius    (km) :  %f\n"
                             "    Latitude  (deg):  %f\n"
                             "    Longitude (deg):  %f\n"
                             "    Emit time using boresight LT (s):  %10.8f\n",
                             radius, lat, lon, etemit);

                     /. ---- A Boundary FOV Surface Intercept Verification ----

                     For verification only, we will calculate the surface
                     intercept coordinates for the selected boundary vector using
                     `sincpt_c' and compare to the faster `surfpt_c' method.
                     ./
                     sincpt_c ( "Ellipsoid",    "Mars",   etrec, "IAU_MARS",
                                ABCORR, "MGS",  obsref,  bounds[1],
                                spoint, &etemit, srfvec, &found );

                     if ( !found  )
                     {
                       setmsg_c("Intercept not found for the boresight vector.");
                       sigerr_c("SPICE(NOINTERCEPT)");
                     }

                     /.
                     Convert the intersection point of the selected boundary
                     vector and Mars from rectangular into latitudinal
                     coordinates. Convert radians to degrees.
                     ./
                     reclat_c ( spoint, &radius, &lon, &lat );

                     lon *= dpr_c();
                     lat *= dpr_c();

                     printf( "Boundary vector surface intercept coordinates "
                             "using surfpt_c:\n"
                             "    Radius    (km) :  %f\n"
                             "    Latitude  (deg):  %f\n"
                             "    Longitude (deg):  %f\n"
                             "    Emit time using boundary LT (s):  %10.8f\n",
                             radius, lat, lon, etemit);

                     /.
                     We expect this to be a very small distance.
                     ./
                     dist = vdist_c ( tmp, spoint );

                     printf( "Distance between surface points of the selected "
                             "boundary vector using surfpt_c and sincpt_c:\n"
                             "    Distance (mm):    %f\n", dist*pow(10,6)   );

                     return(0);

                }

           When this program was executed using gcc on a PC Linux
           64 bit environment, the output was:

                 Observation Reference Frame:  MGS_MOC_NA
                 Boresight surface intercept coordinates:
                     Radius    (km) :  3384.940410
                     Latitude  (deg):  -48.479580
                     Longitude (deg):  -123.436454
                 Boundary vector surface intercept coordinates using surfpt_c:
                     Radius    (km) :  3384.939699
                     Latitude  (deg):  -48.481636
                     Longitude (deg):  -123.398822
                     Emit time using boresight LT (s):  119296864.18105948
                 Boundary vector surface intercept coordinates using surfpt_c:
                     Radius    (km) :  3384.939699
                     Latitude  (deg):  -48.481636
                     Longitude (deg):  -123.398823
                     Emit time using boundary LT (s):  119296864.18105949
                 Distance between surface points of the selected boundary vector
                 using surfpt_c and sincpt_c:
                     Distance (mm):    32.642059

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       S. C. Krening  (JPL)
       W. L. Taber    (JPL)

#### Version

     -CSPICE Version 1.0.0  1-FEB-2012 (SCK) (WLT)

#### Index_Entries

       Position transformation matrix for different epochs

#### Link to routine pxfrm2_c source file pxfrm2_c.c

    Wed Apr  5 17:54:41 2017