void pxfrm2_c ( ConstSpiceChar * from,
ConstSpiceChar * to,
SpiceDouble etfrom,
SpiceDouble etto,
SpiceDouble rotate[3][3] )
Return the 3x3 matrix that transforms position vectors from one
specified frame at a specified epoch to another specified
frame at another specified epoch.
FRAMES
FRAMES
TRANSFORM
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'.
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.
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 |
- - - - - -
None.
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.
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.
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
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
None.
None.
S. C. Krening (JPL)
W. L. Taber (JPL)
-CSPICE Version 1.0.0 1-FEB-2012 (SCK) (WLT)
Position transformation matrix for different epochs
Link to routine pxfrm2_c source file pxfrm2_c.c
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