cspice_pxfrm2

 Abstract I/O Examples Particulars Required Reading Version Index_Entries

#### Abstract

```
CSPICE_PXFRM2 returns the 3x3 matrix that transforms position
vectors from one specified frame at a specified epoch to another
specified frame at another specified epoch.

```

#### I/O

```
Given:

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

[1,m] = size(from); char = class(from)

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

[1,l] = size(to); char = class(to)

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

[1,n] = size(etfrom); double = class(etfrom)

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

[1,n] = size(etto); double = class(etto)

the call:

result = cspice_pxfrm2( from, to, etfrom, etto)

returns:

rotate   operator(s) that transform position vector(s) from the
reference frame 'from' at epoch 'etfrom' to the frame 'to' at
epoch 'etto'.

If [1,1] = size(etfrom) then [3,3]   = size(rotate).
If [1,n] = size(etfrom) then [3,3,n] = size(rotate).
double = class(rotate)

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  |
-   -       -        -     -  -

'rotate' returns with the same vectorization measure (N)
as 'etfrom' and 'etto'.

```

#### Examples

```
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.

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 'cspice_sincpt'
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 'cspice_sincpt' once to get the light time and surface point
associated with the boresight. Then, we will rotate the first
FOV boundary vector from the camera frame at 'etrec' to the
body-fixed Mars frame at 'etemit', and call the faster routine
'cspice_surfpt' to retrieve the surface point for the FOV boundary
vector.

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 'cspice_getfov'
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.

Example program starts here.

% --------------------- Program Setup ---------------------

metakr = 'mgs_ex.tm';
camera = 'MGS_MOC_NA';
NCORNR = 4;
ABCORR = 'CN+S';

%
% Load kernels
%
cspice_furnsh( metakr );

%
% Convert the time the picture was taken from a
% UTC time string to seconds past J2000, TDB.
%
etrec = cspice_str2et( '2003 OCT 13 06:00:00 UTC' );

%
% 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 MGS at 'etrec'.  It would be
% slow to process images using 'cspice_sincpt' for every
% pixel.  Instead, we will use 'cspice_sincpt' on the
% boresight pixel and use 'cspice_surfpt' for the first FOV
% boundary pixel.  If this example program were extended
% to include all of the camera's pixels, 'cspice_surfpt' 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 'cspice_getfov'.
%
[camid, found] = cspice_bodn2c( camera );

if ( ~found )
txt = sprintf( ['SPICE(NOTRANSLATION)' ...
'Could not find ID code for instrument %s.' ], ...
camera );
error( txt )
end

%
% 'cspice_getfov' 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.
%
[shape, obsref, bsight, bounds] = cspice_getfov( camid, NCORNR);

fprintf( '\nObservation 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.
%
[ spoint, etemit, srfvec, found ] = ...
cspice_sincpt( 'Ellipsoid', 'Mars', etrec,  'IAU_MARS', ...
ABCORR,     'MGS' , obsref,  bsight );

if ( ~found )
txt = sprintf( ['SPICE(NOINTERCEPT)' ...
'Intercept not found for boresight vector.' ]);
error( txt )
end

%
% Convert the intersection point of the boresight
% vector and Mars from rectangular into latitudinal
% coordinates. Convert radians to degrees.
%
[ radius, lon, lat ] = cspice_reclat( spoint );

lon = lon * cspice_dpr;
lat = lat * cspice_dpr;

fprintf( ['\n'                                         ...
'Boresight surface intercept coordinates:\n' ...
'    Radius    (km) :  %f\n'                 ...
'    Latitude  (deg):  %f\n'                 ...
'    Longitude (deg):  %f\n' ],              ...
radius, lat, lon );

%
% ------ 1st Boundary FOV Surface Intercept (cspice_surfpt) -----
%
% Now we will transform the first FOV corner vector into the
% IAU_MARS frame so the surface intercept point can be
% calculated using cspice_surfpt, which is faster than
% cspice_subpnt.
%
% 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 semi-axis 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).
%
[rotate] = cspice_pxfrm2( obsref, 'IAU_MARS', etrec, etemit );

%
% Look up the semi-axis values for Mars.
%
radii = cspice_bodvrd( 'MARS', 'RADII', 3 );

%
% 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 'cspice_surfpt'.  Note:
% the apparent position of MGS with respect to Mars is
% not the same as the negative of Mars with respect to MGS.
%
pos_mgs_wrt_mars = spoint - srfvec;

%
% The first boundary FOV pixel must be rotated into the
% IAU_MARS reference frame.
%
bndvec = rotate * bounds(:,1);

%
% Calculate the surface point of the boundary FOV
% vector.
%
[surface_point, found] = cspice_surfpt ( pos_mgs_wrt_mars, ...
bndvec, radii(1), ...
radii(2), radii(3) );

if ( ~found )
txt = 'SPICE(NOTFOUND)Could not calculate surface point.';
error( txt )
end

surf_point_using_surfpt = surface_point;

%
% Convert the intersection point of the boundary
% FOV vector and Mars from rectangular into
% latitudinal coordinates. Convert radians
% to degrees.
%
[ radius, lon, lat ] = cspice_reclat( surface_point );

lon = lon * cspice_dpr;
lat = lat * cspice_dpr;

fprintf( ['\n'                                        ...
'Boundary vector surface intercept\n'       ...
'coordinates using cspice_surfpt:\n'        ...
'    Radius    (km) :  %f\n'                ...
'    Latitude  (deg):  %f\n'                ...
'    Longitude (deg):  %f\n'                ...
'    Emit time using boresight LT (s):  %10.9f\n'], ...
radius, lat, lon, etemit );

%
% ------ 1st Boundary FOV Surface Intercept Verification ----
%
% For verification only, we will calculate the surface
% intercept coordinates for the first boundary vector
% using 'cspice_sincpt' and compare to the faster
% 'cspice_surfpt' method.
%
[ surface_point, etemit, srfvec, found ] = ...
cspice_sincpt( 'Ellipsoid', 'Mars', etrec,  'IAU_MARS', ...
ABCORR,     'MGS' , obsref,  bounds(:,1) );

if ( ~found )
txt = sprintf( ['SPICE(NOTFOUND)' ...
'Intercept not found for ' ...
'the boundary FOV vector.' ]);
error( txt )
end

%
% Convert the intersection point of the first boundary
% vector and Mars from rectangular into latitudinal
% coordinates. Convert radians to degrees.
%
[ radius, lon, lat ] = cspice_reclat( surface_point );

lon = lon * cspice_dpr;
lat = lat * cspice_dpr;

fprintf( ['\n'                                              ...
'Boundary vector surface intercept\n'             ...
'coordinates using cspice_sincpt:\n'              ...
'    Radius    (km) :  %f\n'                      ...
'    Latitude  (deg):  %f\n'                      ...
'    Longitude (deg):  %f\n'                      ...
'    Emit time using boresight LT (s):  %10.9f\n\n'], ...
radius, lat, lon, etemit );

distance = cspice_vdist ( surf_point_using_surfpt, surface_point );

fprintf( [ 'Distance between surface points of the first\n' ...
'boundary vector using cspice_surfpt and\n'      ...
'cspice_sincpt:\n'                               ...
'    Distance (mm):   %f\n' ],                   ...
distance*10^6 );

%
% It's always good form to unload kernels after use,
% particularly in MATLAB due to data persistence.
%
cspice_kclear

MATLAB outputs:

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 cspice_surfpt:
Radius    (km) :  3384.941136
Latitude  (deg):  -48.477482
Longitude (deg):  -123.474080
Emit time using boresight LT (s):  119296864.181059480

Boundary vector surface intercept
coordinates using cspice_sincpt:
Radius    (km) :  3384.941136
Latitude  (deg):  -48.477482
Longitude (deg):  -123.474079
Emit time using boresight LT (s):  119296864.181059465

Distance between surface points of the first
boundary vector using cspice_surfpt and
cspice_sincpt:
Distance (mm):   32.139880

```

```
None.

```

#### Required Reading

```
For important details concerning this module's function, please refer to
the CSPICE routine pxfrm2_c.

MICE.REQ
FRAMES

```

#### Version

```
-Mice Version 1.0.0  12-MAR-2012 SCK (JPL)

```

#### Index_Entries

```
Position transformation matrix for different epochs

```
`Wed Apr  5 18:00:34 2017`