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## NAME

ccxymatch -- Match celestial and pixel coordinate lists using various methods

## USAGE

`ccxymatch input reference output tolerance [ptolerance]`

## PARAMETERS

- input
- The list of input pixel coordinate files.

- reference
- The list of input celestial coordinate files. The number of celestial coordinate files must be one or equal to the number of pixel coordinate files.

- output
- The output matched coordinate files containing: 1) the celestial coordinates of the matched objects in columns 1 and 2, 2) the pixel coordinates of the matched objects in columns 3 and 4, and 3) the line numbers of the matched objects in the celestial coordinate and pixel lists in columns 5 and 6.

- tolerance
- The matching tolerance in arcseconds.

- ptolerance
- The matching tolerance in pixels. The ptolerance parameter is required by the "triangles" matching algorithm but not by the "tolerance" matching algorithm.

- refpoints = ""
- A file of tie points used to compute the linear transformation
from the pixel coordinate system to the celestial coordinate system. Refpoints
is a text file containing the celestial coordinates of 1-3 tie points
in the first line, followed by the pixel coordinates of the same 1-3 tie points
in succeeding lines. The celestial coordinates are assumed to be
in the units specified by
*lngunits*and*latunits*. If refpoints is undefined then the parameters*xin*,*yin*,*xmag*,*ymag*,*xrotation*,*yrotation*,*projection*,*lngref*, and*latref*are used to compute the linear transformation.

- xin = INDEF, yin = INDEF
- The x and y origin of the pixel coordinate system. Xin and yin default to 0.0 and 0.0 respectively.

- xmag = INDEF, ymag = INDEF
- The x and y scale factors in arcseconds per pixel. Xmag and ymag default to 1.0 and 1.0 respectively.

- xrotation = INDEF, yrotation = INDEF
- The x and y rotation angles measured in degrees counter-clockwise. Xrotation and yrotation default to 0.0 and 0.0 degrees respectively. To set east to the up, down, left, and right directions, set xrotation to 90, 270, 180, and 0 respectively. To set north to the up, down, left, and right directions, set yrotation to 0, 180, 90, and 270 degrees respectively. Any global rotation must be added to both the xrotation and yrotation values.

- projection = "tan"
- The sky projection geometry. The most commonly used projections in astronomy are "tan", "arc", "sin", and "lin". Other supported projections are "ait", "car", "csc", "gls", "mer", "mol", "par", "pco", "qsc", "stg", "tsc", and "zea".

- lngref = INDEF, latref = INDEF
- The origin of the celestial coordinate system. Lngref and latref define the
reference point of the sky projection
*projection*, and default to the mean of the ra / longitude and dec / latitude coordinates respectively. Lngref and latref are assumed to be in units of*lngunits*and*latunits*.

- lngcolumn = 1, latcolumn = 2
- The columns in the celestial coordinate list containing the ra / longitude and dec / latitude coordinate values.

- xcolumn = 1, ycolumn = 2
- The columns in the pixel coordinate list containing the x and y coordinate values.

- lngunits = "hours", latunits = "degrees"
- The units of the celestial coordinates. The options are "hours", "degrees", and "radians" for lngunits, and "degrees" and "radians" for latunits.

- separation = 3.0
- The minimum separation in arcseconds for objects in the celestial coordinate lists. Objects closer together than separation arcseconds are removed from the celestial coordinate lists prior to matching.

- pseparation = 9.0
- The minimum separation in pixels for objects in the pixel coordinate lists. Objects closer together than pseparation pixels are removed from the pixel coordinate lists prior to matching.

- matching = "triangles"
- The matching algorithm. The choices are:
- tolerance
- A linear transformation is applied to the pixel coordinates,
the appropriate projection is applied to the celestial coordinates,
the transformed pixel and celestial coordinates are sorted,
points which are too close together are removed, and the pixel coordinates
which most closely match the celestial coordinates to within the
user specified tolerance are determined. The tolerance algorithm requires
an initial estimate for the linear transformation. This estimate can be
derived by supplying the coordinates of tie points via the
*refpoints*file, or by setting the linear transformation parameters*xin*,*yin*,*xmag*,*ymag*,*xrotation*,*yrotation*,*projection*,*lngref*, and*latref*. Assuming that a good initial estimate for the required linear transformaton is supplied, the tolerance algorithm functions well in the presence of shifts, axis flips, x and y scale changes, rotations, and axis skew between the two coordinate systems. The algorithm is sensitive to higher order distortion terms in the coordinate transformation.

- triangles
- A linear transformation is applied to the pixel coordinates, the appropriate projection is applied to the celestial coordinates, the transformed pixel and celestial coordinates are sorted, points which are too close together are removed, and the pixel coordinates are matched to the celestial coordinates using a triangle pattern matching algorithm and user specified tolerance parameters. The triangles pattern matching algorithm does not require prior knowledge of the linear transformation, although it will use a transformation if one is supplied. The algorithm functions well in the presence of shifts, axis flips, magnification, and rotation between the two coordinate systems, as long as both lists have a reasonable number of objects in common and the errors in the computed coordinates are small. However as the algorithm depends on comparisons of similar triangles, it is sensitive to differences in the x and y coordinate scales, skew between the x and y axes, and higher order distortion terms in the coordinate transformation.

- nmatch = 30
- The maximum number of celestial and pixel coordinates used by the "triangles" pattern matching algorithm. If either list contains more coordinates than nmatch, the lists are subsampled. Nmatch should be kept small as the computation and memory requirements of the "triangles" algorithm depend on a high power of the lengths of the respective lists.

- ratio = 10.0
- The maximum ratio of the longest to shortest side of the triangles generated by the "triangles" pattern matching algorithm. Triangles with computed longest to shortest side ratios > ratio are rejected from the pattern matching algorithm. Ratio should never be set higher than 10.0 but may be set as low as 5.0.

- nreject = 10
- The maximum number of rejection iterations for the "triangles" pattern matching algorithm.

- lngformat = "", latformat = ""
- The format of the output celestial coordinates. The default formats are "%13.3h", "%13.3h", and "%13.7g" for units of "hours", "degrees", and "radians respectively.

- xformat = "%13.3f", yformat = "%13.3f"
- The format of the output pixel coordinates. By default the coordinates are output right justified in a field of 13 characters with 3 places following the decimal point.

- verbose = yes
- Print messages about the progress of the task ?

## DESCRIPTION

CCXYMATCH matches ra / dec or longitude / latitude coordinates in the
celestial coordinate list *reference*
to their corresponding x and y
coordinates in the pixel coordinate list *input*
using user specified
tolerances in arcseconds *tolerance*
and pixels *ptolerance*
, and
writes the matched coordinates to the output file *output*
. The output
file is suitable for input to the plate solution computation task CCMAP.

CCXYMATCH matches the coordinate lists by: 1) projecting the celestial
coordinates onto a plane using the sky projection geometry *projection*
and the reference point *lngref*
and *latref*
,
2) computing an initial guess for the linear transformation required to
match the pixel coordinate system to the porjected celestial coordinate system,
3) applying the computed transformation to the pixel coordinates, 4) sorting
the projected celestial and pixel coordinates lists, 5) removing points with a
minimum separation specified by the parameters *separation*
and
*pseparation*
from both lists, 6) matching the two lists using either
the "triangles" or "tolerance" matching algorithms, and 7) writing the matched
list to the output file.

An initial estimate for the linear transformation is computed in one of
two ways. If *refpoints*
is defined, the celestial and pixel coordinates
of up to three tie points are read from succeeding lines in the refpoints file,
and used to compute the linear transformation. The coordinates of the tie
points can be typed in by hand if *refpoints*
is "STDIN". The formats of
two sample refpoints files are shown below.

# First sample refpoints file (1 reference file and N input files) ra1 dec1 [ra2 dec2 [ra3 dec3]] # tie points for reference coordinate file x1 y1 [ x2 y2 [ x3 y3]] # tie points for input coordinate file 1 x1 y1 [ x2 y2 [ x3 y3]] # tie points for input coordinate file 2 .. .. [ .. .. [ .. ..] x1 y1 [ x2 y2 [ x3 y3]] # tie points for input coordinate file N # Second sample refpoints file (N reference files and N input files) ra1 dec1 [ra2 dec2 [ra3 dec3]] # tie points for reference coordinate file 1 x1 y1 [ x2 y2 [ x3 y3]] # tie points for input coordinate file 1 ra1 dec1 [ra2 dec2 [ra3 dec3]] # tie points for reference coordinate file 2 x1 y1 [ x2 y2 [ x3 y3]] # tie points for input coordinate file 2 .. .. [ .. .. [ .. ..]] ra1 dec1 [ra2 dec2 [ra3 dec3]] # tie points for reference coordinate file N x1 y1 [ x2 y2 [ x3 y3]] # tie points for input coordinate file N

If the refpoints file is undefined the parameters *xin*
, *xin*
,
*xmag*
, *ymag*
, *xrotation*
, *xrotation*
are used
to compute a linear transformation from the pixel coordinates to the
standard coordinates xi and eta as shown below. Orientation and skew
are the orientation of the x and y axes and their deviation from
perpendicularity respectively.

xi = a + b * x + c * y eta = d + e * x + f * y xrotation = orientation - skew / 2 yrotation = orientation + skew / 2 b = xmag * cos (xrotation) c = -ymag * sin (yrotation) e = xmag * sin (xrotation) f = ymag * cos (yrotation) a = 0.0 - b * xin - c * yin = xshift d = 0.0 - e * xin - f * yin = yshift

Both methods of computing the initial linear transformation compute the
standard coordinates xi and eta by projecting the celestial coordinates
onto a plane using the sky projection geometry *projection*
and the
reference point *lngref*
and *latref*
. The celestial coordinates
are assumed to be in units of *lngunits*
and *latunits*
and the
standard coordinates are in arcseconds. The linear transformation and its
geometric interpretation are shown below.

The celestial and pixel coordinates are read from columns *lngcolumn*
and
*latcolumn*
in the celestial coordinate list, and *xcolumn*
, and
*ycolumn*
in the pixel coordinate list respectively. The pixel
coordinates are transformed using the linear transformation described above,
the celestial coordinate in units of *lngunits*
and *latunits*
are projected to standard coordinates in arcseconds, and stars closer together
than *separation*
arcseconds and *pseparation*
pixels are removed
from the celestial and pixel coordinate lists respectively.

The coordinate lists are matched using the matching algorithm specified by
*matching*
. If matching is "tolerance", CCXYMATCH searches the transformed
sorted pixel coordinate list for the coordinates that are within the matching
tolerance *tolerance*
and closest to the current standard coordinates.
The major advantage of the "tolerance" algorithm is that it can handle x and y
scale differences and axis skew in the coordinate transformation. The major
disadvantage of the "tolerance" algorithm is that the user must supply
tie point information in all but the simplest case of small x and y
shifts between the pixel and celestial coordinate systems.

If matching is "triangles", CCXYMATCH constructs a list of triangles
using up to *nmatch*
celestial coordinates and transformed pixel
coordinates and performs a pattern matching operation on the resulting
triangle lists. If the number of coordinates in both lists is less than
*nmatch*
the entire list is matched using the "triangles" algorithm
directly, otherwise the "triangles" algorithm is used to estimate a new
linear transformation, the input coordinate list is transformed using
the new transformation, and the entire list is matched using the "tolerance"
algorithm. The major advantage of the "triangles" algorithm is that it
requires no tie point information from the user. The major disadvantages of the
algorithm are that, it is sensitive to x and y scale differences and axis
skew between the celestial and pixel coordinate systems, and can be
computationally expensive.

The matched celestial and pixel coordinates are written to columns 1, 2, 3,
and 4 of the ouput file, in the formats specified by the *lngformat*
,
*latformat*
, *xformat*
and *yformat*
parameters. The original
line numbers in the celestial and pixels coordinate files are written to
columns 5 and 6.

If *verbose*
is yes, detailed messages about actions taken by the
task are written to the terminal as the task executes.

## ALGORITHMS

The "triangles" algorithm uses a sophisticated pattern matching
technique which requires no tie point information from the user.
It is expensive computationally and is therefore restricted to a maximum
of *nmatch*
objects from the celestial and pixel coordinate lists.

The "triangles" algorithm first generates a list
of all the possible triangles that can be formed from the points in each list.
For a list of nmatch points this number is the combinatorial factor
nmatch! / [(nmatch-3)! * 3!] or nmatch * (nmatch-1) * (nmatch-2) / 6.
The length of the perimeter, ratio of longest to shortest side, cosine
of the angle between the longest and shortest side, the tolerances in
the latter two quantities and the direction of the arrangement of the vertices
of each triangle are computed and stored in a table.
Triangles with vertices closer together than *tolerance*
and
*ptolerance*
, or
with a ratio of the longest to shortest side greater than *ratio*
are discarded. The remaining triangles are sorted in order of increasing
ratio. A sort merge algorithm is used to match the triangles using the
ratio and cosine information, the tolerances in these quantities, and
the maximum tolerances for both lists. The ratios of the
perimeters of the matched triangles are compared to the most common ratio
for the entire list, and triangles which deviate too widely from this number
are discarded. The number of triangles remaining are divided into
the number which match in the clockwise sense and the number which match
int the counter-clockwise sense. Those in the minority category
are eliminated.
The rejection step can be repeated up to *nreject*
times or until
no more rejections occur, whichever comes first.
The last step in the algorithm is a voting procedure in which each remaining
matched triangle casts three votes, one for eached matched pair of vertices.
Points which have fewer than half the maximum number of
votes are discarded. The final set of matches are written to the output file.

The "triangles" algorithm functions well when the celestial and
pixel coordinate lists have a sufficient number of objects (50%,
in some cases as low as 25%) of their objects in common, any distortions
including x and y scale differences and skew between the two systems are small,
and the random errors in the coordinates are small. Increasing the value of
the *tolerance*
parameter will increase the ability to deal with
distortions but will also produce more false matches which after some point
will swamp the true matches.

## FORMATS

A format specification has the form "%w.dCn", where w is the field width, d is the number of decimal places or the number of digits of precision, C is the format code, and n is radix character for format code "r" only. The w and d fields are optional. The format codes C are as follows:

b boolean (YES or NO) c single character (c or '\c' or '\0nnn') d decimal integer e exponential format (D specifies the precision) f fixed format (D specifies the number of decimal places) g general format (D specifies the precision) h hms format (hh:mm:ss.ss, D = no. decimal places) m minutes, seconds (or hours, minutes) (mm:ss.ss) o octal integer rN convert integer in any radix N s string (D field specifies max chars to print) t advance To column given as field W u unsigned decimal integer w output the number of spaces given by field W x hexadecimal integer z complex format (r,r) (D = precision) Conventions for w (field width) specification: W = n right justify in field of N characters, blank fill -n left justify in field of N characters, blank fill 0n zero fill at left (only if right justified) absent, 0 use as much space as needed (D field sets precision) Escape sequences (e.g. "\n" for newline): \b backspace (not implemented) \f formfeed \n newline (crlf) \r carriage return \t tab \" string delimiter character \' character constant delimiter character \\ backslash character \nnn octal value of character Examples %s format a string using as much space as required %-10s left justify a string in a field of 10 characters %-10.10s left justify and truncate a string in a field of 10 characters %10s right justify a string in a field of 10 characters %10.10s right justify and truncate a string in a field of 10 characters %7.3f print a real number right justified in floating point format %-7.3f same as above but left justified %15.7e print a real number right justified in exponential format %-15.7e same as above but left justified %12.5g print a real number right justified in general format %-12.5g same as above but left justified %h format as nn:nn:nn.n %15h right justify nn:nn:nn.n in field of 15 characters %-15h left justify nn:nn:nn.n in a field of 15 characters %12.2h right justify nn:nn:nn.nn %-12.2h left justify nn:nn:nn.nn %H / by 15 and format as nn:nn:nn.n %15H / by 15 and right justify nn:nn:nn.n in field of 15 characters %-15H / by 15 and left justify nn:nn:nn.n in field of 15 characters %12.2H / by 15 and right justify nn:nn:nn.nn %-12.2H / by 15 and left justify nn:nn:nn.nn \n insert a newline

## REFERENCES

A detailed description of the "triangles" pattern matching algorithm used here can be found in the article "A Pattern-Matching Algorithm for Two- Dimensional Coordinate Lists" by E.J. Groth, A.J. 91, 1244 (1986).

## EXAMPLES

1. Compute the plate solution for a 1528 by 2288 B band image of M51 by matching a list of reference stars extracted from the Guide Star Catalog with the regions task against a list of bright stars detected with the daofind task. The approximate image center is RA = 13:29:52.8 and DEC = +47:11:41 (J2000) and the image scale is 0.43 arcseconds / pixel.

... Get the guide stars (see stsdas.analysis.gasp package). cl> regions 13:29:52.8 47:11:41 0.27 m51b.gsc.tab ... Convert the binary table to a text file (see package tables.ttools). cl> tprint m51b.gsc.tab > m51b.gsc ... Examine the guide star list. cl> type m51b.gsc # Table m51b.gsc.tab Tue 10:39:55 22-Oct-96 # row RA_HRS RA_DEG DEC_DEG MAG # hours degrees degrees magnitudes 1 13:29:13.33 202:18:19.9 47:14:16.3 12.3 2 13:29:05.51 202:16:22.6 47:10:44.7 14.8 3 13:29:48.60 202:27:09.0 47:07:42.5 15.0 4 13:29:47.30 202:26:49.4 47:13:37.5 10.9 5 13:29:31.65 202:22:54.7 47:18:54.7 15.0 6 13:29:06.16 202:16:32.4 47:04:53.1 14.9 7 13:29:37.40 202:24:21.1 47:09:09.2 15.1 8 13:29:38.70 202:24:40.5 47:13:36.2 15.0 9 13:29:55.42 202:28:51.3 47:10:05.2 15.4 10 13:29:06.91 202:16:43.7 47:04:07.9 12.4 11 13:29:29.73 202:22:25.9 47:12:04.1 15.1 12 13:30:07.96 202:31:59.4 47:05:18.3 14.7 13 13:30:01.82 202:30:27.2 47:12:58.8 11.8 14 13:30:36.75 202:39:11.2 47:04:05.9 14.9 15 13:30:34.04 202:38:30.6 47:16:44.8 13.2 16 13:30:14.95 202:33:44.3 47:10:27.6 13.4 ... Locate bright stars in the image (see noao.digiphot.daophot package). ... Suitable values for fwhmpsf, sigma, ... and threshold can be determined ... using the imstatistics and imexamine tasks. Some experimentation may be ... necessary to determine optimal values. cl> daofind m51b "default" fwhmpsf=4.0 sigma=5.0 threshold=20.0 ... Examine the star list. cl> type m51b.coo.1 ... #N XCENTER YCENTER MAG SHARPNESS SROUND GROUND ID ... 401.034 147.262 -2.315 0.473 -0.075 -0.170 1 261.137 453.696 -1.180 0.481 -0.373 -0.135 2 860.002 480.061 -1.397 0.373 -0.218 -0.178 3 69.342 675.895 -0.955 0.368 -0.294 -0.133 4 1127.791 680.033 -1.166 0.449 -0.515 -0.326 5 972.435 691.544 -1.722 0.449 -0.327 -0.060 6 1348.891 715.084 -1.069 0.389 -0.242 -0.145 7 946.114 797.067 -0.543 0.406 -0.198 -0.069 8 698.455 811.407 -1.620 0.437 -0.038 -0.028 9 964.566 853.201 -0.317 0.382 0.031 -0.086 10 236.088 864.817 -3.515 0.429 -0.164 -0.035 11 919.703 909.835 -3.775 0.447 0.051 0.007 12 406.592 985.807 -0.715 0.424 -0.307 -0.068 13 920.790 986.083 -0.600 0.364 -0.047 0.021 14 761.403 1037.795 -1.944 0.383 -0.023 0.120 15 692.012 1050.603 -0.508 0.339 -0.365 -0.164 16 1023.330 1060.144 -1.897 0.381 -0.246 -0.288 17 681.864 1066.937 -0.059 0.467 -0.175 0.135 18 1307.802 1085.564 -1.173 0.435 0.032 -0.207 19 716.494 1094.800 -0.389 0.421 -0.412 -0.032 20 715.935 1106.616 -3.747 0.649 0.271 0.245 21 1093.813 1300.189 -1.557 0.377 -0.309 -0.078 22 596.406 1353.798 -0.461 0.383 0.029 -0.103 23 1212.117 1362.636 -0.362 0.369 -0.180 0.043 24 251.355 1488.048 -0.909 0.357 -0.390 0.077 25 600.659 1630.261 -1.392 0.423 0.013 -0.312 26 329.448 2179.233 -0.824 0.442 -0.463 0.325 27 ... Match the two lists using the "triangles" algorithm and tolerances of ... 1.0 arcseconds and 3.0 pixels respectively. cl> ccxymatch m51b.coo.1 m51b.gsc m51b.mat.1 1.0 3.0 lngcolumn=2 latcolumn=4 ... Examine the matched file. cl> type m51b.mat.1 # Input: m51b.coo.1 Reference: m51b.gsc Number of tie points: 0 # Initial linear transformation # xref[tie] = 0. + 1. * x[tie] + 0. * y[tie] # yref[tie] = 0. + 0. * x[tie] + 1. * y[tie] # dx: 0.00 dy: 0.00 xmag: 1.000 ymag: 1.000 xrot: 0.0 yrot: 0.0 # # Column definitions # Column 1: Reference Ra / Longitude coordinate # Column 2: Reference Dec / Latitude coordinate # Column 3: Input X coordinate # Column 4: Input Y coordinate # Column 5: Reference line number # Column 6: Input line number 13:29:48.600 47:07:42.50 860.002 480.061 8 44 13:29:38.700 47:13:36.20 1093.813 1300.189 13 63 13:29:55.420 47:10:05.20 698.455 811.407 14 50 13:29:29.730 47:12:04.10 1307.802 1085.564 16 60 13:30:07.960 47:05:18.30 401.034 147.262 17 42 13:30:14.950 47:10:27.60 236.088 864.817 21 52 ... Compute the plate solution. cl> ccmap m51b.mat.1 ccmap.db results=STDOUT xcolumn=3 ycolumn=4 lngcolumn=1 \ latcolumn=2 refpoint=user lngref=13:29:52.8 latref=47:11:41 interactive=no Coords File: m51b.mat.1 Image: Database: ccmap.db Record: m51b.mat.1 Refsystem: j2000 Coordinates: equatorial FK5 Equinox: J2000.000 Epoch: J2000.000 MJD: 51544.50000 Insystem: j2000 Coordinates: equatorial FK5 Equinox: J2000.000 Epoch: J2000.000 MJD: 51544.50000 Coordinate mapping status XI fit ok. ETA fit ok. Ra/Dec or Long/Lat fit rms: 0.206 0.103 (arcsec arcsec) Coordinate mapping parameters Sky projection geometry: tan Reference point: 13:29:52.800 47:11:41.00 (hours degrees) Reference point: 760.656 1033.450 (pixels pixels) X and Y scale: 0.430 0.431 (arcsec/pixel arcsec/pixel) X and Y axis rotation: 180.158 359.991 (degrees degrees) Input Coordinate Listing X Y Ra Dec Ra(fit) Dec(fit) Dra Ddec 860.0 480.1 13:29:48.60 47:07:42.5 13:29:48.62 47:07:42.5 -0.153 0.017 1093.8 1300.2 13:29:38.70 47:13:36.2 13:29:38.73 47:13:36.4 -0.258 -0.164 698.5 811.4 13:29:55.42 47:10:05.2 13:29:55.43 47:10:05.2 -0.062 0.024 1307.8 1085.6 13:29:29.73 47:12:04.1 13:29:29.70 47:12:04.0 0.318 0.123 401.0 147.3 13:30:07.96 47:05:18.3 13:30:07.96 47:05:18.4 0.028 -0.073 236.1 864.8 13:30:14.95 47:10:27.6 13:30:14.94 47:10:27.5 0.127 0.073

2. Repeat example 1 but replace the daofind pixel list with one generated using the center task and a finder chart created with the skymap task.

... Get the guide stars. (see stsdas.analysis.gasp package) cl> regions 13:29:52.8 47:11:41 0.27 m51b.gsc.tab ... Create the finder chart (see stsdas.analysis.gasp package) cl> gasp.skymap m51b.gsc.tab 13:29:52.8 47:11:41 INDEF 0.27 \ objstyle=square racol=RA_HRS deccol=DEC_DEG magcol=MAG interactive- \ dev=stdplot ... Convert the binary table to a text file. (see tables.ttools package) cl> tprint m51b.gsc.tab > m51b.gsc ... Mark and center the guide stars on the image display using the finder ... chart produced by the skymap task and the center task (see the ... digiphot.apphot package). cl> display m51b 1 fi+ cl> center m51b cbox=7.0 ... cl> pdump m51b.ctr.1 xcenter,ycenter yes > m51b.pix ... Display the pixel coordinate list. cl> type m51b.pix 401.022 147.183 236.044 864.882 698.368 811.329 860.003 480.051 1127.754 680.020 1307.819 1085.615 1093.464 1289.595 1212.001 1362.594 1348.963 715.085 ... Match the two lists using the "triangles" algorithm and tolerances of ... 1.0 arcseconds and 3.0 pixels respectively. cl> ccxymatch m51b.pix m51b.gsc m51b.mat.2 1.0 3.0 lngcolumn=2 latcolumn=4 ... Examine the matched file. cl> type m51b.mat.2 # Input: m51b.pix Reference: m51b.gsc Number of tie points: 0 # Initial linear transformation # xi[tie] = 0. + 1. * x[tie] + 0. * y[tie] # eta[tie] = 0. + 0. * x[tie] + 1. * y[tie] # dx: 0.00 dy: 0.00 xmag: 1.000 ymag: 1.000 xrot: 0.0 yrot: 0.0 # # Column definitions # Column 1: Reference Ra / Longitude coordinate # Column 2: Reference Dec / Latitude coordinate # Column 3: Input X coordinate # Column 4: Input Y coordinate # Column 5: Reference line number # Column 6: Input line number 13:29:48.600 47:07:42.50 860.003 480.051 8 4 13:29:37.400 47:09:09.20 1127.754 680.020 12 5 13:29:55.420 47:10:05.20 698.368 811.329 14 3 13:29:29.730 47:12:04.10 1307.819 1085.615 16 6 13:30:07.960 47:05:18.30 401.022 147.183 17 1 13:30:14.950 47:10:27.60 236.044 864.882 21 2 ... Compute the plate solution. cl> ccmap m51b.mat.2 ccmap.db results=STDOUT xcolumn=3 ycolumn=4 lngcolumn=1 \ latcolumn=2 refpoint=user lngref=13:29:52.8 latref=47:11:41 interactive=no Coords File: m51b.mat.2 Image: Database: junk.db Record: m51b.mat.2 Refsystem: j2000 Coordinates: equatorial FK5 Equinox: J2000.000 Epoch: J2000.000 MJD: 51544.50000 Insystem: j2000 Coordinates: equatorial FK5 Equinox: J2000.000 Epoch: J2000.000 MJD: 51544.50000 Coordinate mapping status XI fit ok. ETA fit ok. Ra/Dec or Long/Lat fit rms: 0.312 0.0664 (arcsec arcsec) Coordinate mapping parameters Sky projection geometry: tan Reference point: 13:29:52.800 47:11:41.00 (hours degrees) Reference point: 761.093 1033.230 (pixels pixels) X and Y scale: 0.430 0.431 (arcsec/pixel arcsec/pixel) X and Y axis rotation: 180.175 359.998 (degrees degrees) Input Coordinate Listing X Y Ra Dec Ra(fit) Dec(fit) Dra Ddec

3. Repeat example 1 but use the "tolerance" matching algorithm and apriori knowledge of the celestial and pixel coordinates of the nucleus of M51, the x and y image scales, and the orientation of the detector on the telescope to match the two lists.

... Match the two lists using the ccxymatch "tolerance" algorithm and ... a matching tolerance of 2.0 arcseconds. Note the negative and positive ... signs on the xmag and ymag parameters and lack of any rotation, ... indicating that north is up and east is to the left. cl> ccxymatch m51b.coo.1 m51b.gsc m51b.mat.3 2.0 lngcolumn=2 latcolumn=4 \ matching=tolerance xin=761.40 yin=1037.80 xmag=-0.43 ymag=0.43 xrot=0.0 \ yrot=0.0 lngref=13:29:52.80 latref=47:11:42.9 ... Examine the matched file. cl> type m51b.mat.3 # Input: m51b.coo.1 Reference: m51b.gsc Number of tie points: 0 # Initial linear transformation # xref[tie] = 327.402 + -0.43 * x[tie] + 0. * y[tie] # yref[tie] = -446.254 + 0. * x[tie] + 0.43 * y[tie] # dx: 327.40 dy: -446.25 xmag: 0.430 ymag: 0.430 xrot: 180.0 yrot: 0.0 # # Column definitions # Column 1: Reference Ra / Longitude coordinate # Column 2: Reference Dec / Latitude coordinate # Column 3: Input X coordinate # Column 4: Input Y coordinate # Column 5: Reference line number # Column 6: Input line number 13:30:07.960 47:05:18.30 401.034 147.262 17 42 13:29:48.600 47:07:42.50 860.002 480.061 8 44 13:29:37.400 47:09:09.20 1127.791 680.033 12 46 13:29:55.420 47:10:05.20 698.455 811.407 14 50 13:30:14.950 47:10:27.60 236.088 864.817 21 52 13:29:29.730 47:12:04.10 1307.802 1085.564 16 60 13:29:38.700 47:13:36.20 1093.813 1300.189 13 63 ... Compute the plate solution. cl> ccmap m51b.mat.3 ccmap.db results=STDOUT xcolumn=3 ycolumn=4 lngcolumn=1 \ latcolumn=2 refpoint=user lngref=13:29:52.8 latref=47:11:41 interactive=no Coords File: m51b.mat.3 Image: Database: ccmap.db Record: m51.mat.3 Refsystem: j2000 Coordinates: equatorial FK5 Equinox: J2000.000 Epoch: J2000.000 MJD: 51544.50000 Insystem: j2000 Coordinates: equatorial FK5 Equinox: J2000.000 Epoch: J2000.000 MJD: 51544.50000 Coordinate mapping status XI fit ok. ETA fit ok. Ra/Dec or Long/Lat fit rms: 0.342 0.121 (arcsec arcsec) Coordinate mapping parameters Sky projection geometry: tan Reference point: 13:29:52.800 47:11:41.00 (hours degrees) Reference point: 760.687 1033.441 (pixels pixels) X and Y scale: 0.430 0.431 (arcsec/pixel arcsec/pixel) X and Y axis rotation: 180.174 359.949 (degrees degrees) Input Coordinate Listing X Y Ra Dec Ra(fit) Dec(fit) Dra Ddec 401.0 147.3 13:30:07.96 47:05:18.3 13:30:07.97 47:05:18.4 -0.109 -0.109 860.0 480.1 13:29:48.60 47:07:42.5 13:29:48.64 47:07:42.5 -0.385 -0.045 1127.8 680.0 13:29:37.40 47:09:09.2 13:29:37.34 47:09:09.0 0.572 0.152 698.5 811.4 13:29:55.42 47:10:05.2 13:29:55.43 47:10:05.2 -0.118 0.009 236.1 864.8 13:30:14.95 47:10:27.6 13:30:14.92 47:10:27.5 0.290 0.116 1307.8 1085.6 13:29:29.73 47:12:04.1 13:29:29.72 47:12:04.0 0.082 0.060 1093.8 1300.2 13:29:38.70 47:13:36.2 13:29:38.73 47:13:36.4 -0.332 -0.184

4. Repeat example 3 but input the appropriate linear transformation via a list of tie points, rather than setting the transformation parameters directly.

... Display the tie points. cl> type refpts 13:29:55.42 47:10:05.2 13:29:38.70 47:13:36.2 13:30:14.95 47:10:27.6 698.5 811.4 1093.8 1300.2 236.1 864.8 ... Match the lists using the ccxymatch "tolerance" algorithm and a matching ... tolerance of 2.0 arcseconds. Note the negative and positive signs on the ... xmag and ymag parameters and lack of any rotation, indicating that north ... is up and east is to the left. cl> ccxymatch m51b.coo.1 m51b.gsc m51b.mat.4 2.0 refpoints=refpts \ lngcolumn=2 latcolumn=4 matching=tolerance lngref=13:29:52.80 \ latref=47:11:42.9 ... Examine the matched list. cl> type m51b.mat.4 # Input: m51b.coo.1 Reference: m51b.gsc Number of tie points: 3 # tie point: 1 ref: 26.718 -97.698 input: 698.500 811.400 # tie point: 2 ref: -143.629 113.354 input: 1093.800 1300.200 # tie point: 3 ref: 225.854 -75.167 input: 236.100 864.800 # # Initial linear transformation # xi[tie] = 327.7137 + -0.4306799 * x[tie] + -2.0406E-4 * y[tie] # eta[tie] = -448.0854 + 0.00103896 * x[tie] + 0.430936 * y[tie] # dx: 327.71 dy: -448.09 xmag: 0.431 ymag: 0.431 xrot: 179.9 yrot: 0.0 # # Column definitions # Column 1: Reference Ra / Longitude coordinate # Column 2: Reference Dec / Latitude coordinate # Column 3: Input X coordinate # Column 4: Input Y coordinate # Column 5: Reference line number # Column 6: Input line number 13:30:07.960 47:05:18.30 401.034 147.262 17 42 13:29:48.600 47:07:42.50 860.002 480.061 8 44 13:29:37.400 47:09:09.20 1127.791 680.033 12 46 13:29:55.420 47:10:05.20 698.455 811.407 14 50 13:30:14.950 47:10:27.60 236.088 864.817 21 52 13:29:29.730 47:12:04.10 1307.802 1085.564 16 60 13:29:38.700 47:13:36.20 1093.813 1300.189 13 63 ... Compute the plate solution which is identical to the solution computed ... in example 2. cl> ccmap m51b.mat.4 ccmap.db results=STDOUT xcolumn=3 ycolumn=4 lngcolumn=1 \ latcolumn=2 refpoint=user lngref=13:29:52.8 latref=47:11:41 interactive=no

## TIME REQUIREMENTS

## BUGS

## SEE ALSO

stsdas.gasp.regions, stsdas.gasp.skymap,tables.ttools.tprint,daophot.daofind,ccmap