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+.help skymap Dec96 images.immatch
+.ih
+NAME
+skymap -- compute the spatial transformation function required to register
+a list of images using celestial coordinate WCS information
+.ih
+USAGE
+skymap input reference database
+.ih
+PARAMETERS
+.ls input
+The list of input images containing the input celestial coordinate wcs.
+.le
+.ls reference
+The list of reference images containing the reference celestial coordinate
+wcs. The number of reference images must be one or equal to the number
+of input images.
+.le
+.ls database
+The name of the output text database file containing the computed
+transformations.
+.le
+.ls transforms = ""
+An option transform name list. If transforms is undefined then the
+transforms are assigned record names equal to the input image names.
+.le
+.ls results = ""
+Optional output files containing a summary of the results including a
+description of the transform geometry and a listing of the input coordinates,
+the fitted coordinates, and the fit residuals. The number of results files
+must be one or equal to the number of input files. If results is "STDOUT" the
+results summary is printed on the standard output.
+.le
+.ls xmin = INDEF, xmax = INDEF, ymin = INDEF, ymax = INDEF
+The minimum and maximum logical x and logical y coordinates used to generate
+the grid of reference image control points and define the region of
+validity of the spatial transformation. Xmin, xmax, ymin, and
+ymax are assigned defaults of 1, the number of columns in the reference 
+image, 1, and the number of lines in the reference image, respectively.
+.le
+.ls nx = 10, ny = 10
+The number of points in x and y used to generate the coordinate grid.
+.le
+.ls wcs = "world"
+The world coordinate system of the coordinates.  The options are:
+.ls physical
+Physical coordinates are pixel coordinates which are invariant with
+respect to linear transformations of the physical image data.  For example,
+if the reference 
+image is a rotated section of a larger input image, the physical
+coordinates of an object in the reference image are equal to the physical
+coordinates of the same object in the input image, although the logical
+pixel coordinates are different.
+.le
+.ls world
+World coordinates are image coordinates which are invariant with
+respect to linear transformations of the physical image data and which
+are in degrees for all celestial coordinate
+systems. Obviously if the
+wcs is correct the ra and dec of an object
+should remain the same no matter how the image
+is linearly transformed. The default world coordinate
+system is either 1) the value of the environment variable "defwcs" if
+set in the user's IRAF environment (normally it is undefined) and present
+in the image header, 2) the value of the "system"
+attribute in the image header keyword WAT0_001 if present in the
+image header or, 3) the "physical" coordinate system.
+.le
+.le
+.ls xformat = "%10.3f", yformat = "%10.3f"
+The format of the output logical x and y reference and input pixel
+coordinates in columns 1 and 2 and 3 and 4 respectively. By default the
+coordinates are output right justified in a field of ten spaces with
+3 digits following the decimal point. 
+.le
+.ls rwxformat = "", rwyformat = ""
+The format of the output reference image celestial coordinates
+in columns 5 and 6 respectively. The internal default formats will give
+reasonable output formats and precision for all celestial coordinate
+systems.
+.le
+.ls wxformat = "", wyformat = ""
+The format of the output input image celestial coordinates
+in columns 7 and 8 respectively. The internal default formats will give
+reasonable output formats and precision for all celestial coordinate
+systems.
+.le
+.ls fitgeometry = "general"
+The fitting geometry to be used. The options are the following.
+.ls shift
+X and y shifts only are fit.
+.le
+.ls xyscale
+X and y shifts and x and y magnification factors are fit. Axis flips are
+allowed for.
+.le
+.ls rotate
+X and y shifts and a rotation angle are fit. Axis flips are allowed for.
+.le
+.ls rscale
+X and y shifts, a magnification factor assumed to be the same in x and y, and a
+rotation angle are fit. Axis flips are allowed for.
+.le
+.ls rxyscale
+X and y shifts, x and y magnifications factors, and a rotation angle are fit.
+Axis flips are allowed for.
+.le
+.ls general
+A polynomial of arbitrary order in x and y is fit. A linear term and a
+distortion term are computed separately. The linear term includes an x and y
+shift, an x and y scale factor, a rotation and a skew.  Axis flips are also
+allowed for in the linear portion of the fit. The distortion term consists
+of a polynomial fit to the residuals of the linear term. By default the
+distortion terms is set to zero.
+.le
+
+For all the fitting geometries except "general" no distortion term is fit,
+i.e. the x and y polynomial orders are assumed to be 2 and the cross term
+switches are set to "none" regardless of the values of the \fIxxorder\fR,
+\fIxyorder\fR, \fIxxterms\fR, \fIyxorder\fR, \fIyyorder\fR and \fIyxterms\fR
+parameters set by the user.
+.le
+.ls function = "polynomial"
+The type of analytic coordinate surfaces to be fit. The options are the
+following.
+.ls legendre
+Legendre polynomials in x and y.
+.le
+.ls chebyshev
+Chebyshev polynomials in x and y.
+.le
+.ls polynomial
+Power series polynomials in x and y.
+.le
+.le
+.ls xxorder = 2, xyorder = 2, yxorder = 2, yyorder = 2
+The order of the polynomials in x and y for the x and y fits respectively.
+The default order and cross term settings define the linear term in x
+and y, where the 6 coefficients can be interpreted in terms of an x and y shift,
+an x and y scale change, and rotations of the x and y axes. The "shift",
+"xyscale", "rotation", "rscale", and "rxyscale", fitting geometries
+assume that the polynomial order parameters are 2 regardless of the values
+set by the user. If any of the order parameters are higher than 2 and
+\fIfitgeometry\fR is "general", then a distortion surface is fit to the
+residuals from the linear portion of the fit.
+.le
+
+.ls xxterms = "half", yxterms = "half"
+The options are:
+.ls none
+The individual polynomial terms contain powers of x or powers of y but not
+powers of both.
+.le
+.ls half
+The individual polynomial terms contain powers of x and powers of y, whose
+maximum combined power is MAX (xxorder - 1, xyorder - 1) for the x fit and
+MAX (yxorder - 1, yyorder - 1) for the y fit.
+.le
+.ls full
+The individual polynomial terms contain powers of x and powers of y, whose
+maximum combined power is MAX (xxorder - 1 + xyorder - 1) for the x fit and
+MAX (yxorder - 1 + yyorder - 1) for the y fit.
+.le
+
+The "shift", "xyscale", "rotation", "rscale", and "rxyscale" fitting
+geometries, assume that the cross term switches are set to "none"regardless
+of the values set by the user.  If either of the cross terms parameters is
+set to "half" or "full" and \fIfitgeometry\fR is "general" then a distortion
+surface is fit to the residuals from the linear portion of the fit.
+.le
+
+.ls reject = INDEF
+The rejection limit in units of sigma. The default is no rejection.
+.le
+.ls calctype = "real"
+The precision of coordinate transformation calculations. The options are "real"
+and "double".
+.le
+.ls verbose = yes
+Print messages about the progress of the task?
+.le
+.ls interactive = yes
+Run the task interactively ?
+In interactive mode the user may interact with the fitting process, e.g.
+change the order of the fit, delete points, replot the data etc.
+.le
+.ls graphics = "stdgraph"
+The graphics device.
+.le
+.ls gcommands = ""
+The graphics cursor.
+.le
+
+.ih
+DESCRIPTION
+
+SKYMAP computes the spatial transformation function required to map the
+celestial coordinate system of the reference image \fIreference\fR to
+the celestial coordinate
+system of the input image \fIinput\fR, and stores the computed function in
+the output text database file \fIdatabase\fR.
+The input and reference images may be 1D or 2D but
+must have the same dimensionality. The input image and output
+text database file can be input to the REGISTER or GEOTRAN tasks to
+perform the actual image registration.  SKYMAP assumes that the world
+coordinate systems in the input and reference
+image headers are accurate and that the two systems are compatible, e.g. both
+images have a celestial coordinate system WCS.
+
+SKYMAP computes the required spatial transformation by matching the logical
+x and y pixel coordinates of a grid of points 
+in the input image with the logical x and y pixels coordinates
+of the same grid of points in the reference image,
+using celestial coordinate information stored in the two image headers.
+The coordinate grid consists of \fInx * ny\fR points evenly distributed
+over the logical pixel space of interest in the reference image defined by the
+\fIxmin\fR, \fIxmax\fR, \fIymin\fR, \fIymax\fR parameters.
+The logical x and y reference image pixel coordinates are transformed to
+reference image celestial coordinates using
+world coordinate information stored in the reference image header.
+The reference image celestial coordinates are transformed to
+input image celestial coordinates using world coordinate
+system information in both the reference and the input image headers.
+Finally the input image celestial coordinates are transformed to logical x and y
+input image pixel coordinates using world coordinate system information
+stored in the input image header. The transformation sequence looks
+like the following for an equatorial celestial coordinate system:
+
+.nf
+   (x,y) reference -> (ra,dec) reference  (reference image wcs)
+(ra,dec) reference -> (ra,dec) input      (reference and input image wcs)
+    (ra,dec) input -> (x,y) input         (input image wcs)
+.fi
+
+The computed reference and input logical coordinates and the
+world coordinates are written to temporary coordinates file which is
+deleted on task termination.
+The pixel and celestial coordinates are written using
+the \fIxformat\fR and \fIyformat\fR and the \fIrwxformat\fR, \fIrwyformat\fR,
+\fIwxformat\fR and \fIwxformat\fR
+parameters respectively. If these formats are undefined and, in the
+case of the celestial coordinates a format attribute cannot be
+read from either the reference or the input images, reasonable default
+formats are chosen.
+If the reference and input images are 1D then all the output logical and
+world y coordinates are set to 1.
+
+SKYMAP computes a spatial transformation of the following form.
+
+.nf
+    xin = f (xref, yref)
+    yin = g (xref, yref)
+.fi
+
+The functions f and g are either a power series polynomial or a Legendre or
+Chebyshev polynomial surface of order \fIxxorder\fR and \fIxyorder\fR in x
+and \fIyxorder\fR and \fIyyorder\fR in y.
+
+Several polynomial cross terms options are available. Options "none",
+"half", and "full" are illustrated below for a quadratic polynomial in
+x and y.
+
+.nf
+xxterms = "none", xyterms = "none"
+xxorder = 3, xyorder = 3, yxorder = 3, yyorder = 3
+
+   xin = a11 + a21 * xref + a12 * yref +
+         a31 * xref ** 2 + a13 * yref ** 2
+   yin = a11' + a21' * xref + a12' * yref +
+         a31' * xref ** 2 + a13' * yref ** 2
+
+xxterms = "half", xyterms = "half"
+xxorder = 3, xyorder = 3, yxorder = 3, yyorder = 3
+
+   xin = a11 + a21 * xref + a12 * yref +
+         a31 * xref ** 2 + a22 * xref * yref + a13 * yref ** 2
+   yin = a11' + a21' * xref + a12' * yref +
+         a31' * xref ** 2 + a22' * xref * yref + a13' * yref ** 2
+
+xxterms = "full", xyterms = "full"
+xxorder = 3, xyorder = 3, yxorder = 3, yyorder = 3
+
+   xin = a11 + a21 * xref + a31 * xref ** 2 +
+         a12 * yref + a22 * xref * yref +  a32 * xref ** 2 * yref +
+         a13 * yref ** 2 + a23 * xref *  yref ** 2 +
+         a33 * xref ** 2 * yref ** 2
+   yin = a11' + a21' * xref + a31' * xref ** 2 +
+         a12' * yref + a22' * xref * yref +  a32' * xref ** 2 * yref +
+         a13' * yref ** 2 + a23' * xref *  yref ** 2 +
+         a33' * xref ** 2 * yref ** 2
+.fi
+
+If the \fBfitgeometry\fR parameter is anything other than "general", the
+order parameters assume the value 2 and the cross terms switches assume
+the value "none", regardless of the values set by the user.  The computation
+can be done in either real or double precision by setting the \fIcalctype\fR
+parameter. Automatic pixel rejection may be enabled by setting the \fIreject\fR
+parameter to a positive number other than INDEF.
+
+The transformation computed by the "general" fitting geometry is arbitrary
+and does not necessarily correspond to a physically meaningful model.
+However the computed
+coefficients for the linear term can be given a simple geometrical geometric
+interpretation for all the fitting geometries as shown below.
+
+.nf
+        fitting geometry = general (linear term)
+            xin = a + b * xref + c * yref
+            yin = d + e * xref + f * yref
+
+        fitting geometry = shift
+            xin = a + xref
+            yin = d + yref
+
+        fitting geometry = xyscale
+            xin = a + b * xref
+            yin = d + f * yref
+
+        fitting geometry = rotate
+            xin = a + b * xref + c * yref
+            yin = d + e * xref + f * yref
+            b * f - c * e = +/-1
+            b = f, c = -e or b = -f, c = e
+
+        fitting geometry = rscale
+            xin = a + b * xref + c * yref
+            yin = d + e * xref + f * yref
+            b * f - c * e = +/- const
+            b = f, c = -e or b = -f, c = e
+
+        fitting geometry = rxyscale
+            xin = a + b * xref + c * yref
+            yin = d + e * xref + f * yref
+            b * f - c * e = +/- const
+.fi
+
+
+The coefficients can be interpreted as follows. Xref0, yref0, xin0, yin0
+are the origins in the reference and input frames respectively. Orientation
+and skew are the orientation of the x and y axes and their deviation from
+perpendicularity respectively. Xmag and ymag are the scaling factors in x and
+y and are assumed to be positive.
+
+.nf
+        general (linear term)
+            xrotation = rotation - skew / 2
+            yrotation = rotation + skew / 2
+            b = xmag * cos (xrotation)
+            c = ymag * sin (yrotation)
+            e = -xmag * sin (xrotation)
+            f = ymag * cos (yrotation)
+            a = xin0 - b * xref0 - c * yref0 = xshift
+            d = yin0 - e * xref0 - f * yref0 = yshift
+
+        shift
+            xrotation = 0.0,  yrotation = 0.0
+            xmag = ymag = 1.0
+            b = 1.0
+            c = 0.0
+            e = 0.0
+            f = 1.0
+            a = xin0 - xref0 = xshift
+            d = yin0 - yref0 = yshift
+
+        xyscale
+            xrotation 0.0 / 180.0 yrotation = 0.0
+            b = + /- xmag
+            c = 0.0
+            e = 0.0
+            f = ymag
+            a = xin0 - b * xref0 = xshift
+            d = yin0 - f * yref0 = yshift
+
+        rscale
+            xrotation = rotation + 0 / 180, yrotation = rotation
+            mag = xmag = ymag
+            const = mag * mag
+            b = mag * cos (xrotation)
+            c = mag * sin (yrotation)
+            e = -mag * sin (xrotation)
+            f = mag * cos (yrotation)
+            a = xin0 - b * xref0 - c * yref0 = xshift
+            d = yin0 - e * xref0 - f * yref0 = yshift
+
+        rxyscale
+            xrotation = rotation + 0 / 180, yrotation = rotation
+            const = xmag * ymag
+            b = xmag * cos (xrotation)
+            c = ymag * sin (yrotation)
+            e = -xmag * sin (xrotation)
+            f = ymag * cos (yrotation)
+            a = xin0 - b * xref0 - c * yref0 = xshift
+            d = yin0 - e * xref0 - f * yref0 = yshift
+.fi
+
+
+\fIXmin\fR, \fIxmax\fR, \fIymin\fR and \fIymax\fR define the region of
+validity of the fit as well as the limits of the grid
+in the reference coordinate system.  These parameters are also used to
+reject out of range data before the actual fitting is done.
+
+Each computed transformation is written to the output file \fIdatabase\fR
+in a record whose name is supplied by the user via the \fItransforms\fR
+parameter or set to the name of the corresponding input image. 
+The database file is opened in append mode and new records are written
+to the end of the existing file. If more that one record of the same
+name is written to the database file, the last record written is the
+valid record, i.e. the one that will be used by the REGISTER or
+GEOTRAN tasks.
+
+SKYMAP will terminate with an error if the reference and input images
+are not both either 1D or 2D.
+If the celestial coordinate system information cannot be read from either
+the reference or input image header, the requested transformations
+from the celestial <-> logical coordinate systems cannot be compiled for either
+or both images, or the celestial coordinate systems of the reference and input
+images are fundamentally incompatible in some way, the output logical
+reference and input image coordinates are both set to a grid of points
+spanning the logical pixel space of the input, not the reference image.
+This grid of points defines an identity transformation which will leave
+the input image unchanged if applied by the REGISTER or GEOTRAN tasks.
+
+If \fIverbose\fR is "yes" then messages about the progress of the task
+as well as warning messages indicating potential problems are written to
+the standard output. If \fIresults\fR is set to a file name then the input
+coordinates, the fitted coordinates, and the residuals of the fit are
+written to that file.
+
+SKYMAP may be run interactively by setting the \fIinteractive\fR
+parameter to "yes".
+In interactive mode the user has the option of viewing the fit, changing the
+fit parameters, deleting and undeleting points, and replotting
+the data until a satisfactory
+fit has been achieved.
+
+.ih
+CURSOR COMMANDS
+
+In interactive mode the following cursor commands are currently available.
+
+.nf
+        Interactive Keystroke Commands
+
+?       Print options
+f       Fit the data and graph with the current graph type (g, x, r, y, s)
+g       Graph the data and the current fit
+x,r     Graph the x fit residuals versus x and y respectively
+y,s     Graph the y fit residuals versus x and y respectively
+d,u     Delete or undelete the data point nearest the cursor
+o       Overplot the next graph
+c       Toggle the constant x, y plotting option
+t       Plot a line of constant x, y through the nearest data point
+l       Print xshift, yshift, xmag, ymag, xrotate, yrotate
+q       Exit the interactive curve fitting
+.fi
+
+The parameters listed below can be changed interactively with simple colon
+commands. Typing the parameter name alone will list the current value.
+
+.nf
+	Colon Parameter Editing Commands
+
+:show                           List parameters
+:fitgeometry                    Fitting geometry (shift,xyscale,rotate,
+                                rscale,rxyscale,general)
+:function [value]               Fitting function (chebyshev,legendre,
+                                polynomial)
+:xxorder :xyorder [value]       X fitting function xorder, yorder
+:yxorder :yyorder [value]       Y fitting function xorder, yorder
+:xxterms :yxterms [n/h/f]       X, Y fit cross terms type
+:reject [value]                 Rejection threshold
+.fi
+
+
+.ih
+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:
+ 
+.nf
+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
+.fi
+
+.ih
+REFERENCES
+
+Additional  information  on  IRAF  world  coordinate  systems including
+more detailed descriptions of the "logical", "physical", and "world"
+coordinate systems can be found  in  the  help  pages  for  the  WCSEDIT
+and  WCRESET  tasks. Detailed   documentation   for  the  IRAF  world
+coordinate  system interface MWCS can be found in  the  file
+"iraf$sys/mwcs/MWCS.hlp".  This  file  can  be  formatted  and  printed
+with the command "help iraf$sys/mwcs/MWCS.hlp fi+ | lprint".
+
+Details of the FITS header world coordinate system interface can
+be found in the draft paper "World Coordinate Systems Representations Within the
+FITS Format" by Hanisch and Wells, available from the iraf anonymous ftp
+archive and the draft paper which supersedes it "Representations of Celestial
+Coordinates in FITS" by Greisen and Calabretta available from the NRAO
+anonymous ftp archives.
+
+The spherical astronomy routines employed here are derived from the Starlink
+SLALIB library provided courtesy of Patrick Wallace. These routines
+are very well documented internally with extensive references provided
+where appropriate. Interested users are encouraged to examine the routines
+for this information. Type "help slalib" to get a listing of the SLALIB
+routines, "help slalib opt=sys" to get a concise summary of the library,
+and "help <routine>" to get a description of each routine's calling sequence,
+required input and output, etc. An overview of the library can be found in the
+paper "SLALIB - A Library of Subprograms", Starlink User Note 67.7
+by P.T. Wallace, available from the Starlink archives.
+
+.ih
+EXAMPLES
+
+1. Compute the spatial transformation required to match a radio image to an
+X-ray image of the same field using a 100 point coordinate  grid
+and a simple linear transformation.  Both images have accurate sky
+equatorial world coordinate systems define at different equinoxes.
+Print the output world coordinates
+in the coords file in hh:mm:ss.ss and dd:mm:ss.s format. Run geotran
+on the results to do the actual registration.
+
+.nf
+	cl> skymap radio xray geodb rwxformat=%12.2H rwyformat=%12.1h \
+	    wxformat=%12.2H wyformat=%12.1h interactive-
+
+	cl> geotran radio radio.tran geodb radio
+.fi
+
+2. Repeat the previous command but begin with a higher order fit
+and run the task in interactive mode in order to examine the fit
+residuals.
+
+.nf
+	cl> skymap radio xray geodb rwxformat=%12.2H rwyformat=%12.1h \
+	    wxformat=%12.2H wyformat=%12.1h xxo=4 xyo=4 xxt=half \
+	    yxo=4 yyo=4 yxt=half
+
+            ... a plot of the fit appears
+
+	    ... type x and r to examine the residuals of the x
+                surface fit versus x and y
+
+	    ... type y and s to examine the residuals of the y
+                surface fit versus x and y
+
+	    ... delete 2 deviant points with the d key and
+                recompute the fit with the f key
+
+            ... type q to quit and save the fit
+
+	cl> geotran radio radio.tran geodb radio
+.fi
+
+3. Repeat example 1 but set the transform name specifically.
+
+.nf
+	cl> skymap radio xray geodb trans=m82 rwxformat=%12.2H \
+	    rwyformat=%12.1h wxformat=%12.2H wyformat=%12.1h \
+            interactive-
+
+	cl> geotran radio radio.tran geodb m82
+.fi
+
+.ih
+TIME REQUIREMENTS
+.ih
+BUGS
+.ih
+SEE ALSO
+wcsctran,register,geotran
+.endhelp