FITCOORDS Database

The FITCOORDS fits are stored in text files in the subdirectory given by the "database" parameter. The name of the file is fc<fitname> where <fitname> is the specified fit name. The database text file contains blocks of lines beginning with a time stamp followed by line with the "begin" keyword. The value following "begin" is the fit name, which is often the name of the image used for the fit. If there is more than one block with the same fit name then the last one is used.

The "task" keyword will has the value "fitcoords" and the "axis" keyword identifies the axis to which the surface fit applies. An axis of 1 refers to the first or x axis (the first dimension of the image) and 2 refers to the second or y axis.

The "surface" keyword specifies the number of coefficients for the surface fit given in the following lines . The surface fit is produced by an IRAF math package called "gsurfit". The coefficients recorded in the database are intented to be internal to that package. However the following describes how to interpret the coefficients.

The first 8 lines specify:

   function - Function type (1=chebyshev, 2=legendre)
     xorder - X "order" (highest power of x)
     yorder - Y "order" (highest power of y)
     xterms - Cross-term type (always 1 for FITCOORDS)
       xmin - Minimum x over which the fit is defined
       xmax - Maximum x over which the fit is defined
       ymin - Minimum y over which the fit is defined
       ymax - Maximum y over which the fit is defined

The polynomial coefficients follow in array order with the x index varying fastest:

	C00
	C10
	C20
	...
	C<xorder-1>0
	C01
	C11
	C21
	...
	C<xorder-1>1
	...
	C<xorder-1><yorder-1>

The surface fitting functions have the form

	fit(x,y) = Cmn * Pmn

where the Cmn are the coefficients of the polynomials terms Pmn, and the Pmn are defined as follows:

Chebyshev: Pmn = Pm(xnorm) * Pn(ynorm)

	   xnorm = (2 * x - (xmax + xmin)) / (xmax - xmin)
	   ynorm = (2 * y - (ymax + ymin)) / (ymax - ymin)

	   P0(xnorm) = 1.0
	   P1(xnorm) = xnorm
	   Pm+1(xnorm) = 2.0 * xnorm * Pm(xnorm) - Pm-1(xnorm) 

	   P0(ynorm) = 1.0
	   P1(ynorm) = ynorm
	   Pn+1(ynorm) = 2.0 * ynorm * Pn(ynorm) - Pn-1(ynorm) 

Legendre:  Pmn = Pm(xnorm) * Pn(ynorm)

	   xnorm = (2 * x - (xmax + xmin)) / (xmax - xmin)
	   ynorm = (2 * y - (ymax + ymin)) / (ymax - ymin)

	   P0(xnorm) = 1.0
	   P1(xnorm) = xnorm
	   Pm+1(xnorm) = ((2m+1)*xnorm*Pm(xnorm)-m*Pm-1(xnorm))/(m+1)   

	   P0(ynorm) = 1.0
	   P1(ynorm) = ynorm
	   Pn+1(ynorm) = ((2n+1)*ynorm*Pn(ynorm)-n*Pn-1(ynorm))/(n+1)   

Notice that the x and y values are first normalized to the interval -1 to 1 over the range of the surface as given by the xmin, xmax, ymin, and ymax elements of the database description.