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+.help surfit Aug84 "Math Package"
+
+.ih
+NAME
+surfit -- set of routines for fitting gridded surface data
+
+
+.ih
+SYNOPSIS
+
+The surface is defined in the following way. The x and y values are
+assumed to be integers and lie in the range 0 <= x <= ncols + 1 and
+0 <= y <= nlines + 1. The package prefix is for image surface fit.
+Package routines with a prefix followed by l operate on individual
+image lines only.
+
+.nf
+        isinit	(sf, surf_type, xorder, yorder, xterms, ncols, nlines)
+	iszero	(sf)
+       islzero	(sf, lineno)
+      islaccum	(sf, cols, lineno, z, w, ncols, wtflag)
+      islsolve	(sf, lineno, ier)
+        islfit	(sf, cols, lineno, z, w, ncols, wtflag, ier)
+      islrefit	(sf, cols, lineno, z, w, ier)
+       issolve	(sf, lines, nlines, ier)
+     isresolve	(sf, lines, ier)
+    z = iseval	(sf, x, y)
+      isvector	(sf, x, y, zfit, npts)
+        issave	(sf, surface)
+     isrestore	(sf, surface)
+        isfree	(sf)
+.fi
+
+.ih
+DESCRIPTION
+
+The SURFIT package provides a set of routines for fitting surfaces to functions
+linear in their coefficients using the tensor product method and least squares
+techniques. The basic numerical
+technique employed is the solution of the normal equations by the Cholesky
+method.
+
+.ih
+NOTES
+
+The following series of steps illustrates the use of the package.
+
+.ls 4
+.ls (1)
+Include an include <math/surfit.h> statement in the calling program to make the
+SURFIT package definitions available to the user program.
+.le
+.ls (2)
+Call ISINIT to initialize the surface fitting parameters.
+.le
+.ls (3)
+Call ISLACCUM to select a weighting function and accumulate data points
+for each line into the appropriate arrays and vectors. Call ISLSOLVE
+to compute the coefficients in x for each line. The coefficients are
+stored inside SURFIT. Repeat this procedure for each line. ISLACCUM
+and SFLSOLVE can be combined by a call to SFLFIT. If the x values
+and weights remain the same from line to line ISLREFIT can be called.
+.le
+.ls (4)
+Call ISSOLVE to solve for the surface coefficients.
+.le
+.ls (5)
+Call ISEVAL or ISVECTOR to evaluate the fitted surface at the x and y
+value(s) of interest.
+.le
+.ls (6)
+Call ISFREE to release the space allocated for the fit.
+.le
+.le
+
+.ih
+EXAMPLES
+
+.nf
+Example 1: Fit a 2nd order Lengendre polynomial in x and y to an image
+and output the fitted image
+
+include <imhdr.h>
+include <math/surfit.h>
+
+ 	
+	old = immap (old_image, READ_ONLY, 0)
+	new = immap (new_image, NEW_COPY, 0)
+	
+	ncols = IM_LEN(old, 1)
+	nlines = IM_LEN(old, 2)
+	
+	# initialize surface fit
+	call isinit (sf, LEGENDRE, 3, 3, YES, ncols, nlines)
+        
+	# allocate space for lines, columns and weight arrays
+	call malloc (cols, ncols, TY_INT)
+	call malloc (lines, nlines, TY_INT)
+	call malloc (weight, ncols, TY_REAL)
+
+	# initialize lines and columns arrays
+	do i = 1, ncols
+	    Memi[cols - 1 + i] = i
+	do i = 1, nlines
+	    Memi[lines - 1 + i] = i
+
+	# fit the surface in x line by line
+	call amovkl (long(1), v, IM_MAXDIM)
+	do i = 1, nlines {
+	    if (imgnlr (old, inbuf, v) == EOF)
+		call error (0, "Error reading image.")
+	    if (i == 1) {
+		call islfit (sf, Memi[cols], i, Memr[inbuf], Memr[weight],
+				ncols, SF_WTSUNIFORM, ier)
+		if (ier != OK)
+		    ...
+	    } else
+		call islrefit (sf, Memi[cols], i, Memr[inbuf], Memr[weight],
+				ier)
+	}
+
+	# solve for surface coefficients
+	call issolve (sf, Memi[lines], nlines, ier)
+
+	# free space used in fitting arrays
+	call mfree (cols, TY_INT)
+	call mfree (lines, TY_INT)
+	call mfree (weight, TY_REAL)
+
+	# allocate space for x and y arrays
+	call malloc (x, ncols, TY_REAL)
+	call malloc (y, ncols, TY_REAL)
+
+	# intialize z array
+	do i = 1, ncols
+	    Memr[x - 1 + i] = real (i)
+
+	# create fitted image
+	call amovkl (long(10, v, IM_MAXDIM)
+	do i = 1, nlines {
+	    if (impnlr (new, outbuf, v) == EOF)
+		call error (0, "Error writing image.")
+	    call amovkr (real (i), Memr[y], ncols)
+	    call isvector (sf, Memr[x], Memr[y], Memr[outbuf], ncols)
+	}
+
+	# close files and cleanup
+	call mfree (x, TY_REAL)
+	call mfree (y, TY_REAL
+
+	call isfree (sf)
+
+	call imunmap (old)
+	call imunmap (new)
+
+.fi
+.endhelp