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TENSIONED-SPLINE nfit tension)
Default: FIT B-SPLINE 251 0 0 0
Request that subsequent POLYLINE and POLYGON (but not POLYMARKER or
LINE) data which is plotted be fit to a cubic B-spline, Bezier curve,
or tensioned spline before plotting. The subcommand NONE can be used
to cancel any existing fit option. The fitting methods can be used for
data forming closed curves or multi-valued curves, as well as for
single-valued functions. Caution should be employed with polygon fits,
since the time required to fill a polygon with a pattern is
proportional to the number of vertices. Reasonable defaults are
provided for the numeric parameters, so that in most cases, simply
specifying "FIT method-name" will suffice. See the abstracts of
routines FITBS3, FITBZ3, FITPC3, and FITPO3 for details of the fitting
methods used.
The value nfit specifies the number of points to compute; it is limited
by the size of an internal buffer (currently 1000 points) and will be
reduced if too large. If nfit is smaller than the number of data
points, the fit will be suppressed.
With the B-spline and Bezier curve fits, the curve will not in general
pass through the data points, but will lie inside their convex hull.
The convex hull of a set of points is simply the smallest enclosing
polygon (or polyhedron in 3-D) which has no interior angles exceeding
180 degrees.
The three parameters k1, kn, and kextra define the number of times the
first (k1) and last (kn) points should be implicitly repeated, and the
number of extra points (kextra) to be implicitly generated by wrapping
around from the last to the first. Values of k1 = kn = 1 will ensure
that the curve starts at the first point and ends at the last point.
With a B-spline fit for polygons, the actual values of k1, kn, and
kextra will be ignored, and values of 0, 0, and 3, respectively, will
be assumed in order to obtain a closed curve.
With the tensioned spline fit, and in contrast to the B-spline and
Bezier fits, the curve will pass through each data point, and as the
tension factor is increased, the curve between data points will
approach a straight line segment. This flexibility makes it possible
to smooth out inflections which are often present with ordinary
polynomial spline fits. A tension factor of 0 gives a cubic spline, a
factor of 1 is normal, and a factor as large as 50 will give straight
line segments.