SPLINE(1) SPLINE(1)
October 1996
NAME
spline-interpolate using splines under tension
SYNOPSIS
spline
[infile [outfile]] [options]
DESCRIPTION
spline reads pairs of numbers (x- and y-values) from the standard
input (or the given file), generates a smooth curve through the
points, and writes to the standard output (or given file) points from
the smooth curve. The curve is a spline under tension (see
references), which is somewhat "tighter" than a cubic spline, and less
likely to have spurious inflection points.
A command used to create output data is inserted as a comment,
starting with "#", in the first line of output.
As with graph, each pair of points may optionally be followed by a
comment. If the comment is surrounded by quotes "...", the comment
may contain spaces. The given points, and their comments if any, will
be included in the output. The interpolation may optionally be
restarted after each label, so that a family of curves may be
processed together (see the -b option).
Input lines starting with "#" or ";" are copied to the beginning of
the output file, with ";" replaced by "#", but are otherwise ignored.
A "#" or ";" anywhere else in the line introduces a comment which is
discarded. Other lines not beginning with a number, including blank
lines, are ignored.
If the -c switch is not used, the input points must be from a function
- that is, the x values must be either strictly increasing or strictly
decreasing. The output points will also be from a function. (If the
-b switch is used, this restriction applies only within each segment.)
If the -c switch is used (indicating a general curve), the input
points need not be from a function, but each pair of points must be
separated from the previous pair by a finite distance. (If the -b
switch is used, this restriction applies only within each segment.)
OPTIONS
Options can appear before, among, or after file names provided a file
name cannot be mistaken for the parameter of an option.
-a [step [start]]
Input data contains only y values - generate automatic abscissas
at intervals of step (default 1) starting at start (default 0).
-b break the interpolation at each label. That is, the input curve
is divided into sections with the last point in each section
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SPLINE(1) SPLINE(1)
October 1996
marked by a label (which may be empty: ""). A separate
interpolating curve is to be found for each section. In this
case, the requirements on the number of intervals (specified by
the -n switch or defaulted) and the interpolation range
(specified by the -x switch) are applied to each section
independently.
-c general curve rather than function. In this case, the curve is
parameterized on the polygonal arclength from the first to the
last given point, with the whole length scaled to be 1. Thus,
the values min and max for the -x switch should satisfy 0 <= min
< max <= 1. The -s and -c switches cannot be used together.
-i file
Explicit interpolation at x values given in file. Only 1st
number on each line of file is used - rest of line is ignored.
Lines that don't start with a number are ignored. With the -c
switch, use -ix rather than -i.
-ix file
-iy file
-iz file
Implicit interpolation at x (y, z) values from the file. Only 1st
number on each line of file is used - rest of line is ignored.
Lines that don't start with a number are ignored. Without the -c
switch, use -i rather than -ix.
-n num
interpolate over num intervals (default is 100), yielding n+1
points.
-q Quadruple: increase the number of intervals fourfold.
-s [num [num]]
Specify slopes at beginning and end of curve. Slopes not given
are assumed to be zero. Without the -s switch, slopes are
determined from other information. If only one slope is to be
specified, the other can be given as "n" (for "natural"). The -s
and -c switches cannot be used together.
-t num
Specify tension in interpolating curve. Tension of 50 gives
almost polygonal line, tension of .01 gives almost cubic spline.
Tension must be positive. Default is 1.
-x [min [max]]
Interpolate from min to max only. min and max should be in the
range of the given x values, except that if the -c switch is used
they should satisfy 0 <= min < max <= 1.
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SPLINE(1) SPLINE(1)
October 1996
-xl take log of x values before interpolating, take exponential
afterwards (probably necessary if -xl switch is needed for graph
).
-yl take log of y values before interpolating, take exponential
afterwards (probably necessary if -yl switch is needed for graph
).
-zl take log of z values before interpolating, take exponential
afterwards (implies -3)
-xt -yt -zt
take tanh of x, y, or z values before interpolating, take arc
tanh afterwards. Data values are restricted to (0, 1). (-zt
implies -3).
-3 3D curve: each input line has an x, y, and z
NOTES
Inspired by the Unix routine, but afflicted with creeping featuritis.
REFERENCES
A. K. Cline, "Scalar- and Planar- Valued Curve Fitting Using Splines
Under Tension", Communications of the ACM v 17 n 4 p 218-223 (Apr 74).
Schweikert, D. G. "An interpolation curve using a spline in tension",
J. Math. and Physics v 45 p 312-317 (1966).
SEE ALSO
graph, smooth, dots
AUTHOR
Copyright (c) 1985 - 1992 James R. Van Zandt
Resale forbidden, copying for personal use encouraged.
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