SPLINE(1G) SPLINE(1G)
NAME
spline - interpolate smooth curve
SYNOPSIS
spline [ options ]
DESCRIPTION
Spline takes pairs of numbers from the standard input as
abscissas and ordinates of a function. It produces a
similar set, which is approximately equally spaced and
includes the input set, on the standard output. The cubic
spline output (R. W. Hamming, Numerical Methods for
Scientists and Engineers, 2nd ed., pp. 349ff) has two
continuous derivatives, and sufficiently many points to look
smooth when plotted.
The following options are recognized, each as a separate
argument:
-a Supply abscissas automatically (they are missing from
the input); spacing is given by the next argument, or
is assumed to be 1 if next argument is not a number.
-k The constant k used in the boundary value computation:
tdefine prime2 'sup down 20 ''' ndefine prime2 'sup '''
y sub 0 prime2 ~=~ ky sub 1 prime2 , ~~~~ y sub n
prime2 ~=~ ky sub n-1 prime2
is set by the next argument (default k = 0).
-n Space output points so that approximately n intervals
occur between the lower and upper x limits (default n =
100).
-p Make output periodic, i.e., match derivatives at ends.
First and last input values should normally agree.
-x Next 1 (or 2) arguments are lower (and upper) x limits.
Normally, these limits are calculated from the data.
Automatic abscissas start at lower limit (default 0).
EXAMPLE
spline -n 10 > spline.out
0 0
1 2
2 4
3 9
will create the file "spline.out" with the contents:
3.000000 8.999999
2.666667 7.096296
Page 1 (last mod. 8/20/87)
SPLINE(1G) SPLINE(1G)
2.333333 5.370370
2.000000 4.000000
1.666667 3.096296
1.333333 2.503703
1.000000 2.000000
0.666667 1.407407
0.333333 0.725926
0.000000 0.000000
DIAGNOSTICS
When data is not strictly monotone in x, spline reproduces
the input without interpolating extra points.
BUGS
A limit of 1,000 input points is enforced silently.
ORIGIN
Silicon Graphics, Inc.
Page 2 (last mod. 8/20/87)