NAME

spline − interpolate smooth curve

SYNOPSIS

spline [ option ] ... 

DESCRIPTION

Spline takes pairs of numbers from the standard input as abcissas and ordinates of a function.  Spline produces a similar set, on the standard output, which is approximately equally spaced and includes the input set.  The cubic spline output R. W. Hamming, Numerical Methods for Scientists and Engineers, 2nd ed., 349ff has two continuous derivatives, and a sufficient amount of points to appear smooth when plotted, (for example, by graph(1)).

The following options are each recognized 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 following constant k used in the boundary value computation

y′′0=ky′′1,y′′n=ky′′n−1

is set by the next argument.  By, 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 abcissas start at lower limit (default 0). 

SEE ALSO

graph(1)

DIAGNOSTICS

When data is not strictly monotone in x, spline reproduces the input without interpolating additional points. 

BUGS

A limit of 1000 input points is enforced silently. 

November 01, 1983  —  %W%%Q%%Y%