.th SPLINE VI 5/15/74
.sh NAME
spline \*- interpolate smooth curve
.sh SYNOPSIS
.bd spline
[ option ] ...
.sh DESCRIPTION
.it Spline
takes pairs of numbers from the standard input as abcissas 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,
.ft I
Numerical Methods for Scientists and Engineers,
.ft R
2nd ed., 349ff)
has two continuous derivatives,
and sufficiently many points to look smooth when plotted, for
example by
.it plot
(I).
.s3
The following options are recognized,
each as a separate argument.
.s3
.lp +5 5
\fBa\fR	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.
.s3
.lp +5 5
\fBk\fR	The constant \fIk\fR used in the boundary value computation
.s3
.if n .ig
.ti +1.5i
.ds ' \h'-\w'\(fm\(fm'u'
.EQ
.nr 99 \n(.s
.nr 98 \n(.f
'ps 10
.ft I
.ds 11 "y\(fm\(fm
.nr 11 \w'\*(11'
.ds 12 "\*'
.nr 12 \w'\*(12'
'ps 8
.ds 13 "\fR0\fP
.nr 13 \w'\*(13'
.as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
'ps 10
.nr 12 \n(12+\n(13+\w'\s8\|'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|=\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "ky\(fm\(fm
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\*'
.nr 12 \w'\*(12'
'ps 8
.ds 13 "\fR1\fP
.nr 13 \w'\*(13'
.as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
'ps 10
.nr 12 \n(12+\n(13+\w'\s8\|'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 ",
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "y\(fm\(fm
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\*'
.nr 12 \w'\*(12'
'ps 8
.ds 13 "n
.nr 13 \w'\*(13'
.as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
'ps 10
.nr 12 \n(12+\n(13+\w'\s8\|'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|=\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\|\|
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "ky\(fm\(fm
.nr 12 \w'\*(12'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 12 "\*'
.nr 12 \w'\*(12'
'ps 8
.ds 13 "n\|\(mi\|\fR1\fP
.nr 13 \w'\*(13'
.as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
'ps 10
.nr 12 \n(12+\n(13+\w'\s8\|'
.as 11 "\*(12
.nr 11 \w'\*(11'
.ds 11 \x'0'\fI\*(11\s\n(99\f\n(98
.ne 78u
\*(11
'ps \n(99
.ft \n(98
.EN
..
.if t .ig
.ce
(2nd deriv. at end) = k*(2nd deriv. next to end)
..
.s3
.br
is set by the next argument.
By default \fIk\fR = 0.
.s3
.lp +5 5
\fBn\fR	Space output points
so that approximately
.it n
points occur between the lower and upper
.it x
limits.
(Default
.it n
= 100.)
.s3
.lp +5 5
\fBp\fR	Make output periodic, i.e. match
derivatives at ends.
First and last input values should normally agree.
.s3
.lp +5 5
\fBx\fR	Next 
1 (or 2) arguments are lower (and upper) 
.it x
limits.
Normally these limits are calculated from the data.
Automatic abcissas start at lower limit
(default 0).
.i0
.sh "SEE ALSO"
plot (I)
.sh AUTHOR
M. D. McIlroy
.sh BUGS
A limit of 1000 input points is enforced silently.