V10/man/mana/spline.1

.TH SPLINE 1
.CT 1 numbers graphics
.SH NAME
spline \- fit a curve
.SH SYNOPSIS
.B spline
[
.I option ...
]
.SH DESCRIPTION
.I Spline
is a filter that interpolates extra points in an
input list suitable for
.IR graph (1).
It is useful for making
smooth-looking curves with 
.I graph
or with
.I grap (1).
.PP
The following options are recognized,
each as a separate argument.
.TP
.B  -a
Similar to
.IR graph (1).
Supply abscissas automatically; no
.IR x -values
appear in the input.
Spacing is given by the next
argument (default 1).
A second optional argument is the starting point for
automatic abscissas (default 0,
or the lower limit given by
.BR -x ).
.TP
.B -x
Similar to
.I graph.
Next 1 (or 2) arguments are lower (and upper)
.I x
limits.
Normally these quantities are determined automatically.
.TP
.B  -k
The constant
.I k 
used in the boundary value computation
.IP
.if n .ig
.EQ
y sub 0 sup {prime prime}~=~ky sub 1 sup {prime prime} , ~~~
y sub n sup {prime prime}~=~ky sub n-1 sup {prime prime} , ~~~
.EN
..
.if t .ig
.ce
(2nd deriv. at end) = k*(2nd deriv. next to end)
..
.IP
is set by the next argument.
(Default
.I k
= 0.)
.TP
.B  -n
Space output points
so that approximately
.I n
intervals occur between the lower and upper
.I x
limits.
(Default
.I n
= 100.)
.TP
.B  -p
Make output periodic, i.e. match
derivatives at ends.
First and last input values should normally agree.
.SH SEE ALSO
.IR graph (1),
.IR grap (1),
.IR port (3)
.SH DIAGNOSTICS
When data are not strictly monotone in
.I x,
.I spline
simply reproduces its input.
.SH BUGS
.I Spline
quietly discards points after the first 1000.
.br
.I Spline's
curves exhibit the classic ills of piecewise cubics.