## Interpolating Splines

## Usage

    splinefun(x, y, method = "fmm")
    spline(x, y, n = 3*length(x), method = "fmm",
           xmin = min(x), xmax = max(x))

## Arguments

`x,y` | vectors giving the coordinates of the points to be interpolated. Alternatively a single plotting structure can be specified.
`method` | specifies the type of spline to be used. Possible values are `"fmm"`, `"natural"` and `"periodic"`.
`n` | interpolation takes place at `n` equally spaced points spanning the interval [`xmin`, `xmax`].
`xmin` | left-hand endpoint of the interpolation interval.
`xmax` | right-hand endpoint of the interpolation interval.

## Description

`spline` performs cubic spline interpolation of the given data points. It returns a list containing components `x` and `y` which give the ordinates where interpolation took place and the interpolated values.

`splinefun` returns a function which will perform cubic spline interpolation of the given data points. This is often more useful than `spline`.

If `method="fmm"`, the spline used is that of Forsythe, Malcolm and Moler (an exact cubic is fitted through the four points at each end of the data, and this is used to determine the end conditions). Natural splines are used when `method="natural"`, and periodic splines when `method="periodic"`.

## References

Forsythe, G. E., M. A. Malcolm and C. B. Moler (1977). Computer Methods for Mathematical Computations.

## See Also

`approx` and `approxfun` for constant and linear interpolation.

## Examples

    op <- par(mfrow = c(2,1), mgp = c(2,.8,0), mar = .1+c(3,3,3,1))
    n <- 9
    x <- 1:n
    y <- rnorm(n)
    plot(x, y, main = paste("spline[fun](.) through",n,"points"))
    lines(spline(x, y))
    lines(spline(x, y, n = 201), col = 2)

    y <- (x-6)^2
    plot(x, y, main = "spline(.) -- 3 methods")
    lines(spline(x, y, n = 201), col = 2)
    lines(spline(x, y, n = 201, method = "natural"), col = 3)
    lines(spline(x, y, n = 201, method = "periodic"), col = 4)
    legend(6,25, c("fmm","natural","periodic"), col=2:4, lty=1)

    f <- splinefun(x, y)
    ls(envir = environment(f))
    splinecoef <- eval(expression(z), envir = environment(f))
    curve(f(x), 1, 10, col = "green", lwd = 1.5)
    points(splinecoef, col = "purple", cex = 2)
    par(op)

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