# Interpolation Interpolation methods, including linear, spline, and cubic interpolation. ```r interp1(x, y, xi, method = c("linear", "nearest", "pchip", "cubic", "spline"), extrap = NA, ...) ``` ## Arguments - `x,y`: vectors giving the coordinates of the points to be interpolated. `x` is assumed to be strictly monotonic. - `xi`: points at which to interpolate. - `method`: one of `"linear"`, `"nearest"`, `"pchip"`, `"cubic"`, `"spline"`. - `extrap`: if `TRUE` or `'extrap'`, then extrapolate values beyond the endpoints. If `extrap` is a number, replace values beyond the endpoints with that number (defaults to `NA`). - ``: for `method='spline'`, additional arguments passed to `splinefun`. ## Details The following methods of interpolation are available: `'nearest'`: return nearest neighbour `'linear'`: linear interpolation from nearest neighbours `'pchip'`: piecewise cubic hermite interpolating polynomial `'cubic'`: cubic interpolation from four nearest neighbours `'spline'`: cubic spline interpolation--smooth first and second derivatives throughout the curve ## Returns The interpolated signal, an array of `length(xi)`. ## References Octave Forge [https://octave.sourceforge.io/](https://octave.sourceforge.io/) ## Author(s) Original Octave version by Paul Kienzle pkienzle@user.sf.net . Conversion to R by Tom Short. ## See Also `approx`, `filter`, `resample`, `interp`, `spline` ## Examples ```r xf <- seq(0, 11, length=500) yf <- sin(2*pi*xf/5) #xp <- c(0:1,3:10) #yp <- sin(2*pi*xp/5) xp <- c(0:10) yp <- sin(2*pi*xp/5) extrap <- TRUE lin <- interp1(xp, yp, xf, 'linear', extrap = extrap) spl <- interp1(xp, yp, xf, 'spline', extrap = extrap) pch <- interp1(xp, yp, xf, 'pchip', extrap = extrap) cub <- interp1(xp, yp, xf, 'cubic', extrap = extrap) near <- interp1(xp, yp, xf, 'nearest', extrap = extrap) plot(xp, yp, xlim = c(0, 11)) lines(xf, lin, col = "red") lines(xf, spl, col = "green") lines(xf, pch, col = "orange") lines(xf, cub, col = "blue") lines(xf, near, col = "purple") ```

interp1 function