interp(x, y, z, xo=<<see below>>, yo=<<see below>>, ncp=0, extrap=F)

x:

vector of x-coordinates of data points. Missing values are not accepted.

y:

vector of y-coordinates of data points. Missing values are not accepted.

z:

vector of z-coordinates of data points. Missing values are not accepted.

x, y, and z must be the same length and may contain no fewer than four points. The points of x and y cannot be collinear, i.e, they cannot fall on the same line (two vectors x and y such that y = ax + b for some a, b will not be accepted). interp is meant for cases in which you have x, y values scattered over a plane and a z value for each. If, instead, you are trying to evaluate a mathematical function, or get a graphical interpretation of relationships that can be described by a polynomial, try outer().

xo:

vector of x-coordinates of output grid. The default is 40 points evenly spaced over the range of x. If extrapolation is not being used (extrap=F, the default), xo should have a range that is close to or inside of the range of x for the results to be meaningful.

yo:

vector of y-coordinates of output grid. The default is 40 points evenly spaced over the range of y. If extrapolation is not being used (extrap=F, the default), yo should have a range that is close to or inside of the range of y for the results to be meaningful.

ncp:

number of additional points to be used in computing partial derivatives at each data point. ncp must be either 0 (partial derivatives are not used), or at least 2 but smaller than the number of data points.

extrap:

logical flag: should extrapolation be used outside of the convex hull determined by the data points?

x:

vector of x-coordinates of output grid, the same as the input argument xo, if present. Otherwise, a vector 40 points evenly spaced over the range of the input x.

y:

vector of y-coordinates of output grid, the same as the input argument yo, if present. Otherwise, a vector 40 points evenly spaced over the range of the input x.

z:

matrix of fitted z-values. The value z[i,j] is computed at the x,y point x[i], y[j]. z has dimensions length(x) times length(y) (length(xo) times length(yo)).

The interp function can not handle duplicate (x,y) points (since it wouldnt know what z value to assign at such points). If you have such data, you need to reduce each duplicate point to a single point - giving it, perhaps, the mean or median of the corresponding z values. Or, if your z data is relatively smooth, you can use jitter() on your x or y data.

The triangulation scheme used by interp works well if x and y have similar scales but will appear stretched if they have very different scales. The spreads of x and y must be within four orders of magnitude of each other for interp to work.

# an example with duplicate (x,y) points in the data
airtemp.jit <- jitter(air$temperature)
air.jit <- interp(air$radiation, airtemp.jit, air$ozone) # gives error

#an example averaging the z data over duplicate (x,y) points
f <-
function(x = air$temperature, y = air$radiation, z = air$ozone, FUN = median)
{
        xy <- paste(x, y, sep = ",")
        i <- match(xy, xy)
        z.smoothed <- unlist(lapply(split(z, i), FUN))
        ord <- !duplicated(xy)
        data.frame(x = x[ord], y = y[ord], z = z.smoothed)
}
air.smooth<- f()
air.grid <-  interp(air.smooth$x, air.smooth$y, air.smooth$z)

oz <- interp(ozone.xy$x, ozone.xy$y, ozone.median)
contour(oz)    #contour plot

#example changing xo and yo to get very fine grid
akima.smooth<- interp(akima.x, akima.y, akima.z,
      xo= seq(0,25, length=100),  yo= seq(0,20, length=100))
persp(akima.smooth)