akima (version 0.5-8)

interpp: Pointwise Bivariate Interpolation for Irregular Data

Description

If ncp is zero, linear interpolation is used in the triangles bounded by data points. Cubic interpolation is done if partial derivatives are used. If extrap is FALSE, z-values for points outside the convex hull are returned as NA. No extrapolation can be performed if ncp is zero. The interpp function handles duplicate (x,y) points in different ways. As default it will stop with an error message. But it can give duplicate points an unique z value according to the parameter duplicate (mean,median or any other user defined function). 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 interpp to work.

Usage

interpp(x, y, z, xo, yo, linear=TRUE, extrap=FALSE, duplicate = "error",
dupfun = NULL, ncp)

Arguments

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

xo

vector of x-coordinates of points at which to evaluate the interpolating function.

yo

vector of y-coordinates of points at which to evaluate the interpolating function.

linear

logical -- indicating wether linear or spline interpolation should be used. supersedes old ncp parameter

ncp

deprecated, use parameter linear. Now only used by interpp.old().

meaning was: number of additional points to be used in computing partial derivatives at each data point. ncp must be either

extrap

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

duplicate

indicates how to handle duplicate data points. Possible values are "error" - produces an error message, "strip" - remove duplicate z values, "mean","median","user" - calculate mean ,

dupfun

this function is applied to duplicate points if duplicate="user"

Value

• list with 3 components:
• x
  vector of x-coordinates of output points, the same as the input argument xo.
• y
  vector of y-coordinates of output points, the same as the input argument yo.
• z
  fitted z-values. The value z[i] is computed at the x,y point x[i], y[i].

NOTE

Use interp if interpolation on a regular grid is wanted.

The two versions interpp.old and interpp.new refer to Akimas Fortran code from 1978 and 1996 resp. The call wrapper interpp chooses interpp.old for linear and interpp.new for cubic spline interpolation.

Earlier versions (pre 0.5-1) of interpp used the parameter ncp to choose between linear and cubic interpolation, this is now done by setting the logical parameter linear. Use of ncp is still possible, but is deprecated.

References

Akima, H. (1978). A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points. ACM Transactions on Mathematical Software, 4, 148-164.

Akima, H. (1996). Algorithm 761: scattered-data surface fitting that has the accuracy of a cubic polynomial. ACM Transactions on Mathematical Software, 22, 362-371.

See Also

contour, image, approxfun, splinefun, outer, expand.grid, interp, aspline.

Examples

data(akima)
# linear interpolation at points (1,2), (5,6) and (10,12)
akima.lip<-interpp(akima$x, akima$y, akima$z,c(1,5,10),c(2,6,12))
akima.lip$z
# spline interpolation
akima.sip<-interpp(akima$x, akima$y, akima$z,c(1,5,10),c(2,6,12),
  linear=FALSE)
akima.sip$z