R: Pointwise Bivariate Interpolation for Irregular Data

interpp.old {akima}

R Documentation

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.old(x, y, z, xo, yo, ncp = 0, extrap = FALSE,
                    duplicate = "error", dupfun = NULL)
interpp.new(x, y, z, xo, yo, extrap = FALSE,
                    duplicate = "error", dupfun = NULL)

Arguments

`x`	vector of x-coordinates of data points or a `SpatialPointsDataFrame` object. Missing values are not accepted.
`y`	vector of y-coordinates of data points. Missing values are not accepted. If left as NULL indicates that `x` should be a `SpatialPointsDataFrame` and `z` names the variable of interest in this dataframe.
`z`	vector of z-coordinates of data points or a character variable naming the variable of interest in the `SpatialPointsDataFrame` `x`. Missing values are not accepted. `x`, `y`, and `z` must be the same length (execpt if `x` is a `SpatialPointsDataFrame`) 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).
`xo`	vector of x-coordinates of points at which to evaluate the interpolating function. If `x` is a `SpatialPointsDataFrame` this has also to be a `SpatialPointsDataFrame`.
`yo`	vector of y-coordinates of points at which to evaluate the interpolating function. If operating on `SpatialPointsDataFrame`s this is left as `NULL`
`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 `0` (partial derivatives are not used, = linear interpolation), or at least 2 but smaller than the number of data points (and smaller than 25).
`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 , median or user defined function of duplicate z values.
`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]`.

If input is SpatialPointsDataFrame than an according SpatialPointsDataFrame is returned.

NOTE

Use interp if interpolation on a regular grid is wanted.

The two versions interpp.old and interpp.new are now deprecated, use interpp instead, see details there.

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.