akima: interpp – R documentation

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interpp

Pointwise Bivariate Interpolation for Irregular Data

Description

These functions implement bivariate interpolation onto a set of points for irregularly spaced input data. These functions are only for backward compatibility, use interpp instead.

If linear is \codeTRUE, linear interpolation is used in the triangles bounded by data points, otherwise cubic interpolation is done.

If extrap is FALSE, z-values for points outside the convex hull are returned as NA. No extrapolation can be performed for linear interpolation.

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=NULL, z, xo, yo=NULL, linear=TRUE, extrap=FALSE,
        duplicate = "error", dupfun = NULL,
        jitter = 10^-12, jitter.iter = 6, jitter.random = FALSE)

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`
`linear`	logical – indicating wether linear or spline interpolation should be used.
`extrap`	logical flag: should extrapolation be used outside of the convex hull determined by the data points? Not possible for linear interpolation.
`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"`
`jitter`	Jitter of amount of `diff(range(XX))*jitter` (XX=x or y) will be added to coordinates if collinear points are detected. Afterwards interpolation will be tried once again. Note that the jitter is not generated randomly unless `jitter.random` is set to `TRUE`. This ensures reproducable result. `tri.mesh` of package `tripack` uses the same jitter mechanism. That means you can plot the triangulation on top of the interpolation and see the same triangulation as used for interpolation, see examples below.
`jitter.iter`	number of iterations to retry with jitter, amount will be increased in each iteration by `iter^1.5`
`jitter.random`	logical, see `jitter`, defaults to `FALSE`

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.

See interp for more details.

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.

R. J. Renka (1996). Algorithm 751: TRIPACK: a constrained two-dimensional Delaunay triangulation package. ACM Transactions on Mathematical Software. 22, 1-8.

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
## Not run: 
    ## interaction with sp objects:
    library(sp)
    ## take 30 sample points out of meuse grid:
    data(meuse.grid)
    m0 <- meuse.grid[sample(1:3103,30),]
    coordinates(m0) <- ~x+y
    ## interpolate on this 30 points:
    ## note: both "meuse" and "m0" are sp objects
    ## (SpatialPointsDataFrame) !!
    ## arguments z and xo have to named, y has to be omitted!
    ipp <- interpp(meuse,z="zinc",xo=m0)
    spplot(ipp)

## End(Not run)

akima

Interpolation of Irregularly and Regularly Spaced Data

v0.6-2.1

ACM | file LICENSE

Authors

Hiroshi Akima [aut, cph] (Fortran code (TOMS 760, 761, 697 and 433)), Albrecht Gebhardt [aut, cre, cph] (R port (interp* functions), bicubic* functions), Thomas Petzold [ctb, cph] (aspline function), Martin Maechler [ctb, cph] (interp2xyz function + enhancements), YYYY Association for Computing Machinery, Inc. [cph] (covers code from TOMS 760, 761, 697 and 433)

Initial release

2016-12-16