akima (version 0.6-3.4)

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,
        remove = !linear)

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 SpatialPointsDataFrames 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

remove

logical, indicates whether Akimas removal of thin triangles along the border of the convex hull should be performed, experimental setting! defaults to !linear, so it will be left out for linear interpolation by default. For some point configurations it is the only available option to skip this removal step.

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.

R. J. Renka and Ron Brown (1998). Remark on algorithm 761. ACM Transactions on Mathematical Software. 24, 383-385.

See Also

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

Examples

# NOT RUN {
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 at the same locations
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 given, y has to be omitted!
    ipp <- interpp(meuse,z="zinc",xo=m0)
    spplot(ipp)
# }