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Last data update: 2014.03.03

R: Bivariate Interpolation for Data on a Rectangular grid

bicubic

R Documentation

Bivariate Interpolation for Data on a Rectangular grid

Description

The description in the Fortran code says:

This subroutine performs interpolation of a bivariate function, z(x,y), on a rectangular grid in the x-y plane. It is based on the revised Akima method.

In this subroutine, the interpolating function is a piecewise function composed of a set of bicubic (bivariate third-degree) polynomials, each applicable to a rectangle of the input grid in the x-y plane. Each polynomial is determined locally.

This subroutine has the accuracy of a bicubic polynomial, i.e., it interpolates accurately when all data points lie on a surface of a bicubic polynomial.

The grid lines can be unevenly spaced.

Usage

bicubic(x, y, z, x0, y0)

Arguments

`x`	a vector containing the `x` coordinates of the rectangular data grid.
`y`	a vector containing the `y` coordinates of the rectangular data grid.
`z`	a matrix containing the `z[i,j]` data values for the grid points (`x[i]`,`y[j]`).
`x0`	vector of `x` coordinates used to interpolate at.
`y0`	vector of `y` coordinates used to interpolate at.

Details

This functiuon is a R interface to Akima's Rectangular-Grid-Data Fitting algorithm (TOMS 760). The algorithm has the accuracy of a bicubic (bivariate third-degree) polynomial.

Value

This function produces a list of interpolated points:

`x`	vector of `x` coordinates.
`y`	vector of `y` coordinates.
`z`	vector of interpolated data `z`.

If you need an output grid, see bicubic.grid.

Note

Use interp for the general case of irregular gridded data!

References

Akima, H. (1996) Rectangular-Grid-Data Surface Fitting that Has the Accuracy of a Bicubic Polynomial, J. ACM 22(3), 357-361

Examples

data(akima760)
# interpolate at the diagonal of the grid [0,8]x[0,10]
akima.bic <- bicubic(akima760$x,akima760$y,akima760$z,
                     seq(0,8,length=50), seq(0,10,length=50))
plot(sqrt(akima.bic$x^2+akima.bic$y^2), akima.bic$z, type="l")


##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function (x, y, z, x0, y0) 
{
    nx <- length(x)
    ny <- length(y)
    if (dim(z)[1] != nx) 
        stop("dim(z)[1] and length of x differs!")
    if (dim(z)[2] != ny) 
        stop("dim(z)[2] and length of y differs!")
    n0 <- length(x0)
    if (length(y0) != n0) 
        stop("length of y0 and x0 differs!")
    ret <- .Fortran("rgbi3p", md = as.integer(1), nxd = as.integer(nx), 
        nyd = as.integer(ny), xd = as.double(x), yd = as.double(y), 
        zd = as.double(z), nip = as.integer(n0), xi = as.double(x0), 
        yi = as.double(y0), zi = double(n0), ier = integer(1), 
        wk = double(3 * nx * ny), PACKAGE = "akima")
    list(x = x0, y = y0, z = ret$zi)
  }