R: Bicubic Interpolation for Data on a Rectangular grid

bicubic.grid {akima} | R Documentation

## Bicubic 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.grid(x,y,z,xlim=c(min(x),max(x)),ylim=c(min(y),max(y)),
                 nx=40,ny=40,dx=NULL,dy=NULL)

### 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]`).
`xlim` | vector of length 2 giving lower and upper limit for range `x` coordinates used for output grid.
`ylim` | vector of length 2 giving lower and upper limit for range of `y` coordinates used for output grid.
`nx` | output grid dimension in `x` direction.
`ny` | output grid dimension in `y` direction.
`dx` | output grid spacing in `x` direction, not used by default, overrides `nx` if specified.
`dy` | output grid spacing in `y` direction, not used by default, overrides `ny` if specified..

### 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 grid of interpolated points, feasible to be used directly with `image` and `contour`:

`x` | vector of `x` coordinates of the output grid.
`y` | vector of `y` coordinates of the output grid.
`z` | matrix of interpolated data for the output 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

### See Also

`interp`, `bicubic`

### Examples

    data(akima760)
    # interpolate at a grid [0,8]x[0,10]
    akima.bic <- bicubic.grid(akima760$x,akima760$y,akima760$z)
    zmin <- min(akima.bic$z, na.rm=TRUE)
    zmax <- max(akima.bic$z, na.rm=TRUE)
    breaks <- pretty(c(zmin,zmax),10)
    colors <- heat.colors(length(breaks)-1)
    image(akima.bic, breaks=breaks, col=colors)
    contour(akima.bic, levels=breaks,  add=TRUE)

[Package akima version 0.6-2 Index]