R: Bilinear Interpolation for Data on a Rectangular grid

bilinear {akima} | R Documentation

## Bilinear Interpolation for Data on a Rectangular grid

### Description

This is an implementation of a bilinear interpolating function.

For a point (x0,y0) contained in a rectangle (x1,y1),(x2,y1), (x2,y2),(x1,y2) and x1<x2, y1<y2, the first step is to get z() at locations (x0,y1) and (x0,y2) as convex linear combinations z(x0,y*)=a*z(x1,y*)+(1-a)*z(x2,y*) where a=(x2-x1)/(x0-x1) for y*=y1,y2. In a second step z(x0,y0) is calculated as convex linear combination between z(x0,y1) and z(x0,y2) as z(x0,y1)=b*z(x0,y1)+(1-b)*z(x0,y2) where b=(y2-y1)/(y0-y1).

Finally, z(x0,y0) is a convex linear combination of the z values at the corners of the containing rectangle with weights according to the distance from (x0,y0) to these corners.

The grid lines can be unevenly spaced.

### Usage

    bilinear(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.

### 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 `bilinear.grid`.

### Note

Use `interpp` for the general case of irregular gridded data!

### References

Pascal Getreuer, Linear Methods for Image Interpolation, Image Processing On Line, 2011, http://www.ipol.im/pub/art/2011/g_lmii/article.pdf

### See Also

`interp`, `bilinear.grid`, `bicubic.grid`

### Examples

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

[Package akima version 0.6-2 Index]