R: Bilinear Interpolation for Data on a Rectangular grid

bilinear {interp} | 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

This function was part of the akima package but not related to any of Akimas algorithms and under GPL. So it could be transfered into the interp package without changes.

### 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`

### Examples

    data(akima474)
    # interpolate at the diagonal of the grid [0,8]x[0,10]
    akima.bil <- bilinear(akima474$x,akima474$y,akima474$z,
                         seq(0,8,length=50), seq(0,10,length=50))
    plot(sqrt(akima.bil$x^2+akima.bil$y^2), akima.bil$z, type="l")

[Package interp version 1.1-1 Index]