R: Bilinear Interpolation for Data on a Rectangular grid

bilinear.grid {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.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..

### 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

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.

### 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`

### Examples

    data(akima474)
    # interpolate at a grid [0,8]x[0,10]
    akima.bil <- bilinear.grid(akima474$x,akima474$y,akima474$z)
    zmin <- min(akima.bil$z, na.rm=TRUE)
    zmax <- max(akima.bil$z, na.rm=TRUE)
    breaks <- pretty(c(zmin,zmax),10)
    colors <- heat.colors(length(breaks)-1)
    image(akima.bil, breaks=breaks, col=colors)
    contour(akima.bil, levels=breaks, add=TRUE)

[Package interp version 1.1-1 Index]