# bilinear.grid: Bilinear Interpolation for Data on a Rectangular grid In akima: Interpolation of Irregularly and Regularly Spaced Data

## 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

 ```1 2``` ```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

Use `interp` 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

`interp`, `bicubic`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```data(akima760) # interpolate at a grid [0,8]x[0,10] akima.bil <- bilinear.grid(akima760\$x,akima760\$y,akima760\$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) ```

### Example output

```
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akima documentation built on May 29, 2017, 6:47 p.m.