bilinear.grid {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.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

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)