Bilinear Interpolation for Data on a Rectangular grid

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.

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)
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.

References

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

Note

This Fortran 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.

BiLinear.grid is a C++ reimplementation, maybe this will replace the Fortran implementation later. So its name may change in future versions, dont rely on it currently.

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)