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)x |
a vector containing the |
y |
a vector containing the |
z |
a matrix containing the |
xlim |
vector of length 2 giving lower and upper limit for range |
ylim |
vector of length 2 giving lower and upper limit for range of |
nx |
output grid dimension in |
ny |
output grid dimension in |
dx |
output grid spacing in |
dy |
output grid spacing in |
x |
vector of |
y |
vector of |
z |
matrix of interpolated data for the output grid. |
Use interp for the general case of irregular gridded data!
Pascal Getreuer, Linear Methods for Image Interpolation, Image Processing On Line, 2011, http://www.ipol.im/pub/art/2011/g_lmii/article.pdf
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)
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