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(x, y, z, x0, y0)
x |
a vector containing the |
y |
a vector containing the |
z |
a matrix containing the |
x0 |
vector of |
y0 |
vector of |
This function produces a list of interpolated points:
x |
vector of |
y |
vector of |
z |
vector of interpolated data |
If you need an output grid, see bilinear.grid.
Use interpp 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 the diagonal of the grid [0,8]x[0,10]
akima.bil <- bilinear(akima760$x,akima760$y,akima760$z,
seq(0,8,length=50), seq(0,10,length=50))
plot(sqrt(akima.bil$x^2+akima.bil$y^2), akima.bil$z, type="l")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.