bilinear {interp} | 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(x, y, z, x0, y0)
BiLinear(x, y, z, x0, y0)
Arguments
x |
a vector containing the |
y |
a vector containing the |
z |
a matrix containing the |
x0 |
vector of |
y0 |
vector of |
Value
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
.
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
is a C++ reimplementation, maybe it will replace the Fortran
implementation later, so
its name may change in futrure versions.
Note
Use interpp
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
See Also
Examples
data(akima474)
# interpolate at the diagonal of the grid [0,8]x[0,10]
akima.bil <- bilinear(akima474$x,akima474$y,akima474$z,
seq(0,8,length=50), seq(0,10,length=50))
plot(sqrt(akima.bil$x^2+akima.bil$y^2), akima.bil$z, type="l")