Bicubic Interpolation for Data on a Rectangular grid
The description in the Fortran code says:
This subroutine performs interpolation of a bivariate function, z(x,y), on a rectangular grid in the x-y plane. It is based on the revised Akima method.
In this subroutine, the interpolating function is a piecewise function composed of a set of bicubic (bivariate third-degree) polynomials, each applicable to a rectangle of the input grid in the x-y plane. Each polynomial is determined locally.
This subroutine has the accuracy of a bicubic polynomial, i.e., it interpolates accurately when all data points lie on a surface of a bicubic polynomial.
The grid lines can be unevenly spaced.
bicubic.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 |
This functiuon is a R interface to Akima's Rectangular-Grid-Data Fitting algorithm (TOMS 760). The algorithm has the accuracy of a bicubic (bivariate third-degree) polynomial.
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!
Akima, H. (1996) Rectangular-Grid-Data Surface Fitting that Has the Accuracy of a Bicubic Polynomial, J. ACM 22(3), 357-361
data(akima760) # interpolate at a grid [0,8]x[0,10] akima.bic <- bicubic.grid(akima760$x,akima760$y,akima760$z) zmin <- min(akima.bic$z, na.rm=TRUE) zmax <- max(akima.bic$z, na.rm=TRUE) breaks <- pretty(c(zmin,zmax),10) colors <- heat.colors(length(breaks)-1) image(akima.bic, breaks=breaks, col=colors) contour(akima.bic, levels=breaks, add=TRUE)
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