akima (version 0.5-10)

bicubic.grid: Bivariate Interpolation for Data on a Rectangular grid

Description

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.

Usage

bicubic.grid(x,y,z,xlim,ylim,dx,dy)

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.

dx

output grid spacing in x direction.

dy

output grid spacing in y direction.

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.

Details

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.

References

Akima, H. (1996) Rectangular-Grid-Data Surface Fitting that Has the Accuracy of a Bicubic Polynomial, J. ACM 22(3), 357-361

See Also

interp, bicubic

Examples

data(akima760)
# interpolate at a grid [0,8]x[0,10]
akima.bic <- bicubic.grid(akima760$x,akima760$y,akima760$z,
                          c(0,8),c(0,10),0.1,0.1)
image(akima.bic)
contour(akima.bic, add=TRUE)