bicubic {akima} R Documentation

## 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(x, y, z, x0, y0)


### 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]). x0 vector of x coordinates used to interpolate at. y0 vector of y coordinates used to interpolate at.

### 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.

### Value

This function produces a list of interpolated points:

 x vector of x coordinates. y vector of y coordinates. z vector of interpolated data z.

If you need an output grid, see bicubic.grid.

### Note

Use interp for the general case of irregular gridded data!

### References

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

interp, bicubic.grid
data(akima760)
akima.bic <- bicubic(akima760$x,akima760$y,akima760$z, seq(0,8,length=50), seq(0,10,length=50)) plot(sqrt(akima.bic$x^2+akima.bic$y^2), akima.bic$z, type="l")