akima (version 0.6-3.6)

bicubic: 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)

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.

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.

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.grid

Examples

data(akima760)
# interpolate at the diagonal of the grid [0,8]x[0,10]
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")