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 |

`y` |
a vector containing the |

`z` |
a matrix containing the |

`x0` |
vector of |

`y0` |
vector of |

### 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 |

`y` |
vector of |

`z` |
vector of interpolated data |

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

### See Also

### 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")
```

*akima*version 0.6-3.4 Index]