R: Test datasets from Franke for interpolation of scattered data

franke.data {interp} | R Documentation

## Test datasets from Franke for interpolation of scattered data

### Description

`franke.data` generates the test datasets from Franke, 1979, see references.

### Usage

    franke.data(fn = 1, ds = 1, data)
    franke.fn(x, y, fn = 1)

### Arguments

`fn` | function number, from 1 to 5.
`x` | 'x' value
`y` | 'y' value
`ds` | data set number, from 1 to 3. Dataset 1 consists of 100 points, dataset 2 of 33 points and dataset 3 of 25 points scattered in the square [0,1]x[0,1]. (and partially slightly outside).
`data` | A list of dataframes with 'x' and 'y' to choose from, dataset `franke` should be used here.

### Details

These datasets are mentioned in Akima, (1996) as a testbed for the irregular scattered data interpolator.

Franke used the five functions:

0.75*exp(-((9*x-2)^2+(9*y-2)^2)/4)+ 0.75*exp(-((9*x+1)^2)/49-(9*y+1)/10)+ 0.5*exp(-((9*x-7)^2+(9*y-3)^2)/4)- 0.2*exp(-(9*x-4)^2-(9*y-7)^2)

(tanh(9*y-9*x)+1)/9

(1.25+cos(5.4*y))/(6*(1+(3*x-1)^2))

exp(-81*((x-0.5)^2+(y-0.5)^2)/16)/3

exp(-81*((x-0.5)^2+(y-0.5)^2)/4)/3

sqrt(64-81*((x-0.5)^2+(y-0.5)^2))/9-0.5

and evaluated them on different more or less dense grids over [0,1]x[0,1].

### Value

A data frame with components

`x` | 'x' coordinate
`y` | 'y' coordinate
`z` | 'z' value

### Note

The datasets have to be generated via `franke.data` before use, the dataset `franke` only contains a list of 3 dataframes of 'x' and 'y' coordinates for the above mentioned irregular grids. Do not forget to load the `franke` dataset first.

The 'x' and 'y' values have been taken from Akima (1996).

### Author(s)

Albrecht Gebhardt <albrecht.gebhardt@aau.at>, Roger Bivand <roger.bivand@nhh.no>

### References

FRANKE, R., (1979). A critical comparison of some methods for interpolation of scattered data. Tech. Rep. NPS-53-79-003, Dept. of Mathematics, Naval Postgraduate School, Monterey, Calif.

Akima, H. (1996). Algorithm 761: scattered-data surface fitting that has the accuracy of a cubic polynomial. ACM Transactions on Mathematical Software 22, 362–371.

### See Also

`interp`

### Examples

    ## generate Frankes data set for function 2 and dataset 3:
    data(franke)
    F23 <- franke.data(2,3,franke)
    str(F23)

[Package interp version 1.1-1 Index]