akima (version 0.6-2.1)

franke.data: 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 \([0,1]\times[0,1]\). (and partially slightly outside).

data

A list of dataframes with 'x' and 'y' to choose from, dataset franke should be used here.

Value

A data frame with components

x

'x' coordinate

y

'y' coordinate

z

'z' value

Details

These datasets are mentioned in [Akima 1996] as testbed for the irregular scattered data interpolator.

Franke used the five functions:

$$0.75e^{-\frac{(9x-2)^2+(9y-2)^2}{4}}+ 0.75e^{-\frac{(9x+1)^2}{49}-\frac{9y+1}{10}}+ 0.5e^{-\frac{(9x-7)^2+(9y-3)^2}{4}}- 0.2e^{-((9x-4)^2-(9y-7)^2)} $$

$$\frac{\mbox{tanh}(9y-9x)+1}{9}$$

$$\frac{1.25+\cos(5.4y)}{6(1+(3x-1)^2)}$$

$$e^{-\frac{81((x-0.5)^2+\frac{(y-0.5)^2}{16})}{3}}$$

$$e^{-\frac{81((x-0.5)^2+\frac{(y-0.5)^2}{4})}{3}}$$

$$\frac{\sqrt{64-81((x-0.5)^2+(y-0.5)^2)}}{9}-0.5$$

and evaluated them on different more or less dense grids over \([0,1]\times[0,1]\).

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

# NOT RUN {
## generate Frankes data set for function 2 and dataset 3:
data(franke)
F23 <- franke.data(2,3,franke)
str(F23)
# }