# rfourier_shape: Calculates and draw 'rfourier' shapes.

### Description

`rfourier_shape` calculates a 'Fourier radii variation shape' given Fourier coefficients (see `Details`) or can generate some 'rfourier' shapes.

### Usage

 `1` ```rfourier_shape(an, bn, nb.h, nb.pts = 80, alpha = 2, plot = TRUE) ```

### Arguments

 `an` `numeric`. The a_n Fourier coefficients on which to calculate a shape. `bn` `numeric`. The b_n Fourier coefficients on which to calculate a shape. `nb.h` `integer`. The number of harmonics to use. `nb.pts` `integer`. The number of points to calculate. `alpha` `numeric`. The power coefficient associated with the (usually decreasing) amplitude of the Fourier coefficients (see Details). `plot` `logical`. Whether to plot or not the shape.

### Details

`rfourier_shape` can be used by specifying `nb.h` and `alpha`. The coefficients are then sampled in an uniform distribution (-π ; π) and this amplitude is then divided by harmonicrank^alpha. If `alpha` is lower than 1, consecutive coefficients will thus increase. See rfourier for the mathematical background.

### Value

A matrix of (x; y) coordinates.

### References

Claude, J. (2008) Morphometrics with R, Use R! series, Springer 316 pp.

Other rfourier: `rfourier_i`, `rfourier`

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```data(bot) rf <- rfourier(bot[1], 24) rfourier_shape(rf\$an, rf\$bn) # equivalent to rfourier_i(rf) rfourier_shape() # not very interesting rfourier_shape(nb.h=12) # better rfourier_shape(nb.h=6, alpha=0.4, nb.pts=500) # Butterflies of the vignette' cover panel(Out(a2l(replicate(100, rfourier_shape(nb.h=6, alpha=0.4, nb.pts=200, plot=FALSE))))) ```

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