Calculates a 'Fourier elliptical shape' given Fourier coefficients

## Usage

efourier_shape(
an = NULL,
bn = NULL,
cn = NULL,
dn = NULL,
n = 1,
nharm = NULL,
npoints = 150,
alpha = 4,
plot = TRUE
)

## Arguments

an

The $$a_n$$ Fourier coefficients on which to calculate a shape.

bn

The $$b_n$$ Fourier coefficients on which to calculate a shape.

cn

The $$c_n$$ Fourier coefficients on which to calculate a shape.

dn

The $$d_n$$ Fourier coefficients on which to calculate a shape.

n

The number of shapes to generate. Defaults to 1. If more than one shape is used, a list of coordinates is returned.

nharm

The number of harmonics to use. It must be less than or equal to the length of *_n coefficients.

npoints

The number of points to calculate.

alpha

The power coefficient associated with the (usually decreasing) amplitude of the Fourier coefficients.

plot

Logical indicating Whether to plot the shape. Defaults to ´TRUE

## Value

A list with components:

• x vector of x-coordrdinates

• y vector of y-coordrdinates.

## Details

efourier_shape can be used by specifying nharm and alpha. The coefficients are then sampled in an uniform distribution $$(-\pi ; \pi)$$ and this amplitude is then divided by $$harmonicrank ^ alpha$$. If alpha is lower than 1, consecutive coefficients will thus increase. See Claude (2008) pp.223 for the maths behind inverse ellipitical Fourier

Adapted from Claude (2008). pp. 223.

## References

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

## Examples

library(pliman)
# approximation of the third leaf's perimeter
# 4 harmonics
image_pliman("potato_leaves.jpg", plot = TRUE)

efourier_shape(an = c(-7.34,  1.81,  -1.32, 0.50),
bn = c(-113.88, 21.90, -0.31, -6.14),
cn = c(-147.51, -20.89, 0.66, -14.06),
dn = c(-0.48, 2.36, -4.36, 3.03))

`