Momocs (version 0.2-03)

efourier.shape: Calculates and draw "efourier" shapes.

Description

efourier.shape calculates a "Fourier elliptical shape" given Fourier coefficients (see Details) or can generate some "efourier" shapes.

Usage

efourier.shape(an, bn, cn, dn, 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.

cn

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

dn

numeric. The $d_n$ 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.

Value

• A list with components:
• x
  vector of x-coordinates.
• y
  vector of y-coordinates.

Details

efourier.shape can be used by specifying nb.h 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 efourier for the mathematical background.

References

Claude, J. (2008) Morphometrics with R, Use R! series, Springer 316 pp. Ferson S, Rohlf FJ, Koehn RK. 1985. Measuring shape variation of two-dimensional outlines. Systematic Biology 34: 59-68.

See Also

efourier.i.

Examples

data(bot)
ef <- efourier(bot@coo[[1]], 24)
efourier.shape(ef$an, ef$bn, ef$cn, ef$dn) # equivalent to efourier.i(ef)
efourier.shape() # is autonomous

efourier.shape(nb.h=12)
efourier.shape(nb.h=12, alpha=0.5)

panel(Coo(replicate(100, l2m(efourier.shape(nb.h=6, alpha=2.5, plot=FALSE))))) # Bubble family
panel(Coo(replicate(100, l2m(efourier.shape(nb.h=12, alpha=0.5, nb.pts=80, plot=FALSE)))))# some doodle