Momocs (version 0.2-6)

efourier.norm: Normalizes harmonic coefficients.

Description

efourier.norm normalizes Fourier coefficients for rotation, tranlation, size and orientation of the first ellipse.

Usage

efourier.norm(ef, start = FALSE)

Arguments

ef

list. A list containing $a_n$, $b_n$, $c_n$ and $d_n$ Fourier coefficients, such as returned by efourier.

start

logical. Whether to conserve the position of the first point of the outline.

Value

• A list with following components:
• A
  vector of numeric $A_{1->n}$ normalized harmonic coefficients.
• B
  vector of numeric $B_{1->n}$ normalized harmonic coefficients.
• C
  vector of numeric $C_{1->n}$ normalized harmonic coefficients.
• D
  vector of numeric $D_{1->n}$ normalized harmonic coefficients.
• size
  Magnitude of the semi-major axis of the first fitting ellipse.
• theta
  Angle, in radians, between the starting point and the semi-major axis of the first fitting ellipse.
• psi
  Orientation of the first fitting ellipse.
• ao
  ao Harmonic coefficient.
• co
  co Harmonic coefficient.
• lnef
  A list with A, B, C and D concatenated in a vector that may be convenient for some uses.

Details

See efourier for the mathematical background of the normalization. Other approaches implemented in SHAPE are possible such as manually editing or using the longest radius. They will be implemented in further Momocs versions.

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 and efourier.i. Also eFourier for normalizing harmonic coefficients when calculating it for Coo objects.

Examples

data(bot)
q <- efourier(bot@coo[[1]], 24)
efourier.i(q) # equivalent to efourier.shape(q$an, q$bn, q$cn, q$dn)
efourier.norm(q)
efourier.shape(nb.h=5, alpha=1.2)
efourier.shape(nb.h=12, alpha=0.9)