Inverse elliptical Fourier transform

efourier_i uses the inverse elliptical Fourier transformation to calculate a shape, when given a list with Fourier coefficients, typically obtained computed with efourier.

Usage

efourier_i(ef, nb.h, nb.pts = 120)

Arguments

ef: list. A list containing $a_n$, $b_n$, $c_n$ and $d_n$ Fourier coefficients, such as returned by efourier.
nb.h: integer. The number of harmonics to use. If not specified, length(ef$an) is used.
nb.pts: integer. The number of points to calculate.

Value

A matrix of (x; y) coordinates.

Details

See efourier for the mathematical background.

Note

Directly borrowed for Claude (2008), and also called iefourier there.

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.

Examples

coo <- bot[1]
coo_plot(coo)
ef  <- efourier(coo, 12)
ef
#> $an
#>  [1] -143.1142910    5.2925309   22.9922936  -11.3596452  -14.9412217
#>  [6]   -5.4200881    5.7177112    0.4509076    0.3107020   -3.1633079
#> [11]    0.2814646    3.4927761
#> 
#> $bn
#>  [1] -13.8501141 -21.8994092  11.4235084  13.5870435 -12.6401807   2.5050679
#>  [7]   5.1968464  -0.5366171  -1.0431706   1.0823659   2.3427969   0.1022387
#> 
#> $cn
#>  [1]  64.44753053  -3.15375656 -17.96822626   5.76052596   7.17390949
#>  [6]  -2.98410094  -1.20013013   1.18299684  -0.36305436  -0.46782525
#> [11]   0.67134872   0.08954658
#> 
#> $dn
#>  [1] -484.90299209   -1.04774048   42.07408510    3.40654863   -9.19128141
#>  [6]   -2.99359284    0.96722479    2.22582484    0.02026172   -2.26134728
#> [11]   -0.04679906    0.80569603
#> 
#> $ao
#> [1] 349.02
#> 
#> $co
#> [1] 1080.921
#> 
efi <- efourier_i(ef)
coo_draw(efi, border='red', col=NA)