Inverse tangent angle Fourier transform

tfourier_i uses the inverse tangent angle Fourier transformation to calculate a shape, when given a list with Fourier coefficients, typically obtained computed with tfourier.

Usage

tfourier_i(
  tf,
  nb.h,
  nb.pts = 120,
  force2close = FALSE,
  rescale = TRUE,
  perim = 2 * pi,
  thetao = 0
)

Arguments

tf: a list with ao, an and bn components, typically as returned by tfourier
nb.h: integer. The number of harmonics to calculate/use
nb.pts: integer. The number of points to calculate
force2close: logical. Whether to force the outlines calculated to close (see coo_force2close).
rescale: logical. Whether to rescale the points calculated so that their perimeter equals perim.
perim: The perimeter length to rescale shapes.
thetao: numeric. Radius angle to the reference (in radians)

Value

A list with components:

x: vector of x-coordinates.
y: vector of y-coordinates.
phi: vector of interpolated changes on the tangent angle.
angle: vector of position on the perimeter (in radians).

Details

See tfourier for the mathematical background.

Note

Directly borrowed for Claude (2008), and called ifourier2 there.

References

Zahn CT, Roskies RZ. 1972. Fourier Descriptors for Plane Closed Curves. IEEE Transactions on Computers C-21: 269-281.

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

Examples

tfourier(bot[1], 24)
#> $ao
#> [1] 7.733739
#> 
#> $an
#>  [1]  0.0452247795 -0.3755623338  0.0276855331  0.9411732992 -0.3990148731
#>  [6] -0.7763824605 -0.5768666699  0.0440901651 -0.7604537570 -0.4636638848
#> [11] -0.6086940781 -0.1408419257 -0.2906453466  0.1360186290 -0.2905320818
#> [16] -0.0013913889  0.0999975983  0.2531539067 -0.2409440735 -0.0107735036
#> [21] -0.0386305555 -0.0238992918 -0.1631252535 -0.0004085881
#> 
#> $bn
#>  [1]  0.008457058  2.526564125 -0.554083930  0.313312077 -0.288987146
#>  [6]  0.032821965 -0.226300468  0.409651090 -0.021830547  0.015586993
#> [11]  0.414880500  0.677636372  0.197011887  0.180444429  0.433515510
#> [16]  0.237573437  0.107717915  0.027571558  0.054653201 -0.170505441
#> [21]  0.130595490 -0.014178384 -0.048221455 -0.127039009
#> 
#> $phi
#>   [1] 0.00000000 0.03394792 6.12970584 6.22607257 6.18054224 6.19051042
#>   [7] 6.13580603 5.99700591 5.99842093 5.99084704 5.86041492 5.81488459
#>  [13] 5.76506244 5.62887223 5.58334190 5.53781157 5.39732954 5.35179921
#>  [19] 5.22136709 5.16746875 5.12193843 5.06723404 5.07720222 5.03804123
#>  [25] 5.03308691 5.08250829 5.03697796 5.17966914 5.21216935 5.41953309
#>  [31] 5.77457625 5.99961627 6.05629266 6.19411028 6.06367816 6.15041823
#>  [37] 6.20005411 6.10694068 6.10899345 6.11083173 6.24864935 6.21627616
#>  [43] 0.15041122 0.41687566 0.72706839 0.84208756 0.93719564 0.93924841
#>  [49] 0.94130119 0.84818776 0.80265743 0.85207881 0.75917987 0.75672633
#>  [55] 0.62053611 0.71690284 0.62442716 0.58361378 0.52907469 0.53478153
#>  [61] 0.44702280 0.39677552 0.39819054 0.39061666 0.21281593 0.16728561
#>  [67] 0.07417217 6.26424405 6.21871372 6.07886944 5.99538267 5.94148434
#>  [73] 5.89595401 5.85879168 5.85121780 5.90000142 6.00172285 5.85652387
#>  [79] 5.95289060 6.03171526 6.08391184 6.21482206 6.12821895 6.02776111
#>  [85] 5.90179053 5.77058090 5.73820771 5.54311764 5.45064197 5.40081982
#>  [91] 5.40652666 5.31405098 5.27323760 5.21869850 5.17746000 5.13664661
#>  [97] 5.13334469 5.04086901 4.99104686 4.62111347 5.01682255 4.60719411
#> [103] 5.30626827 6.00978848 6.15257805 6.15247100 6.15452378 6.10899345
#> [109] 6.19573352 0.50480943 1.60303743 0.87544326 1.21632143 1.02825629
#> [115] 1.03030907 0.88982703 0.79735136 0.79876638 0.84818776 0.70770572
#> [121] 0.61523005 0.51420121 0.66606644 0.52558441 0.48434590 0.34125395
#> [127] 0.16219458 0.14695801 6.24944229 6.18612024 6.12136151 6.11662487
#> [133] 6.17219791 6.26019663 0.02904262 0.07417217 0.07622495 0.08278017
#> 
#> $t
#>   [1] 0.00000000 0.04553033 0.09106066 0.13659098 0.18212131 0.22765164
#>   [7] 0.27318197 0.31871230 0.36424263 0.40977295 0.45530328 0.50083361
#>  [13] 0.54636394 0.59189427 0.63742460 0.68295492 0.72848525 0.77401558
#>  [19] 0.81954591 0.86507624 0.91060657 0.95613689 1.00166722 1.04719755
#>  [25] 1.09272788 1.13825821 1.18378854 1.22931886 1.27484919 1.32037952
#>  [31] 1.36590985 1.41144018 1.45697051 1.50250083 1.54803116 1.59356149
#>  [37] 1.63909182 1.68462215 1.73015248 1.77568280 1.82121313 1.86674346
#>  [43] 1.91227379 1.95780412 2.00333445 2.04886477 2.09439510 2.13992543
#>  [49] 2.18545576 2.23098609 2.27651642 2.32204674 2.36757707 2.41310740
#>  [55] 2.45863773 2.50416806 2.54969839 2.59522871 2.64075904 2.68628937
#>  [61] 2.73181970 2.77735003 2.82288036 2.86841068 2.91394101 2.95947134
#>  [67] 3.00500167 3.05053200 3.09606233 3.14159265 3.18712298 3.23265331
#>  [73] 3.27818364 3.32371397 3.36924430 3.41477462 3.46030495 3.50583528
#>  [79] 3.55136561 3.59689594 3.64242627 3.68795659 3.73348692 3.77901725
#>  [85] 3.82454758 3.87007791 3.91560823 3.96113856 4.00666889 4.05219922
#>  [91] 4.09772955 4.14325988 4.18879020 4.23432053 4.27985086 4.32538119
#>  [97] 4.37091152 4.41644185 4.46197217 4.50750250 4.55303283 4.59856316
#> [103] 4.64409349 4.68962382 4.73515414 4.78068447 4.82621480 4.87174513
#> [109] 4.91727546 4.96280579 5.00833611 5.05386644 5.09939677 5.14492710
#> [115] 5.19045743 5.23598776 5.28151808 5.32704841 5.37257874 5.41810907
#> [121] 5.46363940 5.50916973 5.55470005 5.60023038 5.64576071 5.69129104
#> [127] 5.73682137 5.78235170 5.82788202 5.87341235 5.91894268 5.96447301
#> [133] 6.01000334 6.05553367 6.10106399 6.14659432 6.19212465 6.23765498
#> 
#> $perimeter
#> [1] 2513.886
#> 
#> $thetao
#> [1] -1.508378
#> 
#> $x1
#> [1] 37
#> 
#> $y1
#> [1] 561
#> 
tfourier_shape()

#>                 x            y
#>  [1,]  0.09561277 -0.004814825
#>  [2,]  0.17323630  0.012512711
#>  [3,]  0.24247674  0.051646046
#>  [4,]  0.29748929  0.109085359
#>  [5,]  0.33385352  0.179819356
#>  [6,]  0.34893838  0.257909706
#>  [7,]  0.34202693  0.337142828
#>  [8,]  0.31420461  0.411651714
#>  [9,]  0.26805270  0.476425605
#> [10,]  0.20721414  0.527653777
#> [11,]  0.13590836  0.562883614
#> [12,]  0.05846627  0.581004809
#> [13,] -0.02106025  0.582095153
#> [14,] -0.09918242  0.567175968
#> [15,] -0.17314294  0.537927066
#> [16,] -0.24097751  0.496404468
#> [17,] -0.30149084  0.444792525
#> [18,] -0.35417340  0.385208942
#> [19,] -0.39908549  0.319569319
#> [20,] -0.43673077  0.249508712
#> [21,] -0.46793577  0.176352003
#> [22,] -0.49374533  0.101122207
#> [23,] -0.51533859  0.024575573
#> [24,] -0.53396545 -0.052746453
#> [25,] -0.55090089 -0.130456468
#> [26,] -0.56741250 -0.208257641
#> [27,] -0.58473615 -0.285882037
#> [28,] -0.60405502 -0.363034076
#> [29,] -0.62647771 -0.439341866
#> [30,] -0.65301277 -0.514318839
#> [31,] -0.68453815 -0.587338057
#> [32,] -0.72176597 -0.657621374
#> [33,] -0.76520472 -0.724245173
#> [34,] -0.81512229 -0.786163607
#> [35,] -0.87151466 -0.842248868
#> [36,] -0.93408535 -0.891346370
#> [37,] -1.00224041 -0.932340801
#> [38,] -1.07510266 -0.964227287
#> [39,] -1.15154679 -0.986180670
#> [40,] -1.23025448 -0.997615508
#> [41,] -1.30978610 -0.998229998
#> [42,] -1.38866314 -0.988028677
#> [43,] -1.46545414 -0.967321231
#> [44,] -1.53885612 -0.936697614
#> [45,] -1.60776454 -0.896982570
#> [46,] -1.67132626 -0.849175003
#> [47,] -1.72897228 -0.794379083
#> [48,] -1.78042991 -0.733734485
#> [49,] -1.82571635 -0.668352569
#> [50,] -1.86511718 -0.599264002
#> [51,] -1.89915498 -0.527381571
#> [52,] -1.92855271 -0.453480087
#> [53,] -1.95419642 -0.378193596
#> [54,] -1.97710051 -0.302028917
#> [55,] -1.99837709 -0.225393658
#> [56,] -2.01920947 -0.148636458
#> [57,] -2.04082810 -0.072096988
#> [58,] -2.06448584  0.003836979
#> [59,] -2.09142827  0.078668531
#> [60,] -2.12285438  0.151730528
#> [61,] -2.15986277  0.222129640
#> [62,] -2.20337967  0.288702417
#> [63,] -2.25406724  0.349992107
#> [64,] -2.31221382  0.404256561
#> [65,] -2.37761297  0.449518103
#> [66,] -2.44944361  0.483665071
#> [67,] -2.52616994  0.504610845
#> [68,] -2.60548492  0.510509188
#> [69,] -2.68432347  0.500014501
#> [70,] -2.75896986  0.472563240
#> [71,] -2.82527534  0.428640136
#> [72,] -2.87898770  0.369983183
#> [73,] -2.91617419  0.299677983
#> [74,] -2.93369646  0.222098182
#> [75,] -2.92967593  0.142665876
#> [76,] -2.90387517  0.067433061
#> [77,] -2.85792168  0.002518250
#> [78,] -2.79531652 -0.046535279
#> [79,] -2.72120119 -0.075389641
#> [80,] -2.64189714 -0.081433142