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tfourier_shape calculates a 'Fourier tangent angle shape' given Fourier coefficients (see Details) or can generate some 'tfourier' shapes.

Usage

tfourier_shape(an, bn, ao = 0, 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.

ao

ao Harmonic coefficient.

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 matrix of (x; y) coordinates.

References

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

See also

Other tfourier: tfourier(), tfourier_i()

Examples

tf <- tfourier(bot[1], 24)
tfourier_shape(tf$an, tf$bn) # equivalent to rfourier_i(rf)

#>                  x           y
#>  [1,] -0.068536123  0.03816985
#>  [2,]  0.010421770  0.02861438
#>  [3,] -0.063790622  0.05721817
#>  [4,] -0.140579972  0.07793172
#>  [5,] -0.183238239  0.14505793
#>  [6,] -0.247181702  0.19235370
#>  [7,] -0.320133871  0.22403393
#>  [8,] -0.368197883  0.28740195
#>  [9,] -0.418456077  0.34904422
#> [10,] -0.483991433  0.39410832
#> [11,] -0.527015593  0.46100060
#> [12,] -0.558482563  0.53404501
#> [13,] -0.615378810  0.58961904
#> [14,] -0.666002527  0.65096148
#> [15,] -0.703250243  0.72123426
#> [16,] -0.768466384  0.76675910
#> [17,] -0.843721723  0.79249409
#> [18,] -0.920086430  0.81472216
#> [19,] -0.990492372  0.77772677
#> [20,] -1.035089701  0.71187289
#> [21,] -1.107991534  0.68007700
#> [22,] -1.173409209  0.63484224
#> [23,] -1.172271234  0.55531639
#> [24,] -1.245117865  0.52339423
#> [25,] -1.169306190  0.54744097
#> [26,] -1.166890972  0.46794366
#> [27,] -1.134401707  0.39534818
#> [28,] -1.068636587  0.35062006
#> [29,] -1.007856315  0.29932275
#> [30,] -0.955597746  0.23936695
#> [31,] -0.898595892  0.18390125
#> [32,] -0.832707879  0.13935435
#> [33,] -0.769939719  0.09050956
#> [34,] -0.718591641  0.02977217
#> [35,] -0.653105984 -0.01536412
#> [36,] -0.579711689 -0.04600613
#> [37,] -0.541356302 -0.11568052
#> [38,] -0.489158357 -0.17568911
#> [39,] -0.526675851 -0.10555999
#> [40,] -0.483094002 -0.17209027
#> [41,] -0.411233403 -0.20617413
#> [42,] -0.384991638 -0.28125426
#> [43,] -0.346581120 -0.35089827
#> [44,] -0.281483742 -0.39659277
#> [45,] -0.223918101 -0.45147312
#> [46,] -0.163346561 -0.50301673
#> [47,] -0.086698985 -0.52424890
#> [48,] -0.009264515 -0.54240265
#> [49,]  0.061119622 -0.57943951
#> [50,]  0.129392040 -0.62023819
#> [51,]  0.196505793 -0.66291605
#> [52,]  0.256624481 -0.71498715
#> [53,]  0.315395180 -0.76857503
#> [54,]  0.379092808 -0.81620137
#> [55,]  0.442596932 -0.86408541
#> [56,]  0.501564226 -0.91745689
#> [57,]  0.558878373 -0.97259983
#> [58,]  0.616862632 -1.02703770
#> [59,]  0.683127662 -1.07102180
#> [60,]  0.761505112 -1.05750770
#> [61,]  0.789105491 -0.98291631
#> [62,]  0.836639557 -0.91914980
#> [63,]  0.850183366 -0.99752212
#> [64,]  0.787935223 -0.94801632
#> [65,]  0.760460379 -0.87337860
#> [66,]  0.699791505 -0.82194959
#> [67,]  0.638226839 -0.77159636
#> [68,]  0.596708767 -0.70375901
#> [69,]  0.552733618 -0.63748804
#> [70,]  0.492705339 -0.58531274
#> [71,]  0.437325328 -0.52822763
#> [72,]  0.414799359 -0.45195026
#> [73,]  0.364582422 -0.39027438
#> [74,]  0.378601540 -0.46856307
#> [75,]  0.344461362 -0.39672921
#> [76,]  0.268368346 -0.37358815
#> [77,]  0.341471182 -0.34225716
#> [78,]  0.264568188 -0.36254472
#> [79,]  0.260420375 -0.28311896
#> [80,]  0.189614910 -0.24689408
tfourier_shape()

#>                 x            y
#>  [1,]  0.07180984 -0.021600835
#>  [2,]  0.15075934 -0.031225340
#>  [3,]  0.23013665 -0.036215217
#>  [4,]  0.30967032 -0.036441825
#>  [5,]  0.38906775 -0.031783143
#>  [6,]  0.46801342 -0.022127212
#>  [7,]  0.54616750 -0.007376083
#>  [8,]  0.62316501  0.012549767
#>  [9,]  0.69861559  0.037706600
#> [10,]  0.77210399  0.068122234
#> [11,]  0.84319142  0.103790600
#> [12,]  0.91141783  0.144666174
#> [13,]  0.97630519  0.190658426
#> [14,]  1.03736185  0.241626453
#> [15,]  1.09408808  0.297374011
#> [16,]  1.14598265  0.357645144
#> [17,]  1.19255049  0.422120655
#> [18,]  1.23331139  0.490415643
#> [19,]  1.26780941  0.562078342
#> [20,]  1.29562306  0.636590466
#> [21,]  1.31637575  0.713369250
#> [22,]  1.32974637  0.791771305
#> [23,]  1.33547959  0.871098387
#> [24,]  1.33339556  0.950605069
#> [25,]  1.32339853  1.029508271
#> [26,]  1.30548416  1.106998471
#> [27,]  1.27974505  1.182252398
#> [28,]  1.24637417  1.254446860
#> [29,]  1.20566611  1.322773356
#> [30,]  1.15801575  1.386453009
#> [31,]  1.10391438  1.444751364
#> [32,]  1.04394344  1.496992548
#> [33,]  0.97876567  1.542572308
#> [34,]  0.90911431  1.580969494
#> [35,]  0.83578033  1.611755571
#> [36,]  0.75959829  1.634601855
#> [37,]  0.68143127  1.649284259
#> [38,]  0.60215529  1.655685401
#> [39,]  0.52264379  1.653794090
#> [40,]  0.44375265  1.643702265
#> [41,]  0.36630623  1.625599585
#> [42,]  0.29108470  1.599765946
#> [43,]  0.21881319  1.566562268
#> [44,]  0.15015279  1.526419940
#> [45,]  0.08569372  1.479829345
#> [46,]  0.02595051  1.427327877
#> [47,] -0.02864060  1.369487864
#> [48,] -0.07772228  1.306904765
#> [49,] -0.12101498  1.240185969
#> [50,] -0.15831411  1.169940464
#> [51,] -0.18948589  1.096769596
#> [52,] -0.21446215  1.021259053
#> [53,] -0.23323429  0.943972169
#> [54,] -0.24584674  0.865444582
#> [55,] -0.25239008  0.786180211
#> [56,] -0.25299420  0.706648514
#> [57,] -0.24782151  0.627282911
#> [58,] -0.23706051  0.548480268
#> [59,] -0.22091975  0.470601311
#> [60,] -0.19962242  0.393971818
#> [61,] -0.17340136  0.318884456
#> [62,] -0.14249491  0.245601122
#> [63,] -0.10714326  0.174355656
#> [64,] -0.06758551  0.105356812
#> [65,] -0.02405738  0.038791371
#> [66,]  0.02321052 -0.025172689
#> [67,]  0.07399385 -0.086383055
#> [68,]  0.12807514 -0.144700034
#> [69,]  0.18524393 -0.199993666
#> [70,]  0.24529646 -0.252141039
#> [71,]  0.30803503 -0.301023841
#> [72,]  0.37326686 -0.346526198
#> [73,]  0.44080278 -0.388532804
#> [74,]  0.51045557 -0.426927389
#> [75,]  0.58203806 -0.461591535
#> [76,]  0.65536102 -0.492403869
#> [77,]  0.73023088 -0.519239652
#> [78,]  0.80644736 -0.541970784
#> [79,]  0.88380092 -0.560466255
#> [80,]  0.96207026 -0.574593052
tfourier_shape(nb.h=6, alpha=0.4, nb.pts=500)

#>                   x            y
#>   [1,] -0.005594059  0.010939758
#>   [2,] -0.012002519  0.021778525
#>   [3,] -0.018310818  0.032675891
#>   [4,] -0.024511127  0.043635060
#>   [5,] -0.030598364  0.054657436
#>   [6,] -0.036570131  0.065742797
#>   [7,] -0.042426617  0.076889491
#>   [8,] -0.048170472  0.088094640
#>   [9,] -0.053806657  0.099354331
#>  [10,] -0.059342256  0.110663813
#>  [11,] -0.064786257  0.122017670
#>  [12,] -0.070149316  0.133409984
#>  [13,] -0.075443475  0.144834480
#>  [14,] -0.080681881  0.156284647
#>  [15,] -0.085878467  0.167753854
#>  [16,] -0.091047631  0.179235447
#>  [17,] -0.096203900  0.190722836
#>  [18,] -0.101361599  0.202209584
#>  [19,] -0.106534503  0.213689492
#>  [20,] -0.111735513  0.225156694
#>  [21,] -0.116976331  0.236605757
#>  [22,] -0.122267146  0.248031802
#>  [23,] -0.127616348  0.259430629
#>  [24,] -0.133030255  0.270798867
#>  [25,] -0.138512862  0.282134133
#>  [26,] -0.144065622  0.293435198
#>  [27,] -0.149687243  0.304702168
#>  [28,] -0.155373519  0.315936646
#>  [29,] -0.161117173  0.327141897
#>  [30,] -0.166907727  0.338322984
#>  [31,] -0.172731380  0.349486868
#>  [32,] -0.178570898  0.360642461
#>  [33,] -0.184405503  0.371800624
#>  [34,] -0.190210764  0.382974083
#>  [35,] -0.195958467  0.394177258
#>  [36,] -0.201616489  0.405425992
#>  [37,] -0.207148645  0.416737158
#>  [38,] -0.212514536  0.428128138
#>  [39,] -0.217669393  0.439616161
#>  [40,] -0.222563941  0.451217481
#>  [41,] -0.227144292  0.462946403
#>  [42,] -0.231351920  0.474814136
#>  [43,] -0.235123738  0.486827488
#>  [44,] -0.238392329  0.498987403
#>  [45,] -0.241086393  0.511287372
#>  [46,] -0.243131463  0.523711740
#>  [47,] -0.244450956  0.536233967
#>  [48,] -0.244967607  0.548814917
#>  [49,] -0.244605363  0.561401258
#>  [50,] -0.243291736  0.573924102
#>  [51,] -0.240960657  0.586297998
#>  [52,] -0.237555777  0.598420457
#>  [53,] -0.233034174  0.610172152
#>  [54,] -0.227370324  0.621417952
#>  [55,] -0.220560168  0.632008939
#>  [56,] -0.212625049  0.641785498
#>  [57,] -0.203615228  0.650581540
#>  [58,] -0.193612674  0.658229817
#>  [59,] -0.182732781  0.664568204
#>  [60,] -0.171124714  0.669446730
#>  [61,] -0.158970109  0.672735011
#>  [62,] -0.146479940  0.674329662
#>  [63,] -0.133889513  0.674161185
#>  [64,] -0.121451659  0.672199807
#>  [65,] -0.109428385  0.668459740
#>  [66,] -0.098081401  0.663001427
#>  [67,] -0.087662067  0.655931441
#>  [68,] -0.078401406  0.647399889
#>  [69,] -0.070500879  0.637595354
#>  [70,] -0.064124571  0.626737642
#>  [71,] -0.059393351  0.615068761
#>  [72,] -0.056381430  0.602842741
#>  [73,] -0.055115497  0.590314986
#>  [74,] -0.055576442  0.577731872
#>  [75,] -0.057703435  0.565321267
#>  [76,] -0.061399939  0.553284528
#>  [77,] -0.066541125  0.541790380
#>  [78,] -0.072982050  0.530970874
#>  [79,] -0.080565989  0.520919452
#>  [80,] -0.089132320  0.511690952
#>  [81,] -0.098523487  0.503303270
#>  [82,] -0.108590682  0.495740281
#>  [83,] -0.119198011  0.488955607
#>  [84,] -0.130225050  0.482876822
#>  [85,] -0.141567804  0.477409723
#>  [86,] -0.153138156  0.472442412
#>  [87,] -0.164861966  0.467848995
#>  [88,] -0.176675994  0.463492853
#>  [89,] -0.188523836  0.459229535
#>  [90,] -0.200351083  0.454909413
#>  [91,] -0.212099906  0.450380354
#>  [92,] -0.223703296  0.445490715
#>  [93,] -0.235079238  0.440093015
#>  [94,] -0.246125173  0.434048634
#>  [95,] -0.256713202  0.427233880
#>  [96,] -0.266686595  0.419547616
#>  [97,] -0.275858323  0.410920529
#>  [98,] -0.284012383  0.401325815
#>  [99,] -0.290908767  0.390790773
#> [100,] -0.296292817  0.379408364
#> [101,] -0.299909506  0.367347403
#> [102,] -0.301522738  0.354859621
#> [103,] -0.300939169  0.342281597
#> [104,] -0.298035213  0.330029485
#> [105,] -0.292784999  0.318584727
#> [106,] -0.285286156  0.308469660
#> [107,] -0.275779604  0.300212985
#> [108,] -0.264659276  0.294306587
#> [109,] -0.252468028  0.291156870
#> [110,] -0.239877061  0.291035396
#> [111,] -0.227647983  0.294034877
#> [112,] -0.216579061  0.300037059
#> [113,] -0.207439789  0.308698522
#> [114,] -0.200900383  0.319458791
#> [115,] -0.197464472  0.331572491
#> [116,] -0.197413817  0.344163943
#> [117,] -0.200772966  0.356299154
#> [118,] -0.207299474  0.367067251
#> [119,] -0.216501886  0.375661600
#> [120,] -0.227683777  0.381450603
#> [121,] -0.240008395  0.384029556
#> [122,] -0.252575652  0.383247712
#> [123,] -0.264501706  0.379208346
#> [124,] -0.274991598  0.372243478
#> [125,] -0.283397020  0.362868186
#> [126,] -0.289254024  0.351721763
#> [127,] -0.292298714  0.339503863
#> [128,] -0.292462070  0.326913369
#> [129,] -0.289847533  0.314596250
#> [130,] -0.284696566  0.303106483
#> [131,] -0.277347910  0.292881783
#> [132,] -0.268195928  0.284233751
#> [133,] -0.257652364  0.277350403
#> [134,] -0.246114507  0.272308075
#> [135,] -0.233941306  0.269089317
#> [136,] -0.221437713  0.267603589
#> [137,] -0.208846593  0.267708049
#> [138,] -0.196346927  0.269226466
#> [139,] -0.184056786  0.271965014
#> [140,] -0.172039524  0.275724357
#> [141,] -0.160311884  0.280307988
#> [142,] -0.148852920  0.285527124
#> [143,] -0.137613041  0.291202715
#> [144,] -0.126522702  0.297165232
#> [145,] -0.115500565  0.303252902
#> [146,] -0.104461094  0.309309081
#> [147,] -0.093321658  0.315179361
#> [148,] -0.082009250  0.320708976
#> [149,] -0.070466893  0.325740996
#> [150,] -0.058659736  0.330115728
#> [151,] -0.046580720  0.333671651
#> [152,] -0.034255582  0.336248124
#> [153,] -0.021746850  0.337689938
#> [154,] -0.009156360  0.337853643
#> [155,]  0.003374157  0.336615354
#> [156,]  0.015664911  0.333879553
#> [157,]  0.027502621  0.329588185
#> [158,]  0.038647988  0.323729173
#> [159,]  0.048845923  0.316343420
#> [160,]  0.057838114  0.307529356
#> [161,]  0.065377151  0.297444212
#> [162,]  0.071241204  0.286301496
#> [163,]  0.075248023  0.274364469
#> [164,]  0.077267037  0.261935840
#> [165,]  0.077228389  0.249344346
#> [166,]  0.075128038  0.236929204
#> [167,]  0.071028433  0.225023723
#> [168,]  0.065054695  0.213939425
#> [169,]  0.057386706  0.203951974
#> [170,]  0.048247916  0.195290003
#> [171,]  0.037891924  0.188127555
#> [172,]  0.026588062  0.182580490
#> [173,]  0.014607182  0.178706764
#> [174,]  0.002208711  0.176510145
#> [175,] -0.010370228  0.175946659
#> [176,] -0.022923100  0.176932884
#> [177,] -0.035279458  0.179355201
#> [178,] -0.047307739  0.183079137
#> [179,] -0.058915625  0.187958093
#> [180,] -0.070048439  0.193840921
#> [181,] -0.080686047  0.200578022
#> [182,] -0.090838778  0.208025791
#> [183,] -0.100542813  0.216049440
#> [184,] -0.109855387  0.224524296
#> [185,] -0.118850088  0.233335798
#> [186,] -0.127612385  0.242378441
#> [187,] -0.136235465  0.251553936
#> [188,] -0.144816377  0.260768880
#> [189,] -0.153452416  0.269932178
#> [190,] -0.162237694  0.278952495
#> [191,] -0.171259787  0.287735949
#> [192,] -0.180596441  0.296184270
#> [193,] -0.190312281  0.304193619
#> [194,] -0.200455595  0.311654209
#> [195,] -0.211055244  0.318450875
#> [196,] -0.222117877  0.324464641
#> [197,] -0.233625630  0.329575300
#> [198,] -0.245534537  0.333664943
#> [199,] -0.257773880  0.336622257
#> [200,] -0.270246698  0.338347376
#> [201,] -0.282831589  0.338756940
#> [202,] -0.295385883  0.337788997
#> [203,] -0.307750141  0.335407326
#> [204,] -0.319753807  0.331604798
#> [205,] -0.331221748  0.326405418
#> [206,] -0.341981282  0.319864801
#> [207,] -0.351869251  0.312068951
#> [208,] -0.360738678  0.303131362
#> [209,] -0.368464531  0.293188605
#> [210,] -0.374948248  0.282394688
#> [211,] -0.380120735  0.270914592
#> [212,] -0.383943714  0.258917423
#> [213,] -0.386409430  0.246569652
#> [214,] -0.387538874  0.234028855
#> [215,] -0.387378754  0.221438319
#> [216,] -0.385997572  0.208922747
#> [217,] -0.383481169  0.196585205
#> [218,] -0.379928095  0.184505350
#> [219,] -0.375445157  0.172738851
#> [220,] -0.370143409  0.161317875
#> [221,] -0.364134790  0.150252446
#> [222,] -0.357529535  0.139532473
#> [223,] -0.350434411  0.129130240
#> [224,] -0.342951760  0.119003189
#> [225,] -0.335179277  0.109096841
#> [226,] -0.327210423  0.099347760
#> [227,] -0.319135322  0.089686498
#> [228,] -0.311042005  0.080040491
#> [229,] -0.303017823  0.070336898
#> [230,] -0.295150872  0.060505402
#> [231,] -0.287531269  0.050480989
#> [232,] -0.280252126  0.040206686
#> [233,] -0.273410082  0.029636271
#> [234,] -0.267105278  0.018736882
#> [235,] -0.261440680  0.007491459
#> [236,] -0.256520706 -0.004099101
#> [237,] -0.252449151 -0.016014204
#> [238,] -0.249326457 -0.028212401
#> [239,] -0.247246438 -0.040630965
#> [240,] -0.246292639 -0.053186342
#> [241,] -0.246534544 -0.065775572
#> [242,] -0.248023904 -0.078278733
#> [243,] -0.250791470 -0.090562373
#> [244,] -0.254844415 -0.102483818
#> [245,] -0.260164703 -0.113896169
#> [246,] -0.266708586 -0.124653716
#> [247,] -0.274407355 -0.134617460
#> [248,] -0.283169343 -0.143660401
#> [249,] -0.292883113 -0.151672261
#> [250,] -0.303421619 -0.158563350
#> [251,] -0.314647108 -0.164267352
#> [252,] -0.326416421 -0.168742896
#> [253,] -0.338586381 -0.171973886
#> [254,] -0.351018926 -0.173968639
#> [255,] -0.363585713 -0.174757998
#> [256,] -0.376171965 -0.174392630
#> [257,] -0.388679419 -0.172939760
#> [258,] -0.401028304 -0.170479627
#> [259,] -0.413158362 -0.167101919
#> [260,] -0.425028968 -0.162902402
#> [261,] -0.436618476 -0.157979950
#> [262,] -0.447922927 -0.152434086
#> [263,] -0.458954268 -0.146363111
#> [264,] -0.469738225 -0.139862842
#> [265,] -0.480311960 -0.133025930
#> [266,] -0.490721614 -0.125941699
#> [267,] -0.501019808 -0.118696396
#> [268,] -0.511263166 -0.111373770
#> [269,] -0.521509871 -0.104055829
#> [270,] -0.531817303 -0.096823674
#> [271,] -0.542239743 -0.089758267
#> [272,] -0.552826179 -0.082941040
#> [273,] -0.563618234 -0.076454223
#> [274,] -0.574648244 -0.070380830
#> [275,] -0.585937563 -0.064804229
#> [276,] -0.597495147 -0.059807280
#> [277,] -0.609316496 -0.055471046
#> [278,] -0.621383066 -0.051873114
#> [279,] -0.633662197 -0.049085611
#> [280,] -0.646107650 -0.047173046
#> [281,] -0.658660779 -0.046190093
#> [282,] -0.671252328 -0.046179509
#> [283,] -0.683804837 -0.047170338
#> [284,] -0.696235535 -0.049176568
#> [285,] -0.708459614 -0.052196359
#> [286,] -0.720393693 -0.056211951
#> [287,] -0.731959313 -0.061190271
#> [288,] -0.743086240 -0.067084226
#> [289,] -0.753715424 -0.073834609
#> [290,] -0.763801446 -0.081372473
#> [291,] -0.773314360 -0.089621818
#> [292,] -0.782240872 -0.098502393
#> [293,] -0.790584852 -0.107932410
#> [294,] -0.798367224 -0.117830991
#> [295,] -0.805625322 -0.128120172
#> [296,] -0.812411811 -0.138726339
#> [297,] -0.818793295 -0.149581010
#> [298,] -0.824848708 -0.160620902
#> [299,] -0.830667576 -0.171787280
#> [300,] -0.836348199 -0.183024617
#> [301,] -0.841995743 -0.194278615
#> [302,] -0.847720221 -0.205493675
#> [303,] -0.853634258 -0.216609943
#> [304,] -0.859850526 -0.227560067
#> [305,] -0.866478713 -0.238265877
#> [306,] -0.873621848 -0.248635200
#> [307,] -0.881371881 -0.258559121
#> [308,] -0.889804419 -0.267910032
#> [309,] -0.898972629 -0.276540857
#> [310,] -0.908900440 -0.284285906
#> [311,] -0.919575335 -0.290963770
#> [312,] -0.930941203 -0.296382651
#> [313,] -0.942891939 -0.300348393
#> [314,] -0.955266626 -0.302675269
#> [315,] -0.967847270 -0.303199307
#> [316,] -0.980360110 -0.301793574
#> [317,] -0.992481374 -0.298384443
#> [318,] -1.003848143 -0.292967452
#> [319,] -1.014074489 -0.285621088
#> [320,] -1.022772516 -0.276516608
#> [321,] -1.029577205 -0.265922108
#> [322,] -1.034173310 -0.254199351
#> [323,] -1.036321929 -0.241792471
#> [324,] -1.035884053 -0.229208533
#> [325,] -1.032838338 -0.216990888
#> [326,] -1.027290744 -0.205687286
#> [327,] -1.019474378 -0.195815526
#> [328,] -1.009738998 -0.187829939
#> [329,] -0.998530767 -0.182092102
#> [330,] -0.986364085 -0.178848789
#> [331,] -0.973788274 -0.178219344
#> [332,] -0.961352452 -0.180193571
#> [333,] -0.949572090 -0.184639951
#> [334,] -0.938900346 -0.191322846
#> [335,] -0.929706546 -0.199926408
#> [336,] -0.922263156 -0.210082350
#> [337,] -0.916741493 -0.221398642
#> [338,] -0.913215459 -0.233486418
#> [339,] -0.911671771 -0.245982987
#> [340,] -0.912024733 -0.258569593
#> [341,] -0.914133427 -0.270983321
#> [342,] -0.917819333 -0.283023309
#> [343,] -0.922882738 -0.294551932
#> [344,] -0.929116733 -0.305491975
#> [345,] -0.936318068 -0.315820963
#> [346,] -0.944294597 -0.325563766
#> [347,] -0.952869367 -0.334784425
#> [348,] -0.961881672 -0.343577922
#> [349,] -0.971185548 -0.352062325
#> [350,] -0.980646262 -0.360371484
#> [351,] -0.990135351 -0.368648223
#> [352,] -0.999524817 -0.377037810
#> [353,] -1.008681034 -0.385681358
#> [354,] -1.017458988 -0.394708802
#> [355,] -1.025697491 -0.404231107
#> [356,] -1.033216078 -0.414331506
#> [357,] -1.039814343 -0.425055784
#> [358,] -1.045274491 -0.436401885
#> [359,] -1.049367831 -0.448309520
#> [360,] -1.051865718 -0.460650825
#> [361,] -1.052555144 -0.473223490
#> [362,] -1.051258626 -0.485748116
#> [363,] -1.047857363 -0.497871591
#> [364,] -1.042315817 -0.509178160
#> [365,] -1.034705091 -0.519209315
#> [366,] -1.025221822 -0.527492722
#> [367,] -1.014199004 -0.533579158
#> [368,] -1.002105353 -0.537084987
#> [369,] -0.989530653 -0.537736248
#> [370,] -0.977155978 -0.535409312
#> [371,] -0.965709666 -0.530162486
#> [372,] -0.955912153 -0.522253253
#> [373,] -0.948414862 -0.512137036
#> [374,] -0.943739919 -0.500445495
#> [375,] -0.942228108 -0.487945029
#> [376,] -0.944001938 -0.475479045
#> [377,] -0.948949058 -0.463900046
#> [378,] -0.956728637 -0.453999270
#> [379,] -0.966800220 -0.446442124
#> [380,] -0.978471507 -0.441716842
#> [381,] -0.990959065 -0.440101880
#> [382,] -1.003454487 -0.441654834
#> [383,] -1.015188276 -0.446222701
#> [384,] -1.025484670 -0.453470563
#> [385,] -1.033802403 -0.462923740
#> [386,] -1.039758772 -0.474017382
#> [387,] -1.043136741 -0.486147367
#> [388,] -1.043876897 -0.498717148
#> [389,] -1.042057535 -0.511176568
#> [390,] -1.037866923 -0.523050320
#> [391,] -1.031571875 -0.533955347
#> [392,] -1.023486295 -0.543607840
#> [393,] -1.013942553 -0.551821500
#> [394,] -1.003267560 -0.558499206
#> [395,] -0.991764510 -0.563620442
#> [396,] -0.979700403 -0.567226623
#> [397,] -0.967298905 -0.569406091
#> [398,] -0.954737724 -0.570280138
#> [399,] -0.942149493 -0.569990874
#> [400,] -0.929625174 -0.568691398
#> [401,] -0.917219060 -0.566538362
#> [402,] -0.904954653 -0.563686776
#> [403,] -0.892830825 -0.560286770
#> [404,] -0.880827898 -0.556481911
#> [405,] -0.868913364 -0.552408692
#> [406,] -0.857047148 -0.548196787
#> [407,] -0.845186320 -0.543969733
#> [408,] -0.833289270 -0.539845729
#> [409,] -0.821319332 -0.535938324
#> [410,] -0.809247880 -0.532356804
#> [411,] -0.797056870 -0.529206170
#> [412,] -0.784740811 -0.526586642
#> [413,] -0.772308138 -0.524592686
#> [414,] -0.759781921 -0.523311625
#> [415,] -0.747199894 -0.522821922
#> [416,] -0.734613759 -0.523191286
#> [417,] -0.722087789 -0.524474759
#> [418,] -0.709696759 -0.526712970
#> [419,] -0.697523292 -0.529930722
#> [420,] -0.685654755 -0.534136084
#> [421,] -0.674179857 -0.539320092
#> [422,] -0.663185139 -0.545457143
#> [423,] -0.652751557 -0.552506086
#> [424,] -0.642951349 -0.560411979
#> [425,] -0.633845338 -0.569108403
#> [426,] -0.625480821 -0.578520209
#> [427,] -0.617890106 -0.588566515
#> [428,] -0.611089736 -0.599163788
#> [429,] -0.605080370 -0.610228811
#> [430,] -0.599847261 -0.621681400
#> [431,] -0.595361220 -0.633446716
#> [432,] -0.591579950 -0.645457096
#> [433,] -0.588449615 -0.657653334
#> [434,] -0.585906520 -0.669985402
#> [435,] -0.583878781 -0.682412610
#> [436,] -0.582287906 -0.694903260
#> [437,] -0.581050227 -0.707433838
#> [438,] -0.580078136 -0.719987812
#> [439,] -0.579281142 -0.732554117
#> [440,] -0.578566754 -0.745125389
#> [441,] -0.577841248 -0.757696024
#> [442,] -0.577010368 -0.770260134
#> [443,] -0.575980028 -0.782809462
#> [444,] -0.574657102 -0.795331326
#> [445,] -0.572950346 -0.807806670
#> [446,] -0.570771533 -0.820208283
#> [447,] -0.568036822 -0.832499279
#> [448,] -0.564668394 -0.844631918
#> [449,] -0.560596335 -0.856546848
#> [450,] -0.555760727 -0.868172858
#> [451,] -0.550113882 -0.879427207
#> [452,] -0.543622606 -0.890216579
#> [453,] -0.536270363 -0.900438700
#> [454,] -0.528059208 -0.909984597
#> [455,] -0.519011300 -0.918741457
#> [456,] -0.509169875 -0.926595984
#> [457,] -0.498599527 -0.933438130
#> [458,] -0.487385693 -0.939165008
#> [459,] -0.475633300 -0.943684798
#> [460,] -0.463464569 -0.946920415
#> [461,] -0.451016021 -0.948812735
#> [462,] -0.438434818 -0.949323172
#> [463,] -0.425874596 -0.948435449
#> [464,] -0.413491002 -0.946156450
#> [465,] -0.401437158 -0.942516111
#> [466,] -0.389859289 -0.937566347
#> [467,] -0.378892733 -0.931379112
#> [468,] -0.368658527 -0.924043701
#> [469,] -0.359260701 -0.915663481
#> [470,] -0.350784378 -0.906352242
#> [471,] -0.343294718 -0.896230373
#> [472,] -0.336836675 -0.885421076
#> [473,] -0.331435507 -0.874046780
#> [474,] -0.327097933 -0.862225923
#> [475,] -0.323813805 -0.850070194
#> [476,] -0.321558156 -0.837682326
#> [477,] -0.320293469 -0.825154446
#> [478,] -0.319972045 -0.812566995
#> [479,] -0.320538342 -0.799988182
#> [480,] -0.321931192 -0.787473903
#> [481,] -0.324085820 -0.775068065
#> [482,] -0.326935622 -0.762803244
#> [483,] -0.330413666 -0.750701573
#> [484,] -0.334453920 -0.738775820
#> [485,] -0.338992211 -0.727030560
#> [486,] -0.343966933 -0.715463392
#> [487,] -0.349319545 -0.704066166
#> [488,] -0.354994883 -0.692826158
#> [489,] -0.360941322 -0.681727191
#> [490,] -0.367110833 -0.670750654
#> [491,] -0.373458957 -0.659876439
#> [492,] -0.379944726 -0.649083756
#> [493,] -0.386530564 -0.638351842
#> [494,] -0.393182170 -0.627660567
#> [495,] -0.399868416 -0.616990921
#> [496,] -0.406561251 -0.606325408
#> [497,] -0.413235627 -0.595648333
#> [498,] -0.419869444 -0.584946010
#> [499,] -0.426443505 -0.574206879
#> [500,] -0.432941496 -0.563421549
panel(Out(a2l(replicate(100,
coo_force2close(tfourier_shape(nb.h=6, alpha=2, nb.pts=200, plot=FALSE)))))) # biological shapes