sfourier_shape calculates a 'Fourier radii variation shape' given
Fourier coefficients (see Details) or can generate some 'sfourier'
shapes.
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.- 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.
Details
sfourier_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 sfourier for the mathematical
background.
References
Renaud S, Pale JRM, Michaux JR (2003): Adaptive latitudinal trends in the mandible shape of Apodemus wood mice. J Biogeogr 30:1617-1628.
See also
Other sfourier:
sfourier(),
sfourier_i()
Examples
rf <- sfourier(bot[1], 24)
sfourier_shape(rf$an, rf$bn) # equivalent to sfourier_i(rf)
#> x y
#> [1,] -0.290097233 0.000000e+00
#> [2,] -0.271959700 -2.167576e-02
#> [3,] -0.246484918 -3.954193e-02
#> [4,] -0.217733972 -5.296062e-02
#> [5,] -0.189896582 -6.253711e-02
#> [6,] -0.161756328 -6.794564e-02
#> [7,] -0.129280368 -6.684598e-02
#> [8,] -0.093457131 -5.816908e-02
#> [9,] -0.056911599 -4.204430e-02
#> [10,] -0.020498051 -1.782664e-02
#> [11,] 0.012003787 1.224487e-02
#> [12,] 0.037674640 4.510087e-02
#> [13,] 0.059580159 8.409685e-02
#> [14,] 0.077938313 1.309531e-01
#> [15,] 0.087952301 1.787227e-01
#> [16,] 0.089723461 2.260901e-01
#> [17,] 0.084960971 2.763655e-01
#> [18,] 0.070321004 3.163705e-01
#> [19,] 0.046429512 3.314256e-01
#> [20,] 0.019913853 3.334462e-01
#> [21,] -0.006649182 3.343630e-01
#> [22,] -0.031682610 3.176318e-01
#> [23,] -0.049327516 2.726987e-01
#> [24,] -0.057930387 2.191009e-01
#> [25,] -0.060592889 1.723788e-01
#> [26,] -0.056570309 1.275136e-01
#> [27,] -0.044606160 8.221929e-02
#> [28,] -0.026786000 4.118703e-02
#> [29,] -0.003378834 4.388307e-03
#> [30,] 0.025798149 -2.849944e-02
#> [31,] 0.058618676 -5.522233e-02
#> [32,] 0.094446012 -7.575806e-02
#> [33,] 0.130822044 -8.883054e-02
#> [34,] 0.161850879 -9.201979e-02
#> [35,] 0.189408545 -8.857751e-02
#> [36,] 0.220645564 -8.252378e-02
#> [37,] 0.252775395 -7.224049e-02
#> [38,] 0.279699320 -5.635869e-02
#> [39,] 0.302648329 -3.627852e-02
#> [40,] 0.317717406 -1.264133e-02
#> [41,] 0.314194975 1.250118e-02
#> [42,] 0.292885334 3.510823e-02
#> [43,] 0.262693915 5.293215e-02
#> [44,] 0.225005085 6.430404e-02
#> [45,] 0.180944070 6.767500e-02
#> [46,] 0.137869807 6.447525e-02
#> [47,] 0.097568618 5.547232e-02
#> [48,] 0.056393859 3.829245e-02
#> [49,] 0.016752301 1.343754e-02
#> [50,] -0.016789374 -1.581660e-02
#> [51,] -0.044589066 -4.925793e-02
#> [52,] -0.067069580 -8.710755e-02
#> [53,] -0.083178505 -1.278980e-01
#> [54,] -0.093570208 -1.724712e-01
#> [55,] -0.097166720 -2.190209e-01
#> [56,] -0.090346447 -2.570238e-01
#> [57,] -0.073587369 -2.783178e-01
#> [58,] -0.051890843 -2.868696e-01
#> [59,] -0.028919129 -2.899267e-01
#> [60,] -0.005779918 -2.906509e-01
#> [61,] 0.017359802 -2.906800e-01
#> [62,] 0.040168810 -2.867352e-01
#> [63,] 0.059710443 -2.686342e-01
#> [64,] 0.071446661 -2.324054e-01
#> [65,] 0.074293397 -1.872085e-01
#> [66,] 0.069720055 -1.416741e-01
#> [67,] 0.057052553 -9.586057e-02
#> [68,] 0.036028165 -5.085343e-02
#> [69,] 0.009821433 -1.175738e-02
#> [70,] -0.020089825 2.049331e-02
#> [71,] -0.055257428 4.805599e-02
#> [72,] -0.094037716 6.947178e-02
#> [73,] -0.132851358 8.268862e-02
#> [74,] -0.171860865 8.886274e-02
#> [75,] -0.210848274 8.856668e-02
#> [76,] -0.245371280 8.080615e-02
#> [77,] -0.272295567 6.623194e-02
#> [78,] -0.290646288 4.662644e-02
#> [79,] -0.297232987 2.369010e-02
#> [80,] -0.290097233 7.105333e-17
sfourier_shape() # not very interesting
#> x y
#> [1,] -0.56557940 0.000000e+00
#> [2,] -0.79407172 -6.328920e-02
#> [3,] -1.00978938 -1.619938e-01
#> [4,] -1.21554995 -2.956649e-01
#> [5,] -1.40952030 -4.641860e-01
#> [6,] -1.58428160 -6.654765e-01
#> [7,] -1.72771257 -8.933347e-01
#> [8,] -1.82546815 -1.136198e+00
#> [9,] -1.86439781 -1.377352e+00
#> [10,] -1.83599793 -1.596721e+00
#> [11,] -1.73898884 -1.773914e+00
#> [12,] -1.58034385 -1.891853e+00
#> [13,] -1.37450405 -1.940100e+00
#> [14,] -1.14097438 -1.917083e+00
#> [15,] -0.90089034 -1.830647e+00
#> [16,] -0.67336973 -1.696794e+00
#> [17,] -0.47247109 -1.536879e+00
#> [18,] -0.30538243 -1.373900e+00
#> [19,] -0.17212670 -1.228684e+00
#> [20,] -0.06669351 -1.116745e+00
#> [21,] 0.02080825 -1.046371e+00
#> [22,] 0.10155987 -1.018181e+00
#> [23,] 0.18559675 -1.026040e+00
#> [24,] 0.27998160 -1.058930e+00
#> [25,] 0.38781462 -1.103282e+00
#> [26,] 0.50807149 -1.145230e+00
#> [27,] 0.63608113 -1.172442e+00
#> [28,] 0.76437754 -1.175332e+00
#> [29,] 0.88368663 -1.147700e+00
#> [30,] 0.98390507 -1.086928e+00
#> [31,] 1.05504262 -9.939139e-01
#> [32,] 1.08817507 -8.728589e-01
#> [33,] 1.07645903 -7.309352e-01
#> [34,] 1.01619044 -5.777517e-01
#> [35,] 0.90777522 -4.245240e-01
#> [36,] 0.75637734 -2.828931e-01
#> [37,] 0.57196974 -1.634628e-01
#> [38,] 0.36857345 -7.426660e-02
#> [39,] 0.16263143 -1.949467e-02
#> [40,] -0.02930995 1.166184e-03
#> [41,] -0.19321301 -7.687554e-03
#> [42,] -0.31990371 -3.834693e-02
#> [43,] -0.40660206 -8.192927e-02
#> [44,] -0.45720044 -1.306630e-01
#> [45,] -0.48113812 -1.799508e-01
#> [46,] -0.49106278 -2.296471e-01
#> [47,] -0.49978863 -2.841532e-01
#> [48,] -0.51726170 -3.512301e-01
#> [49,] -0.54826366 -4.397792e-01
#> [50,] -0.59141017 -5.571441e-01
#> [51,] -0.63967065 -7.066497e-01
#> [52,] -0.68223984 -8.860685e-01
#> [53,] -0.70723798 -1.087472e+00
#> [54,] -0.70450615 -1.298565e+00
#> [55,] -0.66775737 -1.505174e+00
#> [56,] -0.59554695 -1.694253e+00
#> [57,] -0.49087868 -1.856573e+00
#> [58,] -0.35966685 -1.988357e+00
#> [59,] -0.20860804 -2.091386e+00
#> [60,] -0.04318321 -2.171525e+00
#> [61,] 0.13354169 -2.236080e+00
#> [62,] 0.32090681 -2.290714e+00
#> [63,] 0.51942005 -2.336844e+00
#> [64,] 0.72867357 -2.370267e+00
#> [65,] 0.94509798 -2.381509e+00
#> [66,] 1.16033575 -2.357851e+00
#> [67,] 1.36087907 -2.286570e+00
#> [68,] 1.52927681 -2.158560e+00
#> [69,] 1.64676679 -1.971369e+00
#> [70,] 1.69675911 -1.730837e+00
#> [71,] 1.66831179 -1.450889e+00
#> [72,] 1.55868762 -1.151504e+00
#> [73,] 1.37428350 -8.553740e-01
#> [74,] 1.12963049 -5.840891e-01
#> [75,] 0.84466432 -3.548007e-01
#> [76,] 0.54092393 -1.781381e-01
#> [77,] 0.23762246 -5.779821e-02
#> [78,] -0.05143216 8.250917e-03
#> [79,] -0.31931972 2.545046e-02
#> [80,] -0.56557940 1.385270e-16
sfourier_shape(nb.h=12) # better
#> x y
#> [1,] 2.09428732 0.000000e+00
#> [2,] 2.36530080 1.885195e-01
#> [3,] 2.60114872 4.172849e-01
#> [4,] 2.79798570 6.805693e-01
#> [5,] 2.94689562 9.704774e-01
#> [6,] 3.03414082 1.274489e+00
#> [7,] 3.05008480 1.577083e+00
#> [8,] 2.99673595 1.865212e+00
#> [9,] 2.88549539 2.131703e+00
#> [10,] 2.72699045 2.371595e+00
#> [11,] 2.52327323 2.573950e+00
#> [12,] 2.27066285 2.718244e+00
#> [13,] 1.97101518 2.782070e+00
#> [14,] 1.64055158 2.756480e+00
#> [15,] 1.30713652 2.656156e+00
#> [16,] 0.99749195 2.513535e+00
#> [17,] 0.72513971 2.358772e+00
#> [18,] 0.48906667 2.200285e+00
#> [19,] 0.28319320 2.021505e+00
#> [20,] 0.10730226 1.796715e+00
#> [21,] -0.03009087 1.513160e+00
#> [22,] -0.11788013 1.181799e+00
#> [23,] -0.15004119 8.294770e-01
#> [24,] -0.12725755 4.813060e-01
#> [25,] -0.05254961 1.494968e-01
#> [26,] 0.07219370 -1.627299e-01
#> [27,] 0.24326823 -4.483986e-01
#> [28,] 0.44848143 -6.895998e-01
#> [29,] 0.66545369 -8.642672e-01
#> [30,] 0.87015255 -9.612651e-01
#> [31,] 1.05045055 -9.895879e-01
#> [32,] 1.21242113 -9.725205e-01
#> [33,] 1.37160851 -9.313470e-01
#> [34,] 1.53485053 -8.726342e-01
#> [35,] 1.68828303 -7.895309e-01
#> [36,] 1.80362079 -6.745733e-01
#> [37,] 1.85949060 -5.314224e-01
#> [38,] 1.86064603 -3.749154e-01
#> [39,] 1.83819572 -2.203449e-01
#> [40,] 1.82912627 -7.277722e-02
#> [41,] 1.85065601 7.363385e-02
#> [42,] 1.88940425 2.264833e-01
#> [43,] 1.91320911 3.855067e-01
#> [44,] 1.89529419 5.416547e-01
#> [45,] 1.83176040 6.850978e-01
#> [46,] 1.74062566 8.140091e-01
#> [47,] 1.64638303 9.360457e-01
#> [48,] 1.56429940 1.062188e+00
#> [49,] 1.49567854 1.199730e+00
#> [50,] 1.43373371 1.350664e+00
#> [51,] 1.37110800 1.514675e+00
#> [52,] 1.30161629 1.690492e+00
#> [53,] 1.21716318 1.871550e+00
#> [54,] 1.10659328 2.039703e+00
#> [55,] 0.96070446 2.165498e+00
#> [56,] 0.78009484 2.219267e+00
#> [57,] 0.57827855 2.187131e+00
#> [58,] 0.37619419 2.079725e+00
#> [59,] 0.19210130 1.925898e+00
#> [60,] 0.03491370 1.755682e+00
#> [61,] -0.09469753 1.585656e+00
#> [62,] -0.19854088 1.417235e+00
#> [63,] -0.27708390 1.246586e+00
#> [64,] -0.33045809 1.074931e+00
#> [65,] -0.36074312 9.090202e-01
#> [66,] -0.37025890 7.523815e-01
#> [67,] -0.35584428 5.978950e-01
#> [68,] -0.30566447 4.314426e-01
#> [69,] -0.20505512 2.454745e-01
#> [70,] -0.04971845 5.071699e-02
#> [71,] 0.14440214 -1.255829e-01
#> [72,] 0.34542098 -2.551850e-01
#> [73,] 0.52413473 -3.262291e-01
#> [74,] 0.67414708 -3.485759e-01
#> [75,] 0.81739216 -3.433451e-01
#> [76,] 0.98947382 -3.258554e-01
#> [77,] 1.21523189 -2.955875e-01
#> [78,] 1.49269038 -2.394623e-01
#> [79,] 1.79626724 -1.431663e-01
#> [80,] 2.09428732 -5.129525e-16
sfourier_shape(nb.h=6, alpha=0.4, nb.pts=500)
#> x y
#> [1,] -2.684472804 0.000000e+00
#> [2,] -2.392780915 -3.013042e-02
#> [3,] -2.095933177 -5.279327e-02
#> [4,] -1.795185809 -6.784481e-02
#> [5,] -1.491802110 -7.520002e-02
#> [6,] -1.187045375 -7.483263e-02
#> [7,] -0.882171864 -6.677458e-02
#> [8,] -0.578423847 -5.111522e-02
#> [9,] -0.277022792 -2.799995e-02
#> [10,] 0.020837276 2.371524e-03
#> [11,] 0.313996200 3.974728e-02
#> [12,] 0.601333858 8.382573e-02
#> [13,] 0.881776036 1.342585e-01
#> [14,] 1.154299968 1.906535e-01
#> [15,] 1.417939519 2.525786e-01
#> [16,] 1.671789967 3.195655e-01
#> [17,] 1.915012365 3.911136e-01
#> [18,] 2.146837457 4.666942e-01
#> [19,] 2.366569119 5.457553e-01
#> [20,] 2.573587324 6.277258e-01
#> [21,] 2.767350587 7.120208e-01
#> [22,] 2.947397911 7.980456e-01
#> [23,] 3.113350201 8.852014e-01
#> [24,] 3.264911154 9.728895e-01
#> [25,] 3.401867619 1.060517e+00
#> [26,] 3.524089431 1.147499e+00
#> [27,] 3.631528727 1.233269e+00
#> [28,] 3.724218750 1.317276e+00
#> [29,] 3.802272157 1.398994e+00
#> [30,] 3.865878847 1.477925e+00
#> [31,] 3.915303321 1.553601e+00
#> [32,] 3.950881615 1.625591e+00
#> [33,] 3.973017809 1.693503e+00
#> [34,] 3.982180152 1.756983e+00
#> [35,] 3.978896833 1.815725e+00
#> [36,] 3.963751430 1.869469e+00
#> [37,] 3.937378064 1.918001e+00
#> [38,] 3.900456307 1.961161e+00
#> [39,] 3.853705870 1.998837e+00
#> [40,] 3.797881113 2.030971e+00
#> [41,] 3.733765418 2.057555e+00
#> [42,] 3.662165471 2.078638e+00
#> [43,] 3.583905474 2.094316e+00
#> [44,] 3.499821347 2.104738e+00
#> [45,] 3.410754956 2.110103e+00
#> [46,] 3.317548392 2.110658e+00
#> [47,] 3.221038363 2.106694e+00
#> [48,] 3.122050715 2.098549e+00
#> [49,] 3.021395128 2.086599e+00
#> [50,] 2.919860028 2.071258e+00
#> [51,] 2.818207727 2.052974e+00
#> [52,] 2.717169847 2.032228e+00
#> [53,] 2.617443036 2.009526e+00
#> [54,] 2.519685012 1.985395e+00
#> [55,] 2.424510954 1.960383e+00
#> [56,] 2.332490265 1.935052e+00
#> [57,] 2.244143720 1.909970e+00
#> [58,] 2.159941014 1.885714e+00
#> [59,] 2.080298724 1.862858e+00
#> [60,] 2.005578692 1.841973e+00
#> [61,] 1.936086834 1.823620e+00
#> [62,] 1.872072378 1.808346e+00
#> [63,] 1.813727527 1.796680e+00
#> [64,] 1.761187552 1.789128e+00
#> [65,] 1.714531290 1.786170e+00
#> [66,] 1.673782059 1.788254e+00
#> [67,] 1.638908962 1.795793e+00
#> [68,] 1.609828565 1.809162e+00
#> [69,] 1.586406941 1.828695e+00
#> [70,] 1.568462046 1.854682e+00
#> [71,] 1.555766416 1.887363e+00
#> [72,] 1.548050152 1.926931e+00
#> [73,] 1.545004171 1.973528e+00
#> [74,] 1.546283689 2.027242e+00
#> [75,] 1.551511914 2.088105e+00
#> [76,] 1.560283911 2.156099e+00
#> [77,] 1.572170613 2.231145e+00
#> [78,] 1.586722941 2.313113e+00
#> [79,] 1.603475998 2.401817e+00
#> [80,] 1.621953317 2.497015e+00
#> [81,] 1.641671110 2.598416e+00
#> [82,] 1.662142504 2.705674e+00
#> [83,] 1.682881720 2.818396e+00
#> [84,] 1.703408168 2.936142e+00
#> [85,] 1.723250430 3.058427e+00
#> [86,] 1.741950095 3.184725e+00
#> [87,] 1.759065428 3.314471e+00
#> [88,] 1.774174842 3.447068e+00
#> [89,] 1.786880143 3.581888e+00
#> [90,] 1.796809543 3.718273e+00
#> [91,] 1.803620401 3.855547e+00
#> [92,] 1.807001691 3.993013e+00
#> [93,] 1.806676171 4.129962e+00
#> [94,] 1.802402248 4.265677e+00
#> [95,] 1.793975521 4.399433e+00
#> [96,] 1.781230005 4.530511e+00
#> [97,] 1.764039019 4.658191e+00
#> [98,] 1.742315748 4.781769e+00
#> [99,] 1.716013467 4.900550e+00
#> [100,] 1.685125441 5.013861e+00
#> [101,] 1.649684501 5.121052e+00
#> [102,] 1.609762307 5.221500e+00
#> [103,] 1.565468300 5.314612e+00
#> [104,] 1.516948367 5.399833e+00
#> [105,] 1.464383233 5.476644e+00
#> [106,] 1.407986582 5.544570e+00
#> [107,] 1.348002948 5.603180e+00
#> [108,] 1.284705374 5.652090e+00
#> [109,] 1.218392883 5.690967e+00
#> [110,] 1.149387763 5.719530e+00
#> [111,] 1.078032705 5.737550e+00
#> [112,] 1.004687818 5.744856e+00
#> [113,] 0.929727533 5.741329e+00
#> [114,] 0.853537444 5.726909e+00
#> [115,] 0.776511096 5.701591e+00
#> [116,] 0.699046750 5.665428e+00
#> [117,] 0.621544161 5.618525e+00
#> [118,] 0.544401378 5.561047e+00
#> [119,] 0.468011615 5.493208e+00
#> [120,] 0.392760188 5.415275e+00
#> [121,] 0.319021573 5.327566e+00
#> [122,] 0.247156587 5.230445e+00
#> [123,] 0.177509712 5.124323e+00
#> [124,] 0.110406608 5.009650e+00
#> [125,] 0.046151791 4.886918e+00
#> [126,] -0.014973463 4.756653e+00
#> [127,] -0.072713010 4.619414e+00
#> [128,] -0.126837485 4.475789e+00
#> [129,] -0.177145720 4.326388e+00
#> [130,] -0.223465897 4.171845e+00
#> [131,] -0.265656454 4.012809e+00
#> [132,] -0.303606724 3.849942e+00
#> [133,] -0.337237311 3.683914e+00
#> [134,] -0.366500210 3.515401e+00
#> [135,] -0.391378652 3.345076e+00
#> [136,] -0.411886712 3.173612e+00
#> [137,] -0.428068650 3.001671e+00
#> [138,] -0.439998028 2.829905e+00
#> [139,] -0.447776584 2.658951e+00
#> [140,] -0.451532902 2.489426e+00
#> [141,] -0.451420867 2.321925e+00
#> [142,] -0.447617943 2.157020e+00
#> [143,] -0.440323276 1.995250e+00
#> [144,] -0.429755648 1.837128e+00
#> [145,] -0.416151299 1.683129e+00
#> [146,] -0.399761639 1.533697e+00
#> [147,] -0.380850864 1.389235e+00
#> [148,] -0.359693513 1.250109e+00
#> [149,] -0.336571970 1.116643e+00
#> [150,] -0.311773946 9.891222e-01
#> [151,] -0.285589960 8.677879e-01
#> [152,] -0.258310837 7.528399e-01
#> [153,] -0.230225247 6.444356e-01
#> [154,] -0.201617310 5.426903e-01
#> [155,] -0.172764282 4.476778e-01
#> [156,] -0.143934341 3.594312e-01
#> [157,] -0.115384495 2.779439e-01
#> [158,] -0.087358628 2.031711e-01
#> [159,] -0.060085700 1.350309e-01
#> [160,] -0.033778104 7.340708e-02
#> [161,] -0.008630221 1.814997e-02
#> [162,] 0.015182854 -3.092058e-02
#> [163,] 0.037506372 -7.401313e-02
#> [164,] 0.058206795 -1.113621e-01
#> [165,] 0.077172436 -1.432251e-01
#> [166,] 0.094313898 -1.698804e-01
#> [167,] 0.109564285 -1.916238e-01
#> [168,] 0.122879202 -2.087661e-01
#> [169,] 0.134236540 -2.216299e-01
#> [170,] 0.143636051 -2.305470e-01
#> [171,] 0.151098721 -2.358555e-01
#> [172,] 0.156665948 -2.378968e-01
#> [173,] 0.160398531 -2.370130e-01
#> [174,] 0.162375487 -2.335440e-01
#> [175,] 0.162692711 -2.278254e-01
#> [176,] 0.161461479 -2.201855e-01
#> [177,] 0.158806828 -2.109433e-01
#> [178,] 0.154865814 -2.004063e-01
#> [179,] 0.149785683 -1.888685e-01
#> [180,] 0.143721946 -1.766086e-01
#> [181,] 0.136836410 -1.638885e-01
#> [182,] 0.129295163 -1.509517e-01
#> [183,] 0.121266528 -1.380221e-01
#> [184,] 0.112919034 -1.253035e-01
#> [185,] 0.104419392 -1.129781e-01
#> [186,] 0.095930515 -1.012066e-01
#> [187,] 0.087609591 -9.012749e-02
#> [188,] 0.079606243 -7.985723e-02
#> [189,] 0.072060767 -7.049013e-02
#> [190,] 0.065102498 -6.209882e-02
#> [191,] 0.058848290 -5.473471e-02
#> [192,] 0.053401146 -4.842869e-02
#> [193,] 0.048848999 -4.319206e-02
#> [194,] 0.045263662 -3.901753e-02
#> [195,] 0.042699956 -3.588045e-02
#> [196,] 0.041195024 -3.374012e-02
#> [197,] 0.040767842 -3.254127e-02
#> [198,] 0.041418920 -3.221561e-02
#> [199,] 0.043130219 -3.268344e-02
#> [200,] 0.045865261 -3.385541e-02
#> [201,] 0.049569445 -3.563425e-02
#> [202,] 0.054170573 -3.791653e-02
#> [203,] 0.059579563 -4.059450e-02
#> [204,] 0.065691360 -4.355785e-02
#> [205,] 0.072386028 -4.669549e-02
#> [206,] 0.079530021 -4.989723e-02
#> [207,] 0.086977616 -5.305546e-02
#> [208,] 0.094572494 -5.606672e-02
#> [209,] 0.102149464 -5.883319e-02
#> [210,] 0.109536303 -6.126404e-02
#> [211,] 0.116555707 -6.327667e-02
#> [212,] 0.123027325 -6.479787e-02
#> [213,] 0.128769865 -6.576477e-02
#> [214,] 0.133603247 -6.612564e-02
#> [215,] 0.137350787 -6.584055e-02
#> [216,] 0.139841392 -6.488190e-02
#> [217,] 0.140911742 -6.323467e-02
#> [218,] 0.140408441 -6.089664e-02
#> [219,] 0.138190111 -5.787831e-02
#> [220,] 0.134129423 -5.420272e-02
#> [221,] 0.128115026 -4.990506e-02
#> [222,] 0.120053371 -4.503215e-02
#> [223,] 0.109870397 -3.964175e-02
#> [224,] 0.097513081 -3.380169e-02
#> [225,] 0.082950814 -2.758891e-02
#> [226,] 0.066176603 -2.108828e-02
#> [227,] 0.047208080 -1.439144e-02
#> [228,] 0.026088307 -7.595386e-03
#> [229,] 0.002886367 -8.010583e-04
#> [230,] -0.022302271 5.888175e-03
#> [231,] -0.049355615 1.236810e-02
#> [232,] -0.078125246 1.853526e-02
#> [233,] -0.108436658 2.428865e-02
#> [234,] -0.140089830 2.953128e-02
#> [235,] -0.172860043 3.417192e-02
#> [236,] -0.206498923 3.812665e-02
#> [237,] -0.240735723 4.132045e-02
#> [238,] -0.275278819 4.368871e-02
#> [239,] -0.309817428 4.517866e-02
#> [240,] -0.344023520 4.575068e-02
#> [241,] -0.377553924 4.537956e-02
#> [242,] -0.410052613 4.405554e-02
#> [243,] -0.441153138 4.178532e-02
#> [244,] -0.470481216 3.859279e-02
#> [245,] -0.497657430 3.451975e-02
#> [246,] -0.522300038 2.962627e-02
#> [247,] -0.544027861 2.399108e-02
#> [248,] -0.562463232 1.771157e-02
#> [249,] -0.577234978 1.090372e-02
#> [250,] -0.587981419 3.701849e-03
#> [251,] -0.594353354 -3.741966e-03
#> [252,] -0.596017013 -1.125851e-02
#> [253,] -0.592656953 -1.866234e-02
#> [254,] -0.583978867 -2.575288e-02
#> [255,] -0.569712293 -3.231562e-02
#> [256,] -0.549613193 -3.812363e-02
#> [257,] -0.523466383 -4.293908e-02
#> [258,] -0.491087789 -4.651505e-02
#> [259,] -0.452326523 -4.859740e-02
#> [260,] -0.407066737 -4.892681e-02
#> [261,] -0.355229262 -4.724090e-02
#> [262,] -0.296773004 -4.327648e-02
#> [263,] -0.231696078 -3.677182e-02
#> [264,] -0.160036690 -2.746908e-02
#> [265,] -0.081873730 -1.511665e-02
#> [266,] 0.002672909 5.283954e-04
#> [267,] 0.093442309 1.969787e-02
#> [268,] 0.190232791 4.261010e-02
#> [269,] 0.292802475 6.946758e-02
#> [270,] 0.400870131 1.004547e-01
#> [271,] 0.514116326 1.357354e-01
#> [272,] 0.632184842 1.754513e-01
#> [273,] 0.754684380 2.197199e-01
#> [274,] 0.881190528 2.686320e-01
#> [275,] 1.011247975 3.222511e-01
#> [276,] 1.144372976 3.806111e-01
#> [277,] 1.280056030 4.437155e-01
#> [278,] 1.417764768 5.115361e-01
#> [279,] 1.556947030 5.840125e-01
#> [280,] 1.697034098 6.610511e-01
#> [281,] 1.837444083 7.425251e-01
#> [282,] 1.977585416 8.282743e-01
#> [283,] 2.116860452 9.181050e-01
#> [284,] 2.254669119 1.011791e+00
#> [285,] 2.390412635 1.109074e+00
#> [286,] 2.523497217 1.209665e+00
#> [287,] 2.653337792 1.313244e+00
#> [288,] 2.779361672 1.419463e+00
#> [289,] 2.901012147 1.527949e+00
#> [290,] 3.017752010 1.638301e+00
#> [291,] 3.129066944 1.750098e+00
#> [292,] 3.234468776 1.862899e+00
#> [293,] 3.333498566 1.976244e+00
#> [294,] 3.425729499 2.089660e+00
#> [295,] 3.510769574 2.202661e+00
#> [296,] 3.588264055 2.314753e+00
#> [297,] 3.657897677 2.425436e+00
#> [298,] 3.719396583 2.534209e+00
#> [299,] 3.772529980 2.640571e+00
#> [300,] 3.817111506 2.744027e+00
#> [301,] 3.853000286 2.844090e+00
#> [302,] 3.880101683 2.940283e+00
#> [303,] 3.898367727 3.032148e+00
#> [304,] 3.907797227 3.119240e+00
#> [305,] 3.908435554 3.201141e+00
#> [306,] 3.900374117 3.277455e+00
#> [307,] 3.883749506 3.347814e+00
#> [308,] 3.858742338 3.411882e+00
#> [309,] 3.825575797 3.469357e+00
#> [310,] 3.784513881 3.519971e+00
#> [311,] 3.735859376 3.563496e+00
#> [312,] 3.679951571 3.599743e+00
#> [313,] 3.617163718 3.628568e+00
#> [314,] 3.547900276 3.649867e+00
#> [315,] 3.472593952 3.663583e+00
#> [316,] 3.391702551 3.669702e+00
#> [317,] 3.305705679 3.668261e+00
#> [318,] 3.215101303 3.659337e+00
#> [319,] 3.120402218 3.643059e+00
#> [320,] 3.022132419 3.619598e+00
#> [321,] 2.920823435 3.589171e+00
#> [322,] 2.817010629 3.552039e+00
#> [323,] 2.711229510 3.508504e+00
#> [324,] 2.604012074 3.458912e+00
#> [325,] 2.495883204 3.403643e+00
#> [326,] 2.387357163 3.343116e+00
#> [327,] 2.278934194 3.277782e+00
#> [328,] 2.171097268 3.208123e+00
#> [329,] 2.064308995 3.134648e+00
#> [330,] 1.959008717 3.057888e+00
#> [331,] 1.855609821 2.978398e+00
#> [332,] 1.754497276 2.896745e+00
#> [333,] 1.656025419 2.813511e+00
#> [334,] 1.560516011 2.729284e+00
#> [335,] 1.468256568 2.644659e+00
#> [336,] 1.379498982 2.560227e+00
#> [337,] 1.294458450 2.476577e+00
#> [338,] 1.213312706 2.394288e+00
#> [339,] 1.136201567 2.313927e+00
#> [340,] 1.063226795 2.236041e+00
#> [341,] 0.994452277 2.161158e+00
#> [342,] 0.929904515 2.089780e+00
#> [343,] 0.869573422 2.022378e+00
#> [344,] 0.813413421 1.959391e+00
#> [345,] 0.761344831 1.901222e+00
#> [346,] 0.713255532 1.848233e+00
#> [347,] 0.669002889 1.800745e+00
#> [348,] 0.628415924 1.759032e+00
#> [349,] 0.591297711 1.723321e+00
#> [350,] 0.557427978 1.693789e+00
#> [351,] 0.526565892 1.670563e+00
#> [352,] 0.498453002 1.653715e+00
#> [353,] 0.472816313 1.643265e+00
#> [354,] 0.449371470 1.639178e+00
#> [355,] 0.427826017 1.641367e+00
#> [356,] 0.407882713 1.649687e+00
#> [357,] 0.389242861 1.663943e+00
#> [358,] 0.371609640 1.683886e+00
#> [359,] 0.354691393 1.709217e+00
#> [360,] 0.338204856 1.739588e+00
#> [361,] 0.321878291 1.774604e+00
#> [362,] 0.305454501 1.813825e+00
#> [363,] 0.288693693 1.856771e+00
#> [364,] 0.271376178 1.902923e+00
#> [365,] 0.253304860 1.951729e+00
#> [366,] 0.234307521 2.002604e+00
#> [367,] 0.214238849 2.054939e+00
#> [368,] 0.192982222 2.108100e+00
#> [369,] 0.170451201 2.161438e+00
#> [370,] 0.146590745 2.214291e+00
#> [371,] 0.121378109 2.265986e+00
#> [372,] 0.094823437 2.315850e+00
#> [373,] 0.066970030 2.363211e+00
#> [374,] 0.037894290 2.407402e+00
#> [375,] 0.007705332 2.447770e+00
#> [376,] -0.023455727 2.483679e+00
#> [377,] -0.055416809 2.514513e+00
#> [378,] -0.087976225 2.539684e+00
#> [379,] -0.120904345 2.558635e+00
#> [380,] -0.153945558 2.570845e+00
#> [381,] -0.186820519 2.575833e+00
#> [382,] -0.219228664 2.573160e+00
#> [383,] -0.250850971 2.562437e+00
#> [384,] -0.281352953 2.543325e+00
#> [385,] -0.310387848 2.515540e+00
#> [386,] -0.337599997 2.478853e+00
#> [387,] -0.362628367 2.433097e+00
#> [388,] -0.385110205 2.378164e+00
#> [389,] -0.404684779 2.314008e+00
#> [390,] -0.420997191 2.240649e+00
#> [391,] -0.433702220 2.158169e+00
#> [392,] -0.442468158 2.066716e+00
#> [393,] -0.446980629 1.966501e+00
#> [394,] -0.446946327 1.857800e+00
#> [395,] -0.442096669 1.740951e+00
#> [396,] -0.432191315 1.616352e+00
#> [397,] -0.417021528 1.484458e+00
#> [398,] -0.396413337 1.345785e+00
#> [399,] -0.370230493 1.200897e+00
#> [400,] -0.338377168 1.050411e+00
#> [401,] -0.300800379 8.949906e-01
#> [402,] -0.257492119 7.353398e-01
#> [403,] -0.208491164 5.722020e-01
#> [404,] -0.153884540 4.063536e-01
#> [405,] -0.093808632 2.385997e-01
#> [406,] -0.028449920 6.976880e-02
#> [407,] 0.041954677 -9.929253e-02
#> [408,] 0.117117839 -2.677249e-01
#> [409,] 0.196702299 -4.346619e-01
#> [410,] 0.280321693 -5.992355e-01
#> [411,] 0.367541823 -7.605819e-01
#> [412,] 0.457882313 -9.178472e-01
#> [413,] 0.550818674 -1.070193e+00
#> [414,] 0.645784750 -1.216802e+00
#> [415,] 0.742175543 -1.356884e+00
#> [416,] 0.839350398 -1.489680e+00
#> [417,] 0.936636537 -1.614468e+00
#> [418,] 1.033332907 -1.730568e+00
#> [419,] 1.128714337 -1.837347e+00
#> [420,] 1.222035966 -1.934223e+00
#> [421,] 1.312537911 -2.020667e+00
#> [422,] 1.399450161 -2.096210e+00
#> [423,] 1.481997643 -2.160445e+00
#> [424,] 1.559405446 -2.213029e+00
#> [425,] 1.630904154 -2.253686e+00
#> [426,] 1.695735255 -2.282209e+00
#> [427,] 1.753156588 -2.298460e+00
#> [428,] 1.802447796 -2.302377e+00
#> [429,] 1.842915733 -2.293965e+00
#> [430,] 1.873899796 -2.273303e+00
#> [431,] 1.894777139 -2.240544e+00
#> [432,] 1.904967736 -2.195909e+00
#> [433,] 1.903939239 -2.139690e+00
#> [434,] 1.891211619 -2.072247e+00
#> [435,] 1.866361529 -1.994004e+00
#> [436,] 1.829026377 -1.905449e+00
#> [437,] 1.778908054 -1.807130e+00
#> [438,] 1.715776311 -1.699649e+00
#> [439,] 1.639471733 -1.583663e+00
#> [440,] 1.549908305 -1.459874e+00
#> [441,] 1.447075534 -1.329030e+00
#> [442,] 1.331040107 -1.191915e+00
#> [443,] 1.201947082 -1.049347e+00
#> [444,] 1.060020573 -9.021738e-01
#> [445,] 0.905563949 -7.512627e-01
#> [446,] 0.738959513 -5.974995e-01
#> [447,] 0.560667669 -4.417802e-01
#> [448,] 0.371225586 -2.850062e-01
#> [449,] 0.171245337 -1.280780e-01
#> [450,] -0.038588449 2.811045e-02
#> [451,] -0.257521441 1.826777e-01
#> [452,] -0.484732929 3.347603e-01
#> [453,] -0.719339611 4.835186e-01
#> [454,] -0.960399824 6.281418e-01
#> [455,] -1.206918185 7.678535e-01
#> [456,] -1.457850630 9.019162e-01
#> [457,] -1.712109807 1.029636e+00
#> [458,] -1.968570801 1.150368e+00
#> [459,] -2.226077155 1.263517e+00
#> [460,] -2.483447138 1.368546e+00
#> [461,] -2.739480246 1.464976e+00
#> [462,] -2.992963868 1.552388e+00
#> [463,] -3.242680093 1.630429e+00
#> [464,] -3.487412607 1.698811e+00
#> [465,] -3.725953645 1.757314e+00
#> [466,] -3.957110937 1.805784e+00
#> [467,] -4.179714621 1.844137e+00
#> [468,] -4.392624069 1.872360e+00
#> [469,] -4.594734577 1.890505e+00
#> [470,] -4.784983895 1.898692e+00
#> [471,] -4.962358525 1.897109e+00
#> [472,] -5.125899773 1.886005e+00
#> [473,] -5.274709500 1.865693e+00
#> [474,] -5.407955536 1.836545e+00
#> [475,] -5.524876728 1.798988e+00
#> [476,] -5.624787574 1.753502e+00
#> [477,] -5.707082433 1.700616e+00
#> [478,] -5.771239263 1.640904e+00
#> [479,] -5.816822876 1.574979e+00
#> [480,] -5.843487674 1.503490e+00
#> [481,] -5.850979866 1.427117e+00
#> [482,] -5.839139134 1.346566e+00
#> [483,] -5.807899747 1.262561e+00
#> [484,] -5.757291106 1.175843e+00
#> [485,] -5.687437731 1.087164e+00
#> [486,] -5.598558666 9.972754e-01
#> [487,] -5.490966333 9.069321e-01
#> [488,] -5.365064823 8.168802e-01
#> [489,] -5.221347634 7.278541e-01
#> [490,] -5.060394887 6.405713e-01
#> [491,] -4.882870025 5.557273e-01
#> [492,] -4.689516009 4.739906e-01
#> [493,] -4.481151062 3.959986e-01
#> [494,] -4.258663958 3.223527e-01
#> [495,] -4.023008905 2.536148e-01
#> [496,] -3.775200057 1.903035e-01
#> [497,] -3.516305674 1.328905e-01
#> [498,] -3.247441985 8.179797e-02
#> [499,] -2.969766783 3.739595e-02
#> [500,] -2.684472804 6.575062e-16
# Butterflies of the vignette' cover
panel(Out(a2l(replicate(100,
sfourier_shape(nb.h=6, alpha=0.4, nb.pts=200, plot=FALSE)))))
