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_i(),
sfourier()
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,] -0.945118007 0.000000e+00
#> [2,] -1.089655560 -8.684786e-02
#> [3,] -1.224220418 -1.963935e-01
#> [4,] -1.343537389 -3.267959e-01
#> [5,] -1.442069318 -4.749051e-01
#> [6,] -1.515125904 -6.364277e-01
#> [7,] -1.559856027 -8.065425e-01
#> [8,] -1.575773677 -9.807844e-01
#> [9,] -1.564617563 -1.155885e+00
#> [10,] -1.529566340 -1.330225e+00
#> [11,] -1.474053174 -1.503658e+00
#> [12,] -1.400572047 -1.676645e+00
#> [13,] -1.309892716 -1.848902e+00
#> [14,] -1.200988990 -2.017920e+00
#> [15,] -1.071767042 -2.177875e+00
#> [16,] -0.920422241 -2.319330e+00
#> [17,] -0.747034817 -2.429994e+00
#> [18,] -0.554907030 -2.496498e+00
#> [19,] -0.351185770 -2.506853e+00
#> [20,] -0.146498336 -2.453031e+00
#> [21,] 0.046394820 -2.333025e+00
#> [22,] 0.214638297 -2.151842e+00
#> [23,] 0.347504343 -1.921118e+00
#> [24,] 0.438218807 -1.657405e+00
#> [25,] 0.484901075 -1.379480e+00
#> [26,] 0.490363516 -1.105315e+00
#> [27,] 0.460828661 -8.494120e-01
#> [28,] 0.403923046 -6.210854e-01
#> [29,] 0.326508157 -4.240570e-01
#> [30,] 0.232951810 -2.573439e-01
#> [31,] 0.124314258 -1.171115e-01
#> [32,] -0.001340897 1.075575e-03
#> [33,] -0.147624087 1.002394e-01
#> [34,] -0.317886999 1.807336e-01
#> [35,] -0.513251749 2.400238e-01
#> [36,] -0.731178192 2.734684e-01
#> [37,] -0.964983613 2.757819e-01
#> [38,] -1.204450247 2.426936e-01
#> [39,] -1.437343375 1.722947e-01
#> [40,] -1.651408292 6.570619e-02
#> [41,] -1.836292173 -7.306234e-02
#> [42,] -1.984880367 -2.379280e-01
#> [43,] -2.093730023 -4.218812e-01
#> [44,] -2.162566216 -6.180382e-01
#> [45,] -2.193090184 -8.202390e-01
#> [46,] -2.187549211 -1.023014e+00
#> [47,] -2.147572924 -1.220996e+00
#> [48,] -2.073675643 -1.408063e+00
#> [49,] -1.965592490 -1.576662e+00
#> [50,] -1.823330567 -1.717688e+00
#> [51,] -1.648565296 -1.821184e+00
#> [52,] -1.445874819 -1.877850e+00
#> [53,] -1.223327227 -1.881028e+00
#> [54,] -0.992112686 -1.828689e+00
#> [55,] -0.765194301 -1.724804e+00
#> [56,] -0.555254267 -1.579625e+00
#> [57,] -0.372444248 -1.408637e+00
#> [58,] -0.222539419 -1.230271e+00
#> [59,] -0.106013852 -1.062835e+00
#> [60,] -0.018321147 -9.213033e-01
#> [61,] 0.048656444 -8.147245e-01
#> [62,] 0.104343507 -7.448305e-01
#> [63,] 0.156966287 -7.061831e-01
#> [64,] 0.211445246 -6.878001e-01
#> [65,] 0.268211852 -6.758548e-01
#> [66,] 0.323221424 -6.567994e-01
#> [67,] 0.369109956 -6.201842e-01
#> [68,] 0.397141945 -5.605622e-01
#> [69,] 0.399402278 -4.781304e-01
#> [70,] 0.370649888 -3.780940e-01
#> [71,] 0.309378472 -2.690586e-01
#> [72,] 0.217877577 -1.609604e-01
#> [73,] 0.101379497 -6.310007e-02
#> [74,] -0.033373044 1.725594e-02
#> [75,] -0.179667239 7.546911e-02
#> [76,] -0.332009446 1.093380e-01
#> [77,] -0.486653324 1.183713e-01
#> [78,] -0.641391147 1.028941e-01
#> [79,] -0.794775929 6.334533e-02
#> [80,] -0.945118007 2.314871e-16
sfourier_shape(nb.h=12) # better
#> x y
#> [1,] -3.73028216 0.000000e+00
#> [2,] -3.79081371 -3.021359e-01
#> [3,] -3.74114732 -6.001673e-01
#> [4,] -3.61177769 -8.785124e-01
#> [5,] -3.43507276 -1.131245e+00
#> [6,] -3.22637825 -1.355238e+00
#> [7,] -2.98195669 -1.541857e+00
#> [8,] -2.69374968 -1.676629e+00
#> [9,] -2.36746422 -1.749000e+00
#> [10,] -2.02848468 -1.764122e+00
#> [11,] -1.71086482 -1.745226e+00
#> [12,] -1.43868404 -1.722270e+00
#> [13,] -1.21456649 -1.714350e+00
#> [14,] -1.02323427 -1.719254e+00
#> [15,] -0.84545308 -1.717996e+00
#> [16,] -0.67059890 -1.689812e+00
#> [17,] -0.49955732 -1.624986e+00
#> [18,] -0.33920388 -1.526061e+00
#> [19,] -0.19602476 -1.399275e+00
#> [20,] -0.07446420 -1.246861e+00
#> [21,] 0.02125625 -1.068899e+00
#> [22,] 0.08706282 -8.728423e-01
#> [23,] 0.12298195 -6.798846e-01
#> [24,] 0.13720637 -5.189339e-01
#> [25,] 0.14417303 -4.101533e-01
#> [26,] 0.15553796 -3.505940e-01
#> [27,] 0.17054532 -3.143538e-01
#> [28,] 0.17457563 -2.684332e-01
#> [29,] 0.14836597 -1.926924e-01
#> [30,] 0.08076147 -8.921790e-02
#> [31,] -0.02595140 2.444779e-02
#> [32,] -0.16280016 1.305870e-01
#> [33,] -0.32648936 2.216922e-01
#> [34,] -0.52516205 2.985792e-01
#> [35,] -0.77085296 3.604918e-01
#> [36,] -1.06420436 3.980237e-01
#> [37,] -1.38501767 3.958232e-01
#> [38,] -1.69830982 3.422051e-01
#> [39,] -1.97268399 2.364661e-01
#> [40,] -2.19714866 8.742009e-02
#> [41,] -2.38344487 -9.483244e-02
#> [42,] -2.55272406 -3.059956e-01
#> [43,] -2.71784631 -5.476390e-01
#> [44,] -2.87509273 -8.216706e-01
#> [45,] -3.01006409 -1.125796e+00
#> [46,] -3.11033755 -1.454559e+00
#> [47,] -3.17270089 -1.803829e+00
#> [48,] -3.19899367 -2.172175e+00
#> [49,] -3.18554363 -2.555223e+00
#> [50,] -3.11700723 -2.936409e+00
#> [51,] -2.97140412 -3.282536e+00
#> [52,] -2.73341309 -3.550058e+00
#> [53,] -2.40622080 -3.699884e+00
#> [54,] -2.01370848 -3.711722e+00
#> [55,] -1.59238058 -3.589343e+00
#> [56,] -1.17931764 -3.355004e+00
#> [57,] -0.80341929 -3.038645e+00
#> [58,] -0.48285695 -2.669392e+00
#> [59,] -0.22670844 -2.272850e+00
#> [60,] -0.03722754 -1.872036e+00
#> [61,] 0.08884098 -1.487592e+00
#> [62,] 0.15903666 -1.135244e+00
#> [63,] 0.18276462 -8.222485e-01
#> [64,] 0.16785204 -5.459978e-01
#> [65,] 0.11761273 -2.963670e-01
#> [66,] 0.02989255 -6.074290e-02
#> [67,] -0.10145958 1.704739e-01
#> [68,] -0.28309891 3.995915e-01
#> [69,] -0.51751306 6.195225e-01
#> [70,] -0.79872291 8.147643e-01
#> [71,] -1.11093808 9.661547e-01
#> [72,] -1.43263632 1.058382e+00
#> [73,] -1.74574192 1.086575e+00
#> [74,] -2.04499551 1.057390e+00
#> [75,] -2.34006808 9.829441e-01
#> [76,] -2.64618338 8.714462e-01
#> [77,] -2.96731752 7.217568e-01
#> [78,] -3.28344281 5.267408e-01
#> [79,] -3.55279054 2.831649e-01
#> [80,] -3.73028216 9.136556e-16
sfourier_shape(nb.h=6, alpha=0.4, nb.pts=500)
#> x y
#> [1,] -4.627376537 0.000000e+00
#> [2,] -4.433329065 -5.582545e-02
#> [3,] -4.224758345 -1.064150e-01
#> [4,] -4.002543436 -1.512667e-01
#> [5,] -3.767629800 -1.899219e-01
#> [6,] -3.521024150 -2.219692e-01
#> [7,] -3.263788935 -2.470472e-01
#> [8,] -2.997036513 -2.648476e-01
#> [9,] -2.721923035 -2.751171e-01
#> [10,] -2.439642077 -2.776596e-01
#> [11,] -2.151418074 -2.723378e-01
#> [12,] -1.858499581 -2.590742e-01
#> [13,] -1.562152419 -2.378520e-01
#> [14,] -1.263652728 -2.087150e-01
#> [15,] -0.964280000 -1.717679e-01
#> [16,] -0.665310099 -1.271752e-01
#> [17,] -0.368008349 -7.516038e-02
#> [18,] -0.073622700 -1.600461e-02
#> [19,] 0.216622959 4.995549e-02
#> [20,] 0.501535323 1.223299e-01
#> [21,] 0.779957967 2.006780e-01
#> [22,] 1.050777396 2.845114e-01
#> [23,] 1.312928801 3.732977e-01
#> [24,] 1.565401492 4.664638e-01
#> [25,] 1.807243971 5.634001e-01
#> [26,] 2.037568623 6.634647e-01
#> [27,] 2.255555987 7.659880e-01
#> [28,] 2.460458599 8.702773e-01
#> [29,] 2.651604365 9.756215e-01
#> [30,] 2.828399466 1.081296e+00
#> [31,] 2.990330767 1.186570e+00
#> [32,] 3.136967724 1.290706e+00
#> [33,] 3.267963782 1.392973e+00
#> [34,] 3.383057253 1.492643e+00
#> [35,] 3.482071683 1.589005e+00
#> [36,] 3.564915697 1.681362e+00
#> [37,] 3.631582343 1.769040e+00
#> [38,] 3.682147928 1.851395e+00
#> [39,] 3.716770372 1.927811e+00
#> [40,] 3.735687085 1.997711e+00
#> [41,] 3.739212390 2.060557e+00
#> [42,] 3.727734519 2.115855e+00
#> [43,] 3.701712184 2.163158e+00
#> [44,] 3.661670782 2.202072e+00
#> [45,] 3.608198236 2.232254e+00
#> [46,] 3.541940509 2.253418e+00
#> [47,] 3.463596839 2.265338e+00
#> [48,] 3.373914701 2.267845e+00
#> [49,] 3.273684558 2.260832e+00
#> [50,] 3.163734428 2.244255e+00
#> [51,] 3.044924295 2.218130e+00
#> [52,] 2.918140422 2.182539e+00
#> [53,] 2.784289581 2.137621e+00
#> [54,] 2.644293265 2.083581e+00
#> [55,] 2.499081894 2.020679e+00
#> [56,] 2.349589075 1.949237e+00
#> [57,] 2.196745937 1.869630e+00
#> [58,] 2.041475583 1.782289e+00
#> [59,] 1.884687703 1.687693e+00
#> [60,] 1.727273364 1.586370e+00
#> [61,] 1.570100018 1.478893e+00
#> [62,] 1.414006763 1.365873e+00
#> [63,] 1.259799875 1.247959e+00
#> [64,] 1.108248641 1.125831e+00
#> [65,] 0.960081515 1.000197e+00
#> [66,] 0.815982618 8.717886e-01
#> [67,] 0.676588603 7.413547e-01
#> [68,] 0.542485892 6.096580e-01
#> [69,] 0.414208305 4.774694e-01
#> [70,] 0.292235085 3.455634e-01
#> [71,] 0.176989328 2.147129e-01
#> [72,] 0.068836826 8.568446e-02
#> [73,] -0.031914693 -4.076659e-02
#> [74,] -0.125015907 -1.639010e-01
#> [75,] -0.210275850 -2.830002e-01
#> [76,] -0.287561464 -3.973705e-01
#> [77,] -0.356796774 -5.063479e-01
#> [78,] -0.417961694 -6.093015e-01
#> [79,] -0.471090475 -7.056376e-01
#> [80,] -0.516269827 -7.948032e-01
#> [81,] -0.553636720 -8.762891e-01
#> [82,] -0.583375898 -9.496328e-01
#> [83,] -0.605717121 -1.014421e+00
#> [84,] -0.620932169 -1.070293e+00
#> [85,] -0.629331624 -1.116939e+00
#> [86,] -0.631261470 -1.154105e+00
#> [87,] -0.627099534 -1.181595e+00
#> [88,] -0.617251795 -1.199267e+00
#> [89,] -0.602148591 -1.207036e+00
#> [90,] -0.582240768 -1.204875e+00
#> [91,] -0.557995780 -1.192811e+00
#> [92,] -0.529893781 -1.170930e+00
#> [93,] -0.498423747 -1.139369e+00
#> [94,] -0.464079635 -1.098320e+00
#> [95,] -0.427356630 -1.048023e+00
#> [96,] -0.388747489 -9.887688e-01
#> [97,] -0.348739018 -9.208941e-01
#> [98,] -0.307808706 -8.447780e-01
#> [99,] -0.266421528 -7.608402e-01
#> [100,] -0.225026950 -6.695371e-01
#> [101,] -0.184056148 -5.713584e-01
#> [102,] -0.143919460 -4.668239e-01
#> [103,] -0.105004083 -3.564786e-01
#> [104,] -0.067672028 -2.408900e-01
#> [105,] -0.032258349 -1.206429e-01
#> [106,] 0.000930360 3.663704e-03
#> [107,] 0.031617179 1.314216e-01
#> [108,] 0.059555797 2.620170e-01
#> [109,] 0.084531157 3.948349e-01
#> [110,] 0.106359826 5.292628e-01
#> [111,] 0.124890076 6.646951e-01
#> [112,] 0.140001702 8.005368e-01
#> [113,] 0.151605574 9.362071e-01
#> [114,] 0.159642930 1.071143e+00
#> [115,] 0.164084435 1.204802e+00
#> [116,] 0.164929016 1.336668e+00
#> [117,] 0.162202475 1.466249e+00
#> [118,] 0.155955923 1.593086e+00
#> [119,] 0.146264033 1.716749e+00
#> [120,] 0.133223137 1.836846e+00
#> [121,] 0.116949199 1.953017e+00
#> [122,] 0.097575667 2.064943e+00
#> [123,] 0.075251245 2.172341e+00
#> [124,] 0.050137591 2.274971e+00
#> [125,] 0.022406980 2.372629e+00
#> [126,] -0.007760058 2.465155e+00
#> [127,] -0.040177094 2.552427e+00
#> [128,] -0.074654133 2.634364e+00
#> [129,] -0.110999897 2.710924e+00
#> [130,] -0.149024040 2.782103e+00
#> [131,] -0.188539275 2.847934e+00
#> [132,] -0.229363393 2.908485e+00
#> [133,] -0.271321155 2.963859e+00
#> [134,] -0.314246041 3.014189e+00
#> [135,] -0.357981845 3.059637e+00
#> [136,] -0.402384096 3.100393e+00
#> [137,] -0.447321296 3.136673e+00
#> [138,] -0.492675970 3.168710e+00
#> [139,] -0.538345508 3.196760e+00
#> [140,] -0.584242813 3.221092e+00
#> [141,] -0.630296726 3.241990e+00
#> [142,] -0.676452245 3.259746e+00
#> [143,] -0.722670536 3.274659e+00
#> [144,] -0.768928722 3.287031e+00
#> [145,] -0.815219480 3.297166e+00
#> [146,] -0.861550426 3.305363e+00
#> [147,] -0.907943314 3.311917e+00
#> [148,] -0.954433052 3.317116e+00
#> [149,] -1.001066541 3.321233e+00
#> [150,] -1.047901360 3.324532e+00
#> [151,] -1.095004306 3.327258e+00
#> [152,] -1.142449802 3.329639e+00
#> [153,] -1.190318193 3.331882e+00
#> [154,] -1.238693949 3.334174e+00
#> [155,] -1.287663792 3.336676e+00
#> [156,] -1.337314765 3.339528e+00
#> [157,] -1.387732261 3.342839e+00
#> [158,] -1.438998042 3.346696e+00
#> [159,] -1.491188260 3.351156e+00
#> [160,] -1.544371493 3.356251e+00
#> [161,] -1.598606842 3.361983e+00
#> [162,] -1.653942074 3.368329e+00
#> [163,] -1.710411865 3.375238e+00
#> [164,] -1.768036130 3.382633e+00
#> [165,] -1.826818484 3.390412e+00
#> [166,] -1.886744835 3.398450e+00
#> [167,] -1.947782128 3.406598e+00
#> [168,] -2.009877256 3.414689e+00
#> [169,] -2.072956149 3.422533e+00
#> [170,] -2.136923057 3.429927e+00
#> [171,] -2.201660027 3.436652e+00
#> [172,] -2.267026591 3.442474e+00
#> [173,] -2.332859667 3.447151e+00
#> [174,] -2.398973676 3.450435e+00
#> [175,] -2.465160879 3.452068e+00
#> [176,] -2.531191939 3.451794e+00
#> [177,] -2.596816695 3.449354e+00
#> [178,] -2.661765154 3.444494e+00
#> [179,] -2.725748693 3.436964e+00
#> [180,] -2.788461461 3.426521e+00
#> [181,] -2.849581979 3.412935e+00
#> [182,] -2.908774916 3.395985e+00
#> [183,] -2.965693039 3.375468e+00
#> [184,] -3.019979320 3.351197e+00
#> [185,] -3.071269177 3.323005e+00
#> [186,] -3.119192842 3.290745e+00
#> [187,] -3.163377841 3.254293e+00
#> [188,] -3.203451545 3.213552e+00
#> [189,] -3.239043804 3.168446e+00
#> [190,] -3.269789615 3.118929e+00
#> [191,] -3.295331819 3.064983e+00
#> [192,] -3.315323806 3.006617e+00
#> [193,] -3.329432188 2.943869e+00
#> [194,] -3.337339447 2.876805e+00
#> [195,] -3.338746512 2.805523e+00
#> [196,] -3.333375252 2.730147e+00
#> [197,] -3.320970870 2.650830e+00
#> [198,] -3.301304172 2.567752e+00
#> [199,] -3.274173686 2.481120e+00
#> [200,] -3.239407629 2.391167e+00
#> [201,] -3.196865687 2.298148e+00
#> [202,] -3.146440608 2.202341e+00
#> [203,] -3.088059580 2.104048e+00
#> [204,] -3.021685390 2.003584e+00
#> [205,] -2.947317354 1.901284e+00
#> [206,] -2.864991998 1.797499e+00
#> [207,] -2.774783494 1.692590e+00
#> [208,] -2.676803843 1.586927e+00
#> [209,] -2.571202796 1.480890e+00
#> [210,] -2.458167516 1.374862e+00
#> [211,] -2.337921982 1.269229e+00
#> [212,] -2.210726134 1.164378e+00
#> [213,] -2.076874767 1.060692e+00
#> [214,] -1.936696174 9.585491e-01
#> [215,] -1.790550564 8.583193e-01
#> [216,] -1.638828235 7.603634e-01
#> [217,] -1.481947546 6.650295e-01
#> [218,] -1.320352681 5.726511e-01
#> [219,] -1.154511226 4.835452e-01
#> [220,] -0.984911582 3.980103e-01
#> [221,] -0.812060220 3.163244e-01
#> [222,] -0.636478812 2.387439e-01
#> [223,] -0.458701243 1.655015e-01
#> [224,] -0.279270541 9.680565e-02
#> [225,] -0.098735734 3.283887e-02
#> [226,] 0.082351332 -2.624263e-02
#> [227,] 0.263439206 -8.030977e-02
#> [228,] 0.443980029 -1.292610e-01
#> [229,] 0.623432721 -1.730224e-01
#> [230,] 0.801266107 -2.115477e-01
#> [231,] 0.976961978 -2.448184e-01
#> [232,] 1.150018056 -2.728425e-01
#> [233,] 1.319950846 -2.956548e-01
#> [234,] 1.486298345 -3.133153e-01
#> [235,] 1.648622604 -3.259088e-01
#> [236,] 1.806512109 -3.335429e-01
#> [237,] 1.959583970 -3.363477e-01
#> [238,] 2.107485904 -3.344731e-01
#> [239,] 2.249897996 -3.280880e-01
#> [240,] 2.386534221 -3.173782e-01
#> [241,] 2.517143730 -3.025445e-01
#> [242,] 2.641511868 -2.838008e-01
#> [243,] 2.759460944 -2.613717e-01
#> [244,] 2.870850727 -2.354911e-01
#> [245,] 2.975578676 -2.063994e-01
#> [246,] 3.073579898 -1.743418e-01
#> [247,] 3.164826842 -1.395657e-01
#> [248,] 3.249328723 -1.023190e-01
#> [249,] 3.327130692 -6.284809e-02
#> [250,] 3.398312748 -2.139530e-02
#> [251,] 3.462988412 2.180249e-02
#> [252,] 3.521303171 6.651593e-02
#> [253,] 3.573432693 1.125248e-01
#> [254,] 3.619580855 1.596199e-01
#> [255,] 3.659977569 2.076038e-01
#> [256,] 3.694876447 2.562932e-01
#> [257,] 3.724552310 3.055188e-01
#> [258,] 3.749298571 3.551275e-01
#> [259,] 3.769424505 4.049823e-01
#> [260,] 3.785252431 4.549631e-01
#> [261,] 3.797114832 5.049672e-01
#> [262,] 3.805351432 5.549097e-01
#> [263,] 3.810306249 6.047228e-01
#> [264,] 3.812324661 6.543565e-01
#> [265,] 3.811750493 7.037775e-01
#> [266,] 3.808923154 7.529688e-01
#> [267,] 3.804174856 8.019294e-01
#> [268,] 3.797827914 8.506726e-01
#> [269,] 3.790192174 8.992255e-01
#> [270,] 3.781562572 9.476275e-01
#> [271,] 3.772216846 9.959287e-01
#> [272,] 3.762413426 1.044189e+00
#> [273,] 3.752389504 1.092476e+00
#> [274,] 3.742359318 1.140863e+00
#> [275,] 3.732512645 1.189428e+00
#> [276,] 3.723013520 1.238250e+00
#> [277,] 3.713999198 1.287412e+00
#> [278,] 3.705579358 1.336990e+00
#> [279,] 3.697835550 1.387062e+00
#> [280,] 3.690820904 1.437697e+00
#> [281,] 3.684560088 1.488959e+00
#> [282,] 3.679049519 1.540900e+00
#> [283,] 3.674257826 1.593565e+00
#> [284,] 3.670126556 1.646983e+00
#> [285,] 3.666571124 1.701171e+00
#> [286,] 3.663481986 1.756129e+00
#> [287,] 3.660726033 1.811841e+00
#> [288,] 3.658148195 1.868273e+00
#> [289,] 3.655573232 1.925372e+00
#> [290,] 3.652807708 1.983065e+00
#> [291,] 3.649642117 2.041258e+00
#> [292,] 3.645853154 2.099837e+00
#> [293,] 3.641206113 2.158667e+00
#> [294,] 3.635457372 2.217592e+00
#> [295,] 3.628356972 2.276435e+00
#> [296,] 3.619651246 2.335000e+00
#> [297,] 3.609085484 2.393070e+00
#> [298,] 3.596406612 2.450409e+00
#> [299,] 3.581365857 2.506766e+00
#> [300,] 3.563721386 2.561871e+00
#> [301,] 3.543240883 2.615441e+00
#> [302,] 3.519704048 2.667179e+00
#> [303,] 3.492905004 2.716779e+00
#> [304,] 3.462654575 2.763923e+00
#> [305,] 3.428782438 2.808289e+00
#> [306,] 3.391139102 2.849548e+00
#> [307,] 3.349597726 2.887372e+00
#> [308,] 3.304055742 2.921431e+00
#> [309,] 3.254436270 2.951399e+00
#> [310,] 3.200689328 2.976956e+00
#> [311,] 3.142792800 2.997792e+00
#> [312,] 3.080753184 3.013605e+00
#> [313,] 3.014606088 3.024111e+00
#> [314,] 2.944416478 3.029039e+00
#> [315,] 2.870278686 3.028141e+00
#> [316,] 2.792316158 3.021188e+00
#> [317,] 2.710680960 3.007976e+00
#> [318,] 2.625553034 2.988330e+00
#> [319,] 2.537139220 2.962102e+00
#> [320,] 2.445672038 2.929173e+00
#> [321,] 2.351408260 2.889461e+00
#> [322,] 2.254627259 2.842915e+00
#> [323,] 2.155629168 2.789522e+00
#> [324,] 2.054732853 2.729304e+00
#> [325,] 1.952273723 2.662321e+00
#> [326,] 1.848601387 2.588674e+00
#> [327,] 1.744077187 2.508499e+00
#> [328,] 1.639071619 2.421975e+00
#> [329,] 1.533961667 2.329317e+00
#> [330,] 1.429128070 2.230778e+00
#> [331,] 1.324952549 2.126652e+00
#> [332,] 1.221815014 2.017265e+00
#> [333,] 1.120090768 1.902982e+00
#> [334,] 1.020147745 1.784200e+00
#> [335,] 0.922343796 1.661348e+00
#> [336,] 0.827024043 1.534883e+00
#> [337,] 0.734518334 1.405291e+00
#> [338,] 0.645138807 1.273083e+00
#> [339,] 0.559177600 1.138791e+00
#> [340,] 0.476904708 1.002964e+00
#> [341,] 0.398566021 8.661696e-01
#> [342,] 0.324381551 7.289846e-01
#> [343,] 0.254543865 5.919958e-01
#> [344,] 0.189216744 4.557947e-01
#> [345,] 0.128534065 3.209738e-01
#> [346,] 0.072598937 1.881230e-01
#> [347,] 0.021483077 5.782568e-02
#> [348,] -0.024773551 -6.934495e-02
#> [349,] -0.066162841 -1.928298e-01
#> [350,] -0.102708380 -3.120876e-01
#> [351,] -0.134465034 -4.265987e-01
#> [352,] -0.161518265 -5.358683e-01
#> [353,] -0.183983198 -6.394304e-01
#> [354,] -0.202003441 -7.368507e-01
#> [355,] -0.215749669 -8.277298e-01
#> [356,] -0.225417978 -9.117059e-01
#> [357,] -0.231228029 -9.884580e-01
#> [358,] -0.233420990 -1.057708e+00
#> [359,] -0.232257302 -1.119221e+00
#> [360,] -0.228014273 -1.172813e+00
#> [361,] -0.220983540 -1.218343e+00
#> [362,] -0.211468397 -1.255725e+00
#> [363,] -0.199781029 -1.284918e+00
#> [364,] -0.186239670 -1.305936e+00
#> [365,] -0.171165703 -1.318842e+00
#> [366,] -0.154880737 -1.323751e+00
#> [367,] -0.137703676 -1.320828e+00
#> [368,] -0.119947813 -1.310286e+00
#> [369,] -0.101917969 -1.292390e+00
#> [370,] -0.083907703 -1.267447e+00
#> [371,] -0.066196621 -1.235813e+00
#> [372,] -0.049047805 -1.197883e+00
#> [373,] -0.032705378 -1.154094e+00
#> [374,] -0.017392248 -1.104919e+00
#> [375,] -0.003308021 -1.050866e+00
#> [376,] 0.009372866 -9.924735e-01
#> [377,] 0.020502798 -9.303053e-01
#> [378,] 0.029962396 -8.649498e-01
#> [379,] 0.037661667 -7.970141e-01
#> [380,] 0.043540906 -7.271203e-01
#> [381,] 0.047571307 -6.559008e-01
#> [382,] 0.049755300 -5.839945e-01
#> [383,] 0.050126593 -5.120419e-01
#> [384,] 0.048749926 -4.406810e-01
#> [385,] 0.045720529 -3.705422e-01
#> [386,] 0.041163292 -3.022446e-01
#> [387,] 0.035231645 -2.363908e-01
#> [388,] 0.028106155 -1.735634e-01
#> [389,] 0.019992857 -1.143202e-01
#> [390,] 0.011121318 -5.919034e-02
#> [391,] 0.001742456 -8.670729e-03
#> [392,] -0.007873869 3.677790e-02
#> [393,] -0.017441487 7.673421e-02
#> [394,] -0.026660735 1.108194e-01
#> [395,] -0.035221452 1.387000e-01
#> [396,] -0.042806122 1.600905e-01
#> [397,] -0.049093143 1.747553e-01
#> [398,] -0.053760193 1.825106e-01
#> [399,] -0.056487671 1.832260e-01
#> [400,] -0.056962178 1.768255e-01
#> [401,] -0.054880017 1.632880e-01
#> [402,] -0.049950676 1.426479e-01
#> [403,] -0.041900270 1.149949e-01
#> [404,] -0.030474909 8.047325e-02
#> [405,] -0.015443962 3.928130e-02
#> [406,] 0.003396802 -8.330104e-03
#> [407,] 0.026222243 -6.205918e-02
#> [408,] 0.053175058 -1.215553e-01
#> [409,] 0.084363200 -1.864212e-01
#> [410,] 0.119857537 -2.562160e-01
#> [411,] 0.159689775 -3.304580e-01
#> [412,] 0.203850648 -4.086285e-01
#> [413,] 0.252288427 -4.901746e-01
#> [414,] 0.304907735 -5.745141e-01
#> [415,] 0.361568698 -6.610389e-01
#> [416,] 0.422086443 -7.491195e-01
#> [417,] 0.486230956 -8.381099e-01
#> [418,] 0.553727293 -9.273516e-01
#> [419,] 0.624256173 -1.016179e+00
#> [420,] 0.697454933 -1.103923e+00
#> [421,] 0.772918855 -1.189917e+00
#> [422,] 0.850202861 -1.273503e+00
#> [423,] 0.928823565 -1.354032e+00
#> [424,] 1.008261682 -1.430874e+00
#> [425,] 1.087964768 -1.503418e+00
#> [426,] 1.167350287 -1.571081e+00
#> [427,] 1.245808989 -1.633307e+00
#> [428,] 1.322708566 -1.689576e+00
#> [429,] 1.397397580 -1.739407e+00
#> [430,] 1.469209627 -1.782357e+00
#> [431,] 1.537467710 -1.818031e+00
#> [432,] 1.601488808 -1.846081e+00
#> [433,] 1.660588581 -1.866207e+00
#> [434,] 1.714086213 -1.878166e+00
#> [435,] 1.761309336 -1.881767e+00
#> [436,] 1.801599004 -1.876876e+00
#> [437,] 1.834314694 -1.863415e+00
#> [438,] 1.858839286 -1.841367e+00
#> [439,] 1.874583988 -1.810772e+00
#> [440,] 1.880993174 -1.771726e+00
#> [441,] 1.877549095 -1.724387e+00
#> [442,] 1.863776434 -1.668967e+00
#> [443,] 1.839246654 -1.605735e+00
#> [444,] 1.803582132 -1.535012e+00
#> [445,] 1.756460015 -1.457173e+00
#> [446,] 1.697615797 -1.372639e+00
#> [447,] 1.626846559 -1.281880e+00
#> [448,] 1.544013874 -1.185407e+00
#> [449,] 1.449046324 -1.083772e+00
#> [450,] 1.341941624 -9.775617e-01
#> [451,] 1.222768332 -8.673937e-01
#> [452,] 1.091667110 -7.539138e-01
#> [453,] 0.948851551 -6.377897e-01
#> [454,] 0.794608527 -5.197074e-01
#> [455,] 0.629298075 -4.003658e-01
#> [456,] 0.453352805 -2.804720e-01
#> [457,] 0.267276829 -1.607361e-01
#> [458,] 0.071644204 -4.186650e-02
#> [459,] -0.132903085 7.543553e-02
#> [460,] -0.345657620 1.904806e-01
#> [461,] -0.565849492 3.025960e-01
#> [462,] -0.792649690 4.111309e-01
#> [463,] -1.025173911 5.154605e-01
#> [464,] -1.262486771 6.149909e-01
#> [465,] -1.503606402 7.091629e-01
#> [466,] -1.747509396 7.974565e-01
#> [467,] -1.993136078 8.793942e-01
#> [468,] -2.239396075 9.545447e-01
#> [469,] -2.485174143 1.022526e+00
#> [470,] -2.729336218 1.083007e+00
#> [471,] -2.970735659 1.135712e+00
#> [472,] -3.208219638 1.180420e+00
#> [473,] -3.440635644 1.216971e+00
#> [474,] -3.666838049 1.245260e+00
#> [475,] -3.885694707 1.265244e+00
#> [476,] -4.096093533 1.276938e+00
#> [477,] -4.296949032 1.280420e+00
#> [478,] -4.487208720 1.275823e+00
#> [479,] -4.665859408 1.263341e+00
#> [480,] -4.831933307 1.243224e+00
#> [481,] -4.984513904 1.215777e+00
#> [482,] -5.122741581 1.181357e+00
#> [483,] -5.245818935 1.140372e+00
#> [484,] -5.353015765 1.093276e+00
#> [485,] -5.443673693 1.040568e+00
#> [486,] -5.517210379 9.827848e-01
#> [487,] -5.573123322 9.205018e-01
#> [488,] -5.610993200 8.543250e-01
#> [489,] -5.630486731 7.848879e-01
#> [490,] -5.631359050 7.128469e-01
#> [491,] -5.613455564 6.388764e-01
#> [492,] -5.576713280 5.636637e-01
#> [493,] -5.521161607 4.879042e-01
#> [494,] -5.446922605 4.122960e-01
#> [495,] -5.354210692 3.375352e-01
#> [496,] -5.243331809 2.643103e-01
#> [497,] -5.114682038 1.932973e-01
#> [498,] -4.968745690 1.251549e-01
#> [499,] -4.806092870 6.051937e-02
#> [500,] -4.627376537 1.133380e-15
# Butterflies of the vignette' cover
panel(Out(a2l(replicate(100,
sfourier_shape(nb.h=6, alpha=0.4, nb.pts=200, plot=FALSE)))))
