rfourier_shape calculates a 'Fourier radii variation shape' given
Fourier coefficients (see Details) or can generate some 'rfourier'
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
rfourier_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 rfourier for the mathematical
background.
See also
Other rfourier:
rfourier_i(),
rfourier()
Examples
data(bot)
rf <- rfourier(bot[1], 24)
rfourier_shape(rf$an, rf$bn) # equivalent to rfourier_i(rf)
#> x y
#> [1,] -504.032401 0.000000e+00
#> [2,] 152.277511 1.213684e+01
#> [3,] 123.922985 1.988014e+01
#> [4,] -405.769720 -9.869758e+01
#> [5,] -299.257786 -9.855215e+01
#> [6,] -64.033528 -2.689724e+01
#> [7,] -297.588603 -1.538718e+02
#> [8,] -247.659860 -1.541471e+02
#> [9,] 34.115634 2.520344e+01
#> [10,] -81.118036 -7.054630e+01
#> [11,] -96.952489 -9.889967e+01
#> [12,] 181.738917 2.175623e+02
#> [13,] 320.377819 4.522104e+02
#> [14,] 650.392457 1.092799e+03
#> [15,] 1019.781679 2.072239e+03
#> [16,] 766.774556 1.932160e+03
#> [17,] 840.274273 2.733288e+03
#> [18,] 1733.216439 7.797650e+03
#> [19,] 1683.030508 1.201390e+04
#> [20,] 472.998568 7.920093e+03
#> [21,] -3.693822 1.857488e+02
#> [22,] 193.709205 -1.942018e+03
#> [23,] 21.862735 -1.208644e+02
#> [24,] 53.714265 -2.031549e+02
#> [25,] 370.520921 -1.054083e+03
#> [26,] 216.540448 -4.880980e+02
#> [27,] 135.732670 -2.501862e+02
#> [28,] 466.908353 -7.179336e+02
#> [29,] 411.781716 -5.348072e+02
#> [30,] 235.560214 -2.602254e+02
#> [31,] 517.224029 -4.872563e+02
#> [32,] 572.278421 -4.590422e+02
#> [33,] 346.348891 -2.351772e+02
#> [34,] 534.117025 -3.036705e+02
#> [35,] 679.577570 -3.178066e+02
#> [36,] 455.098727 -1.702117e+02
#> [37,] 529.331468 -1.512772e+02
#> [38,] 725.483690 -1.461831e+02
#> [39,] 545.014188 -6.533097e+01
#> [40,] 512.204019 -2.037956e+01
#> [41,] 711.685148 2.831651e+01
#> [42,] 599.323333 7.184102e+01
#> [43,] 487.280383 9.818574e+01
#> [44,] 648.008281 1.851938e+02
#> [45,] 605.439186 2.264407e+02
#> [46,] 453.428917 2.120475e+02
#> [47,] 549.059655 3.121661e+02
#> [48,] 558.226691 3.790460e+02
#> [49,] 404.964997 3.248349e+02
#> [50,] 430.145214 4.052228e+02
#> [51,] 461.416259 5.097305e+02
#> [52,] 334.454312 4.343772e+02
#> [53,] 303.642443 4.668906e+02
#> [54,] 326.758921 6.022910e+02
#> [55,] 236.290598 5.326163e+02
#> [56,] 176.846385 5.031047e+02
#> [57,] 171.184806 6.474451e+02
#> [58,] 109.884528 6.074778e+02
#> [59,] 51.833348 5.196517e+02
#> [60,] 12.809119 6.441236e+02
#> [61,] -38.593591 6.462278e+02
#> [62,] -72.750399 5.193108e+02
#> [63,] -133.044116 5.985585e+02
#> [64,] -196.546600 6.393370e+02
#> [65,] -198.662349 5.006002e+02
#> [66,] -256.653752 5.215311e+02
#> [67,] -347.381274 5.836753e+02
#> [68,] -324.847387 4.585191e+02
#> [69,] -354.756103 4.246838e+02
#> [70,] -474.501207 4.840310e+02
#> [71,] -445.049745 3.870485e+02
#> [72,] -429.185843 3.170675e+02
#> [73,] -566.188571 3.524040e+02
#> [74,] -546.614528 2.826337e+02
#> [75,] -483.371296 2.030398e+02
#> [76,] -622.486699 2.049985e+02
#> [77,] -607.488016 1.477626e+02
#> [78,] -514.459992 8.253138e+01
#> [79,] -692.324999 5.517977e+01
#> [80,] -504.032401 1.234523e-13
rfourier_shape() # not very interesting
#> x y
#> [1,] -1.70783049 0.000000e+00
#> [2,] -1.42387492 -1.134858e-01
#> [3,] -1.12842604 -1.810258e-01
#> [4,] -0.83525063 -2.031626e-01
#> [5,] -0.55314503 -1.821628e-01
#> [6,] -0.28573344 -1.200222e-01
#> [7,] -0.03274864 -1.693308e-02
#> [8,] 0.20762473 1.292287e-01
#> [9,] 0.43605675 3.221435e-01
#> [10,] 0.64983694 5.651467e-01
#> [11,] 0.84177670 8.586828e-01
#> [12,] 1.00061227 1.197848e+00
#> [13,] 1.11285389 1.570783e+00
#> [14,] 1.16562637 1.958503e+00
#> [15,] 1.14977127 2.336383e+00
#> [16,] 1.06240688 2.677111e+00
#> [17,] 0.90828491 2.954516e+00
#> [18,] 0.69959955 3.147462e+00
#> [19,] 0.45430408 3.242938e+00
#> [20,] 0.19336079 3.237717e+00
#> [21,] -0.06240765 3.138252e+00
#> [22,] -0.29514415 2.958947e+00
#> [23,] -0.49188023 2.719276e+00
#> [24,] -0.64526044 2.440466e+00
#> [25,] -0.75311265 2.142507e+00
#> [26,] -0.81720368 1.842037e+00
#> [27,] -0.84168817 1.551423e+00
#> [28,] -0.83175975 1.278941e+00
#> [29,] -0.79285960 1.029737e+00
#> [30,] -0.73054609 8.070406e-01
#> [31,] -0.65086608 6.131551e-01
#> [32,] -0.56087882 4.498982e-01
#> [33,] -0.46892701 3.184099e-01
#> [34,] -0.38434108 2.185159e-01
#> [35,] -0.31647156 1.479989e-01
#> [36,] -0.27319902 1.021793e-01
#> [37,] -0.25928964 7.410219e-02
#> [38,] -0.27507300 5.542650e-02
#> [39,] -0.31587991 3.786459e-02
#> [40,] -0.37249857 1.482096e-02
#> [41,] -0.43263981 -1.721386e-02
#> [42,] -0.48312454 -5.791225e-02
#> [43,] -0.51230209 -1.032276e-01
#> [44,] -0.51213827 -1.463636e-01
#> [45,] -0.47949724 -1.793370e-01
#> [46,] -0.41635659 -1.947105e-01
#> [47,] -0.32897716 -1.870389e-01
#> [48,] -0.22631518 -1.536721e-01
#> [49,] -0.11813866 -9.476267e-02
#> [50,] -0.01334510 -1.257189e-02
#> [51,] 0.08113017 8.962521e-02
#> [52,] 0.16063793 2.086307e-01
#> [53,] 0.22244168 3.420336e-01
#> [54,] 0.26492212 4.883117e-01
#> [55,] 0.28673533 6.463225e-01
#> [56,] 0.28627059 8.144022e-01
#> [57,] 0.26160815 9.894390e-01
#> [58,] 0.21096982 1.166311e+00
#> [59,] 0.13345744 1.337968e+00
#> [60,] 0.02975436 1.496238e+00
#> [61,] -0.09753442 1.633159e+00
#> [62,] -0.24410623 1.742492e+00
#> [63,] -0.40474725 1.820937e+00
#> [64,] -0.57446280 1.868642e+00
#> [65,] -0.74957661 1.888824e+00
#> [66,] -0.92838875 1.886525e+00
#> [67,] -1.11108727 1.866866e+00
#> [68,] -1.29882939 1.833286e+00
#> [69,] -1.49218159 1.786313e+00
#> [70,] -1.68934733 1.723276e+00
#> [71,] -1.88473800 1.639109e+00
#> [72,] -2.06840699 1.528067e+00
#> [73,] -2.22666734 1.385910e+00
#> [74,] -2.34389910 1.211941e+00
#> [75,] -2.40520955 1.010307e+00
#> [76,] -2.39933834 7.901548e-01
#> [77,] -2.32108398 5.645699e-01
#> [78,] -2.17260957 3.485372e-01
#> [79,] -1.96325086 1.564753e-01
#> [80,] -1.70783049 4.182978e-16
rfourier_shape(nb.h=12) # better
#> x y
#> [1,] 3.17350221 0.000000e+00
#> [2,] 2.82968114 2.255316e-01
#> [3,] 2.43948432 3.913502e-01
#> [4,] 2.06536164 5.023692e-01
#> [5,] 1.74268302 5.739037e-01
#> [6,] 1.47564178 6.198424e-01
#> [7,] 1.24842809 6.455149e-01
#> [8,] 1.04054160 6.476482e-01
#> [9,] 0.83709685 6.184180e-01
#> [10,] 0.63206684 5.496925e-01
#> [11,] 0.42754983 4.361367e-01
#> [12,] 0.23216062 2.779229e-01
#> [13,] 0.05887461 8.310097e-02
#> [14,] -0.07873057 -1.322843e-01
#> [15,] -0.17140187 -3.482958e-01
#> [16,] -0.21769695 -5.485646e-01
#> [17,] -0.22348979 -7.269792e-01
#> [18,] -0.19763895 -8.891673e-01
#> [19,] -0.14677845 -1.047742e+00
#> [20,] -0.07253700 -1.214591e+00
#> [21,] 0.02774197 -1.395042e+00
#> [22,] 0.15824615 -1.586486e+00
#> [23,] 0.32205629 -1.780433e+00
#> [24,] 0.51961489 -1.965257e+00
#> [25,] 0.74804094 -2.128078e+00
#> [26,] 1.00099083 -2.256307e+00
#> [27,] 1.26941847 -2.339827e+00
#> [28,] 1.54350539 -2.373345e+00
#> [29,] 1.81487968 -2.357100e+00
#> [30,] 2.07741451 -2.294938e+00
#> [31,] 2.32588321 -2.191122e+00
#> [32,] 2.55405607 -2.048687e+00
#> [33,] 2.75500192 -1.870696e+00
#> [34,] 2.92452011 -1.662726e+00
#> [35,] 3.06492303 -1.433321e+00
#> [36,] 3.18450875 -1.191040e+00
#> [37,] 3.29071918 -9.404522e-01
#> [38,] 3.38068991 -6.812003e-01
#> [39,] 3.43662398 -4.119489e-01
#> [40,] 3.43105716 -1.365148e-01
#> [41,] 3.33973942 1.328815e-01
#> [42,] 3.15355628 3.780175e-01
#> [43,] 2.88139811 5.805943e-01
#> [44,] 2.54314959 7.268048e-01
#> [45,] 2.15980801 8.077911e-01
#> [46,] 1.74916782 8.180039e-01
#> [47,] 1.32926781 7.557509e-01
#> [48,] 0.92374397 6.272389e-01
#> [49,] 0.56104073 4.500281e-01
#> [50,] 0.26536741 2.499921e-01
#> [51,] 0.04586366 5.066599e-02
#> [52,] -0.10657467 -1.384153e-01
#> [53,] -0.21116372 -3.246923e-01
#> [54,] -0.28370198 -5.229272e-01
#> [55,] -0.32811803 -7.396021e-01
#> [56,] -0.33890179 -9.641311e-01
#> [57,] -0.31062985 -1.174846e+00
#> [58,] -0.24514106 -1.355220e+00
#> [59,] -0.15025456 -1.506367e+00
#> [60,] -0.03270006 -1.644366e+00
#> [61,] 0.10654541 -1.784042e+00
#> [62,] 0.26942175 -1.923201e+00
#> [63,] 0.45383040 -2.041759e+00
#> [64,] 0.65099261 -2.117583e+00
#> [65,] 0.85157720 -2.145851e+00
#> [66,] 1.05549177 -2.144803e+00
#> [67,] 1.27470132 -2.141773e+00
#> [68,] 1.52343457 -2.150314e+00
#> [69,] 1.80214577 -2.157375e+00
#> [70,] 2.08954349 -2.131510e+00
#> [71,] 2.35233176 -2.045763e+00
#> [72,] 2.56756650 -1.896829e+00
#> [73,] 2.74007725 -1.705464e+00
#> [74,] 2.89889227 -1.498907e+00
#> [75,] 3.07230123 -1.290518e+00
#> [76,] 3.25891076 -1.073231e+00
#> [77,] 3.41707300 -8.311533e-01
#> [78,] 3.48261728 -5.586930e-01
#> [79,] 3.40428186 -2.713285e-01
#> [80,] 3.17350221 -7.772839e-16
rfourier_shape(nb.h=6, alpha=0.4, nb.pts=500)
#> x y
#> [1,] -0.0491200860 0.000000e+00
#> [2,] -0.2084169677 -2.624432e-03
#> [3,] -0.3651579671 -9.197757e-03
#> [4,] -0.5187481480 -1.960486e-02
#> [5,] -0.6686120572 -3.370396e-02
#> [6,] -0.8141968885 -5.132785e-02
#> [7,] -0.9549754990 -7.228533e-02
#> [8,] -1.0904492617 -9.636282e-02
#> [9,] -1.2201507346 -1.233262e-01
#> [10,] -1.3436461299 -1.529225e-01
#> [11,] -1.4605375691 -1.848825e-01
#> [12,] -1.5704651080 -2.189223e-01
#> [13,] -1.6731085219 -2.547461e-01
#> [14,] -1.7681888383 -2.920483e-01
#> [15,] -1.8554696101 -3.305162e-01
#> [16,] -1.9347579196 -3.698323e-01
#> [17,] -2.0059051113 -4.096771e-01
#> [18,] -2.0688072476 -4.497315e-01
#> [19,] -2.1234052862 -4.896792e-01
#> [20,] -2.1696849807 -5.292097e-01
#> [21,] -2.2076765055 -5.680204e-01
#> [22,] -2.2374538086 -6.058192e-01
#> [23,] -2.2591336999 -6.423268e-01
#> [24,] -2.2728746803 -6.772791e-01
#> [25,] -2.2788755223 -7.104290e-01
#> [26,] -2.2773736126 -7.415490e-01
#> [27,] -2.2686430689 -7.704324e-01
#> [28,] -2.2529926444 -7.968955e-01
#> [29,] -2.2307634363 -8.207789e-01
#> [30,] -2.2023264132 -8.419489e-01
#> [31,] -2.1680797801 -8.602988e-01
#> [32,] -2.1284461984 -8.757498e-01
#> [33,] -2.0838698812 -8.882515e-01
#> [34,] -2.0348135832 -8.977828e-01
#> [35,] -1.9817555060 -9.043521e-01
#> [36,] -1.9251861395 -9.079973e-01
#> [37,] -1.8656050613 -9.087858e-01
#> [38,] -1.8035177144 -9.068141e-01
#> [39,] -1.7394321860 -9.022073e-01
#> [40,] -1.6738560068 -8.951181e-01
#> [41,] -1.6072929924 -8.857264e-01
#> [42,] -1.5402401484 -8.742373e-01
#> [43,] -1.4731846559 -8.608803e-01
#> [44,] -1.4066009599 -8.459079e-01
#> [45,] -1.3409479759 -8.295930e-01
#> [46,] -1.2766664334 -8.122281e-01
#> [47,] -1.2141763720 -7.941224e-01
#> [48,] -1.1538748044 -7.756002e-01
#> [49,] -1.0961335611 -7.569983e-01
#> [50,] -1.0412973273 -7.386639e-01
#> [51,] -0.9896818842 -7.209517e-01
#> [52,] -0.9415725634 -7.042219e-01
#> [53,] -0.8972229215 -6.888374e-01
#> [54,] -0.8568536420 -6.751610e-01
#> [55,] -0.8206516680 -6.635532e-01
#> [56,] -0.7887695698 -6.543692e-01
#> [57,] -0.7613251464 -6.479569e-01
#> [58,] -0.7384012629 -6.446535e-01
#> [59,] -0.7200459201 -6.447840e-01
#> [60,] -0.7062725530 -6.486581e-01
#> [61,] -0.6970605534 -6.565683e-01
#> [62,] -0.6923560095 -6.687876e-01
#> [63,] -0.6920726546 -6.855676e-01
#> [64,] -0.6960930158 -7.071363e-01
#> [65,] -0.7042697506 -7.336965e-01
#> [66,] -0.7164271618 -7.654244e-01
#> [67,] -0.7323628762 -8.024680e-01
#> [68,] -0.7518496727 -8.449458e-01
#> [69,] -0.7746374472 -8.929461e-01
#> [70,] -0.8004552968 -9.465258e-01
#> [71,] -0.8290137076 -1.005710e+00
#> [72,] -0.8600068311 -1.070491e+00
#> [73,] -0.8931148291 -1.140830e+00
#> [74,] -0.9280062735 -1.216654e+00
#> [75,] -0.9643405812 -1.297860e+00
#> [76,] -1.0017704669 -1.384310e+00
#> [77,] -1.0399443990 -1.475836e+00
#> [78,] -1.0785090381 -1.572243e+00
#> [79,] -1.1171116449 -1.673301e+00
#> [80,] -1.1554024393 -1.778755e+00
#> [81,] -1.1930368966 -1.888324e+00
#> [82,] -1.2296779651 -2.001698e+00
#> [83,] -1.2649981922 -2.118548e+00
#> [84,] -1.2986817448 -2.238521e+00
#> [85,] -1.3304263137 -2.361242e+00
#> [86,] -1.3599448889 -2.486323e+00
#> [87,] -1.3869673977 -2.613356e+00
#> [88,] -1.4112421967 -2.741922e+00
#> [89,] -1.4325374086 -2.871590e+00
#> [90,] -1.4506421003 -3.001923e+00
#> [91,] -1.4653672949 -3.132473e+00
#> [92,] -1.4765468151 -3.262792e+00
#> [93,] -1.4840379560 -3.392429e+00
#> [94,] -1.4877219855 -3.520935e+00
#> [95,] -1.4875044727 -3.647863e+00
#> [96,] -1.4833154461 -3.772773e+00
#> [97,] -1.4751093840 -3.895232e+00
#> [98,] -1.4628650411 -4.014819e+00
#> [99,] -1.4465851166 -4.131123e+00
#> [100,] -1.4262957691 -4.243749e+00
#> [101,] -1.4020459862 -4.352318e+00
#> [102,] -1.3739068164 -4.456468e+00
#> [103,] -1.3419704722 -4.555859e+00
#> [104,] -1.3063493139 -4.650170e+00
#> [105,] -1.2671747247 -4.739105e+00
#> [106,] -1.2245958881 -4.822388e+00
#> [107,] -1.1787784776 -4.899772e+00
#> [108,] -1.1299032728 -4.971034e+00
#> [109,] -1.0781647115 -5.035978e+00
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#> [112,] -0.9078864223 -5.191341e+00
#> [113,] -0.8468588211 -5.229591e+00
#> [114,] -0.7840914015 -5.260953e+00
#> [115,] -0.7198281696 -5.285393e+00
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#> [117,] -0.5878027086 -5.313515e+00
#> [118,] -0.5205363974 -5.317267e+00
#> [119,] -0.4527632100 -5.314232e+00
#> [120,] -0.3847263775 -5.304507e+00
#> [121,] -0.3166648409 -5.288209e+00
#> [122,] -0.2488120312 -5.265479e+00
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#> [125,] -0.0487343464 -5.160380e+00
#> [126,] 0.0160973966 -5.113696e+00
#> [127,] 0.0796725679 -5.061551e+00
#> [128,] 0.1418114731 -5.004184e+00
#> [129,] 0.2023459158 -4.941846e+00
#> [130,] 0.2611196546 -4.874796e+00
#> [131,] 0.3179887584 -4.803302e+00
#> [132,] 0.3728218614 -4.727637e+00
#> [133,] 0.4255003222 -4.648082e+00
#> [134,] 0.4759182873 -4.564918e+00
#> [135,] 0.5239826665 -4.478430e+00
#> [136,] 0.5696130218 -4.388902e+00
#> [137,] 0.6127413771 -4.296619e+00
#> [138,] 0.6533119534 -4.201861e+00
#> [139,] 0.6912808373 -4.104908e+00
#> [140,] 0.7266155877 -4.006033e+00
#> [141,] 0.7592947892 -3.905504e+00
#> [142,] 0.7893075590 -3.803583e+00
#> [143,] 0.8166530147 -3.700524e+00
#> [144,] 0.8413397116 -3.596575e+00
#> [145,] 0.8633850551 -3.491972e+00
#> [146,] 0.8828146984 -3.386944e+00
#> [147,] 0.8996619308 -3.281709e+00
#> [148,] 0.9139670646 -3.176477e+00
#> [149,] 0.9257768282 -3.071445e+00
#> [150,] 0.9351437707 -2.966802e+00
#> [151,] 0.9421256853 -2.862724e+00
#> [152,] 0.9467850565 -2.759379e+00
#> [153,] 0.9491885368 -2.656923e+00
#> [154,] 0.9494064572 -2.555503e+00
#> [155,] 0.9475123753 -2.455254e+00
#> [156,] 0.9435826648 -2.356304e+00
#> [157,] 0.9376961491 -2.258769e+00
#> [158,] 0.9299337804 -2.162759e+00
#> [159,] 0.9203783660 -2.068372e+00
#> [160,] 0.9091143424 -1.975701e+00
#> [161,] 0.8962275968 -1.884830e+00
#> [162,] 0.8818053352 -1.795837e+00
#> [163,] 0.8659359955 -1.708793e+00
#> [164,] 0.8487092038 -1.623763e+00
#> [165,] 0.8302157700 -1.540806e+00
#> [166,] 0.8105477206 -1.459978e+00
#> [167,] 0.7897983634 -1.381328e+00
#> [168,] 0.7680623804 -1.304902e+00
#> [169,] 0.7454359438 -1.230744e+00
#> [170,] 0.7220168495 -1.158893e+00
#> [171,] 0.6979046618 -1.089385e+00
#> [172,] 0.6732008652 -1.022254e+00
#> [173,] 0.6480090149 -9.575309e-01
#> [174,] 0.6224348813 -8.952457e-01
#> [175,] 0.5965865813 -8.354251e-01
#> [176,] 0.5705746901 -7.780943e-01
#> [177,] 0.5445123285 -7.232763e-01
#> [178,] 0.5185152175 -6.709918e-01
#> [179,] 0.4927016963 -6.212598e-01
#> [180,] 0.4671926980 -5.740964e-01
#> [181,] 0.4421116760 -5.295157e-01
#> [182,] 0.4175844799 -4.875285e-01
#> [183,] 0.3937391733 -4.481428e-01
#> [184,] 0.3707057924 -4.113631e-01
#> [185,] 0.3486160418 -3.771903e-01
#> [186,] 0.3276029246 -3.456207e-01
#> [187,] 0.3078003067 -3.166465e-01
#> [188,] 0.2893424132 -2.902547e-01
#> [189,] 0.2723632581 -2.664268e-01
#> [190,] 0.2569960074 -2.451388e-01
#> [191,] 0.2433722778 -2.263602e-01
#> [192,] 0.2316213732 -2.100539e-01
#> [193,] 0.2218694622 -1.961760e-01
#> [194,] 0.2142387017 -1.846750e-01
#> [195,] 0.2088463099 -1.754920e-01
#> [196,] 0.2058035963 -1.685601e-01
#> [197,] 0.2052149531 -1.638045e-01
#> [198,] 0.2071768177 -1.611420e-01
#> [199,] 0.2117766109 -1.604812e-01
#> [200,] 0.2190916621 -1.617224e-01
#> [201,] 0.2291881286 -1.647577e-01
#> [202,] 0.2421199188 -1.694711e-01
#> [203,] 0.2579276294 -1.757388e-01
#> [204,] 0.2766375062 -1.834295e-01
#> [205,] 0.2982604381 -1.924048e-01
#> [206,] 0.3227909968 -2.025195e-01
#> [207,] 0.3502065298 -2.136224e-01
#> [208,] 0.3804663197 -2.255571e-01
#> [209,] 0.4135108174 -2.381624e-01
#> [210,] 0.4492609619 -2.512732e-01
#> [211,] 0.4876175946 -2.647216e-01
#> [212,] 0.5284609771 -2.783377e-01
#> [213,] 0.5716504229 -2.919508e-01
#> [214,] 0.6170240493 -3.053901e-01
#> [215,] 0.6643986583 -3.184865e-01
#> [216,] 0.7135697522 -3.310734e-01
#> [217,] 0.7643116904 -3.429877e-01
#> [218,] 0.8163779912 -3.540719e-01
#> [219,] 0.8695017848 -3.641744e-01
#> [220,] 0.9233964170 -3.731515e-01
#> [221,] 0.9777562091 -3.808685e-01
#> [222,] 1.0322573710 -3.872008e-01
#> [223,] 1.0865590706 -3.920356e-01
#> [224,] 1.1403046542 -3.952724e-01
#> [225,] 1.1931230181 -3.968250e-01
#> [226,] 1.2446301253 -3.966222e-01
#> [227,] 1.2944306629 -3.946088e-01
#> [228,] 1.3421198325 -3.907467e-01
#> [229,] 1.3872852681 -3.850157e-01
#> [230,] 1.4295090700 -3.774145e-01
#> [231,] 1.4683699469 -3.679610e-01
#> [232,] 1.5034454531 -3.566934e-01
#> [233,] 1.5343143114 -3.436699e-01
#> [234,] 1.5605588062 -3.289696e-01
#> [235,] 1.5817672343 -3.126924e-01
#> [236,] 1.5975363993 -2.949590e-01
#> [237,] 1.6074741327 -2.759107e-01
#> [238,] 1.6112018279 -2.557092e-01
#> [239,] 1.6083569694 -2.345362e-01
#> [240,] 1.5985956413 -2.125926e-01
#> [241,] 1.5815949977 -1.900976e-01
#> [242,] 1.5570556790 -1.672881e-01
#> [243,] 1.5247041559 -1.444175e-01
#> [244,] 1.4842949853 -1.217543e-01
#> [245,] 1.4356129607 -9.958054e-02
#> [246,] 1.3784751417 -7.819084e-02
#> [247,] 1.3127327457 -5.789019e-02
#> [248,] 1.2382728880 -3.899233e-02
#> [249,] 1.1550201551 -2.181784e-02
#> [250,] 1.0629379977 -6.692109e-03
#> [251,] 0.9620299310 6.056806e-03
#> [252,] 0.8523405308 1.610035e-02
#> [253,] 0.7339562151 2.311176e-02
#> [254,] 0.6070058016 2.676834e-02
#> [255,] 0.4716608340 2.675388e-02
#> [256,] 0.3281356702 2.276096e-02
#> [257,] 0.1766873280 1.449337e-02
#> [258,] 0.0176150845 1.668473e-03
#> [259,] -0.1487401725 -1.598046e-02
#> [260,] -0.3219968412 -3.870196e-02
#> [261,] -0.5017337489 -6.672411e-02
#> [262,] -0.6874915390 -1.002524e-01
#> [263,] -0.8787742964 -1.394678e-01
#> [264,] -1.0750514062 -1.845244e-01
#> [265,] -1.2757596359 -2.355482e-01
#> [266,] -1.4803054332 -2.926349e-01
#> [267,] -1.6880674276 -3.558488e-01
#> [268,] -1.8983991234 -4.252210e-01
#> [269,] -2.1106317703 -5.007487e-01
#> [270,] -2.3240773954 -5.823941e-01
#> [271,] -2.5380319828 -6.700832e-01
#> [272,] -2.7517787794 -7.637059e-01
#> [273,] -2.9645917117 -8.631154e-01
#> [274,] -3.1757388921 -9.681279e-01
#> [275,] -3.3844861954 -1.078523e+00
#> [276,] -3.5901008841 -1.194044e+00
#> [277,] -3.7918552610 -1.314399e+00
#> [278,] -3.9890303282 -1.439261e+00
#> [279,] -4.1809194290 -1.568267e+00
#> [280,] -4.3668318522 -1.701026e+00
#> [281,] -4.5460963756 -1.837112e+00
#> [282,] -4.7180647275 -1.976072e+00
#> [283,] -4.8821149447 -2.117426e+00
#> [284,] -5.0376546055 -2.260666e+00
#> [285,] -5.1841239189 -2.405266e+00
#> [286,] -5.3209986490 -2.550677e+00
#> [287,] -5.4477928568 -2.696333e+00
#> [288,] -5.5640614420 -2.841653e+00
#> [289,] -5.6694024686 -2.986046e+00
#> [290,] -5.7634592592 -3.128912e+00
#> [291,] -5.8459222440 -3.269645e+00
#> [292,] -5.9165305543 -3.407638e+00
#> [293,] -5.9750733473 -3.542286e+00
#> [294,] -6.0213908563 -3.672987e+00
#> [295,] -6.0553751569 -3.799149e+00
#> [296,] -6.0769706462 -3.920192e+00
#> [297,] -6.0861742300 -4.035549e+00
#> [298,] -6.0830352171 -4.144672e+00
#> [299,] -6.0676549213 -4.247037e+00
#> [300,] -6.0401859731 -4.342140e+00
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#> [302,] -5.9498431002 -4.508703e+00
#> [303,] -5.8875208598 -4.579310e+00
#> [304,] -5.8142100201 -4.640957e+00
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#> [306,] -5.6362205080 -4.736073e+00
#> [307,] -5.5324419493 -4.768996e+00
#> [308,] -5.4194698055 -4.791870e+00
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#> [311,] -5.0309310732 -4.798816e+00
#> [312,] -4.8868620859 -4.780348e+00
#> [313,] -4.7365648154 -4.751499e+00
#> [314,] -4.5806962193 -4.712346e+00
#> [315,] -4.4199262834 -4.663017e+00
#> [316,] -4.2549343536 -4.603689e+00
#> [317,] -4.0864054489 -4.534584e+00
#> [318,] -3.9150265759 -4.455973e+00
#> [319,] -3.7414830713 -4.368169e+00
#> [320,] -3.5664549920 -4.271531e+00
#> [321,] -3.3906135775 -4.166459e+00
#> [322,] -3.2146178059 -4.053391e+00
#> [323,] -3.0391110633 -3.932804e+00
#> [324,] -2.8647179495 -3.805208e+00
#> [325,] -2.6920412365 -3.671144e+00
#> [326,] -2.5216590002 -3.531185e+00
#> [327,] -2.3541219405 -3.385924e+00
#> [328,] -2.1899509060 -3.235982e+00
#> [329,] -2.0296346383 -3.081995e+00
#> [330,] -1.8736277460 -2.924614e+00
#> [331,] -1.7223489218 -2.764504e+00
#> [332,] -1.5761794099 -2.602335e+00
#> [333,] -1.4354617320 -2.438783e+00
#> [334,] -1.3004986772 -2.274524e+00
#> [335,] -1.1715525591 -2.110228e+00
#> [336,] -1.0488447423 -1.946562e+00
#> [337,] -0.9325554379 -1.784179e+00
#> [338,] -0.8228237665 -1.623718e+00
#> [339,] -0.7197480838 -1.465800e+00
#> [340,] -0.6233865647 -1.311026e+00
#> [341,] -0.5337580368 -1.159971e+00
#> [342,] -0.4508430560 -1.013182e+00
#> [343,] -0.3745852119 -8.711775e-01
#> [344,] -0.3048926515 -7.344407e-01
#> [345,] -0.2416398079 -6.034202e-01
#> [346,] -0.1846693177 -4.785269e-01
#> [347,] -0.1337941121 -3.601316e-01
#> [348,] -0.0887996638 -2.485638e-01
#> [349,] -0.0494463715 -1.441101e-01
#> [350,] -0.0154720622 -4.701310e-02
#> [351,] 0.0134054074 4.252949e-02
#> [352,] 0.0374854712 1.243654e-01
#> [353,] 0.0570821171 1.983879e-01
#> [354,] 0.0725211136 2.645363e-01
#> [355,] 0.0841372209 3.227948e-01
#> [356,] 0.0922714074 3.731929e-01
#> [357,] 0.0972680931 4.158035e-01
#> [358,] 0.0994724381 4.507425e-01
#> [359,] 0.0992276988 4.781669e-01
#> [360,] 0.0968726680 4.982736e-01
#> [361,] 0.0927392197 5.112970e-01
#> [362,] 0.0871499740 5.175069e-01
#> [363,] 0.0804160985 5.172066e-01
#> [364,] 0.0728352630 5.107299e-01
#> [365,] 0.0646897580 4.984384e-01
#> [366,] 0.0562447922 4.807189e-01
#> [367,] 0.0477469784 4.579800e-01
#> [368,] 0.0394230163 4.306493e-01
#> [369,] 0.0314785819 3.991701e-01
#> [370,] 0.0240974266 3.639978e-01
#> [371,] 0.0174406929 3.255972e-01
#> [372,] 0.0116464470 2.844384e-01
#> [373,] 0.0068294301 2.409941e-01
#> [374,] 0.0030810269 1.957358e-01
#> [375,] 0.0004694488 1.491308e-01
#> [376,] -0.0009598730 1.016390e-01
#> [377,] -0.0011836908 5.370944e-02
#> [378,] -0.0002001469 5.777811e-03
#> [379,] 0.0019722053 -4.173675e-02
#> [380,] 0.0052955579 -8.843425e-02
#> [381,] 0.0097141677 -1.339364e-01
#> [382,] 0.0151558267 -1.778890e-01
#> [383,] 0.0215334678 -2.199639e-01
#> [384,] 0.0287468917 -2.598611e-01
#> [385,] 0.0366845972 -2.973105e-01
#> [386,] 0.0452256982 -3.320731e-01
#> [387,] 0.0542419100 -3.639424e-01
#> [388,] 0.0635995851 -3.927453e-01
#> [389,] 0.0731617813 -4.183428e-01
#> [390,] 0.0827903424 -4.406302e-01
#> [391,] 0.0923479727 -4.595377e-01
#> [392,] 0.1017002861 -4.750298e-01
#> [393,] 0.1107178119 -4.871055e-01
#> [394,] 0.1192779386 -4.957969e-01
#> [395,] 0.1272667785 -5.011692e-01
#> [396,] 0.1345809348 -5.033190e-01
#> [397,] 0.1411291575 -5.023730e-01
#> [398,] 0.1468338708 -4.984867e-01
#> [399,] 0.1516325589 -4.918424e-01
#> [400,] 0.1554789968 -4.826475e-01
#> [401,] 0.1583443157 -4.711320e-01
#> [402,] 0.1602178907 -4.575464e-01
#> [403,] 0.1611080441 -4.421595e-01
#> [404,] 0.1610425565 -4.252554e-01
#> [405,] 0.1600689790 -4.071311e-01
#> [406,] 0.1582547442 -3.880940e-01
#> [407,] 0.1556870729 -3.684587e-01
#> [408,] 0.1524726756 -3.485441e-01
#> [409,] 0.1487372509 -3.286714e-01
#> [410,] 0.1446247831 -3.091602e-01
#> [411,] 0.1402966432 -2.903264e-01
#> [412,] 0.1359305000 -2.724793e-01
#> [413,] 0.1317190495 -2.559187e-01
#> [414,] 0.1278685704 -2.409329e-01
#> [415,] 0.1245973187 -2.277954e-01
#> [416,] 0.1221337714 -2.167632e-01
#> [417,] 0.1207147347 -2.080744e-01
#> [418,] 0.1205833303 -2.019462e-01
#> [419,] 0.1219868758 -1.985731e-01
#> [420,] 0.1251746763 -1.981249e-01
#> [421,] 0.1303957451 -2.007457e-01
#> [422,] 0.1378964703 -2.065525e-01
#> [423,] 0.1479182489 -2.156342e-01
#> [424,] 0.1606951045 -2.280504e-01
#> [425,] 0.1764513113 -2.438315e-01
#> [426,] 0.1953990416 -2.629782e-01
#> [427,] 0.2177360577 -2.854609e-01
#> [428,] 0.2436434683 -3.112207e-01
#> [429,] 0.2732835666 -3.401690e-01
#> [430,] 0.3067977706 -3.721887e-01
#> [431,] 0.3443046826 -4.071349e-01
#> [432,] 0.3858982853 -4.448357e-01
#> [433,] 0.4316462915 -4.850940e-01
#> [434,] 0.4815886611 -5.276885e-01
#> [435,] 0.5357363014 -5.723759e-01
#> [436,] 0.5940699617 -6.188922e-01
#> [437,] 0.6565393349 -6.669551e-01
#> [438,] 0.7230623754 -7.162661e-01
#> [439,] 0.7935248421 -7.665126e-01
#> [440,] 0.8677800724 -8.173707e-01
#> [441,] 0.9456489928 -8.685073e-01
#> [442,] 1.0269203697 -9.195827e-01
#> [443,] 1.1113513010 -9.702536e-01
#> [444,] 1.1986679491 -1.020175e+00
#> [445,] 1.2885665117 -1.069005e+00
#> [446,] 1.3807144290 -1.116402e+00
#> [447,] 1.4747518185 -1.162036e+00
#> [448,] 1.5702931325 -1.205583e+00
#> [449,] 1.6669290275 -1.246731e+00
#> [450,] 1.7642284357 -1.285184e+00
#> [451,] 1.8617408256 -1.320661e+00
#> [452,] 1.9589986377 -1.352900e+00
#> [453,] 2.0555198811 -1.381659e+00
#> [454,] 2.1508108725 -1.406721e+00
#> [455,] 2.2443691025 -1.427890e+00
#> [456,] 2.3356862074 -1.444999e+00
#> [457,] 2.4242510296 -1.457907e+00
#> [458,] 2.5095527440 -1.466500e+00
#> [459,] 2.5910840309 -1.470694e+00
#> [460,] 2.6683442720 -1.470437e+00
#> [461,] 2.7408427500 -1.465704e+00
#> [462,] 2.8081018272 -1.456504e+00
#> [463,] 2.8696600830 -1.442874e+00
#> [464,] 2.9250753866 -1.424882e+00
#> [465,] 2.9739278858 -1.402627e+00
#> [466,] 3.0158228871 -1.376237e+00
#> [467,] 3.0503936105 -1.345868e+00
#> [468,] 3.0773037961 -1.311704e+00
#> [469,] 3.0962501455 -1.273953e+00
#> [470,] 3.1069645794 -1.232850e+00
#> [471,] 3.1092162952 -1.188653e+00
#> [472,] 3.1028136086 -1.141638e+00
#> [473,] 3.0876055668 -1.092103e+00
#> [474,] 3.0634833183 -1.040361e+00
#> [475,] 3.0303812321 -9.867403e-01
#> [476,] 2.9882777541 -9.315820e-01
#> [477,] 2.9371959947 -8.752358e-01
#> [478,] 2.8772040430 -8.180593e-01
#> [479,] 2.8084150020 -7.604142e-01
#> [480,] 2.7309867450 -7.026646e-01
#> [481,] 2.6451213919 -6.451738e-01
#> [482,] 2.5510645094 -5.883018e-01
#> [483,] 2.4491040361 -5.324030e-01
#> [484,] 2.3395689420 -4.778231e-01
#> [485,] 2.2228276275 -4.248973e-01
#> [486,] 2.0992860718 -3.739474e-01
#> [487,] 1.9693857436 -3.252796e-01
#> [488,] 1.8336012848 -2.791826e-01
#> [489,] 1.6924379826 -2.359253e-01
#> [490,] 1.5464290467 -1.957551e-01
#> [491,] 1.3961327068 -1.588961e-01
#> [492,] 1.2421291512 -1.255476e-01
#> [493,] 1.0850173244 -9.588280e-02
#> [494,] 0.9254116045 -7.004754e-02
#> [495,] 0.7639383824 -4.815950e-02
#> [496,] 0.6012325644 -3.030744e-02
#> [497,] 0.4379340204 -1.655068e-02
#> [498,] 0.2746840012 -6.918859e-03
#> [499,] 0.1121215474 -1.411859e-03
#> [500,] -0.0491200860 1.203095e-17
# Butterflies of the vignette' cover
panel(Out(a2l(replicate(100,
rfourier_shape(nb.h=6, alpha=0.4, nb.pts=200, plot=FALSE)))))
