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(),
rfourier_i()
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,] 0.68425866 0.000000e+00
#> [2,] 0.57941416 4.618054e-02
#> [3,] 0.44646972 7.162415e-02
#> [4,] 0.28445884 6.919048e-02
#> [5,] 0.09763201 3.215236e-02
#> [6,] -0.10488714 -4.405778e-02
#> [7,] -0.31035979 -1.604753e-01
#> [8,] -0.50431853 -3.138952e-01
#> [9,] -0.67269202 -4.969614e-01
#> [10,] -0.80376313 -6.990124e-01
#> [11,] -0.88962727 -9.074944e-01
#> [12,] -0.92694598 -1.109661e+00
#> [13,] -0.91694098 -1.294254e+00
#> [14,] -0.86471096 -1.452901e+00
#> [15,] -0.77805105 -1.581032e+00
#> [16,] -0.66600504 -1.678236e+00
#> [17,] -0.53738360 -1.748029e+00
#> [18,] -0.39945454 -1.797125e+00
#> [19,] -0.25696594 -1.834288e+00
#> [20,] -0.11161485 -1.868927e+00
#> [21,] 0.03797401 -1.909574e+00
#> [22,] 0.19574395 -1.962418e+00
#> [23,] 0.36721604 -2.030091e+00
#> [24,] 0.55811706 -2.110878e+00
#> [25,] 0.77279975 -2.198514e+00
#> [26,] 1.01269299 -2.282684e+00
#> [27,] 1.27505716 -2.350220e+00
#> [28,] 1.55231284 -2.386887e+00
#> [29,] 1.83214602 -2.379525e+00
#> [30,] 2.09847063 -2.318199e+00
#> [31,] 2.33316732 -2.197985e+00
#> [32,] 2.51834896 -2.020046e+00
#> [33,] 2.63876902 -1.791772e+00
#> [34,] 2.68392651 -1.525938e+00
#> [35,] 2.64945603 -1.239027e+00
#> [36,] 2.53752291 -9.490604e-01
#> [37,] 2.35614875 -6.733620e-01
#> [38,] 2.11762486 -4.266960e-01
#> [39,] 1.83637374 -2.201265e-01
#> [40,] 1.52673998 -6.074589e-02
#> [41,] 1.20119747 4.779321e-02
#> [42,] 0.86934519 1.042086e-01
#> [43,] 0.53785580 1.083766e-01
#> [44,] 0.21129246 6.038512e-02
#> [45,] -0.10651591 -3.983808e-02
#> [46,] -0.41099251 -1.922020e-01
#> [47,] -0.69569559 -3.955354e-01
#> [48,] -0.95193089 -6.463783e-01
#> [49,] -1.16925251 -9.378936e-01
#> [50,] -1.33676153 -1.259310e+00
#> [51,] -1.44488745 -1.596180e+00
#> [52,] -1.48719856 -1.931520e+00
#> [53,] -1.46177212 -2.247669e+00
#> [54,] -1.37176705 -2.528478e+00
#> [55,] -1.22504973 -2.761352e+00
#> [56,] -1.03296930 -2.938662e+00
#> [57,] -0.80859515 -3.058221e+00
#> [58,] -0.56485651 -3.122712e+00
#> [59,] -0.31302883 -3.138249e+00
#> [60,] -0.06189444 -3.112445e+00
#> [61,] 0.18229894 -3.052492e+00
#> [62,] 0.41518984 -2.963731e+00
#> [63,] 0.63326554 -2.849029e+00
#> [64,] 0.83283614 -2.709093e+00
#> [65,] 1.00939964 -2.543540e+00
#> [66,] 1.15764337 -2.352380e+00
#> [67,] 1.27211885 -2.137433e+00
#> [68,] 1.34840668 -1.903264e+00
#> [69,] 1.38441870 -1.657308e+00
#> [70,] 1.38141712 -1.409161e+00
#> [71,] 1.34438468 -1.169177e+00
#> [72,] 1.28154373 -9.467598e-01
#> [73,] 1.20304954 -7.487955e-01
#> [74,] 1.11911378 -5.786513e-01
#> [75,] 1.03798250 -4.360039e-01
#> [76,] 0.96425428 -3.175501e-01
#> [77,] 0.89795982 -2.184157e-01
#> [78,] 0.83465136 -1.338975e-01
#> [79,] 0.76651250 -6.109267e-02
#> [80,] 0.68425866 -1.675950e-16
rfourier_shape(nb.h=12) # better
#> x y
#> [1,] 1.374855047 0.000000e+00
#> [2,] 1.118455576 8.914328e-02
#> [3,] 0.933228096 1.497115e-01
#> [4,] 0.812263699 1.975713e-01
#> [5,] 0.731045405 2.407493e-01
#> [6,] 0.660053516 2.772551e-01
#> [7,] 0.576956028 2.983221e-01
#> [8,] 0.472919199 2.943518e-01
#> [9,] 0.352038010 2.600734e-01
#> [10,] 0.226364885 1.968638e-01
#> [11,] 0.109831250 1.120371e-01
#> [12,] 0.013352905 1.598496e-02
#> [13,] -0.057785808 -8.156414e-02
#> [14,] -0.103944395 -1.746490e-01
#> [15,] -0.128977174 -2.620870e-01
#> [16,] -0.137307879 -3.459959e-01
#> [17,] -0.131980684 -4.293136e-01
#> [18,] -0.114453020 -5.149182e-01
#> [19,] -0.085118203 -6.075954e-01
#> [20,] -0.042804855 -7.167430e-01
#> [21,] 0.017009787 -8.553598e-01
#> [22,] 0.103006997 -1.032690e+00
#> [23,] 0.224949450 -1.243594e+00
#> [24,] 0.386761596 -1.462787e+00
#> [25,] 0.580381539 -1.651109e+00
#> [26,] 0.786633621 -1.773130e+00
#> [27,] 0.985149974 -1.815855e+00
#> [28,] 1.167623558 -1.795376e+00
#> [29,] 1.343983572 -1.745517e+00
#> [30,] 1.534708999 -1.695406e+00
#> [31,] 1.752967549 -1.651401e+00
#> [32,] 1.989484646 -1.595827e+00
#> [33,] 2.212690605 -1.502457e+00
#> [34,] 2.385772610 -1.356423e+00
#> [35,] 2.488897206 -1.163941e+00
#> [36,] 2.530069418 -9.462728e-01
#> [37,] 2.536382096 -7.248708e-01
#> [38,] 2.532522083 -5.102967e-01
#> [39,] 2.523148106 -3.024503e-01
#> [40,] 2.492192929 -9.915930e-02
#> [41,] 2.418331016 9.622049e-02
#> [42,] 2.293273400 2.748952e-01
#> [43,] 2.128349203 4.288569e-01
#> [44,] 1.945358267 5.559625e-01
#> [45,] 1.760581373 6.584761e-01
#> [46,] 1.575391850 7.367370e-01
#> [47,] 1.380117516 7.846613e-01
#> [48,] 1.166346166 7.919702e-01
#> [49,] 0.936712396 7.513660e-01
#> [50,] 0.704836709 6.639987e-01
#> [51,] 0.487226451 5.382433e-01
#> [52,] 0.295133659 3.833089e-01
#> [53,] 0.132755931 2.041299e-01
#> [54,] 0.001357492 2.502167e-03
#> [55,] -0.096278037 -2.170178e-01
#> [56,] -0.155741083 -4.430629e-01
#> [57,] -0.174657531 -6.605795e-01
#> [58,] -0.155521208 -8.597723e-01
#> [59,] -0.104099417 -1.043642e+00
#> [60,] -0.024406575 -1.227317e+00
#> [61,] 0.085334253 -1.428874e+00
#> [62,] 0.232275007 -1.658038e+00
#> [63,] 0.424626679 -1.910373e+00
#> [64,] 0.666953473 -2.169501e+00
#> [65,] 0.957843010 -2.413625e+00
#> [66,] 1.289647153 -2.620617e+00
#> [67,] 1.648217480 -2.769360e+00
#> [68,] 2.011983124 -2.839896e+00
#> [69,] 2.352466609 -2.816173e+00
#> [70,] 2.638816728 -2.691814e+00
#> [71,] 2.845838687 -2.474954e+00
#> [72,] 2.961023122 -2.187501e+00
#> [73,] 2.985475393 -1.858203e+00
#> [74,] 2.927871618 -1.513892e+00
#> [75,] 2.796360797 -1.174610e+00
#> [76,] 2.595418614 -8.547283e-01
#> [77,] 2.330662560 -5.668998e-01
#> [78,] 2.017582758 -3.236673e-01
#> [79,] 1.686029578 -1.343801e-01
#> [80,] 1.374855047 -3.367424e-16
rfourier_shape(nb.h=6, alpha=0.4, nb.pts=500)
#> x y
#> [1,] 1.560669671 0.000000e+00
#> [2,] 1.607484398 2.024180e-02
#> [3,] 1.647596741 4.150038e-02
#> [4,] 1.680761742 6.352042e-02
#> [5,] 1.706773237 8.603647e-02
#> [6,] 1.725465124 1.087752e-01
#> [7,] 1.736712373 1.314576e-01
#> [8,] 1.740431779 1.538017e-01
#> [9,] 1.736582425 1.755243e-01
#> [10,] 1.725165889 1.963439e-01
#> [11,] 1.706226168 2.159830e-01
#> [12,] 1.679849327 2.341704e-01
#> [13,] 1.646162885 2.506434e-01
#> [14,] 1.605334930 2.651500e-01
#> [15,] 1.557572979 2.774516e-01
#> [16,] 1.503122587 2.873245e-01
#> [17,] 1.442265719 2.945619e-01
#> [18,] 1.375318890 2.989762e-01
#> [19,] 1.302631095 3.004002e-01
#> [20,] 1.224581537 2.986887e-01
#> [21,] 1.141577176 2.937202e-01
#> [22,] 1.054050106 2.853975e-01
#> [23,] 0.962454787 2.736494e-01
#> [24,] 0.867265150 2.584307e-01
#> [25,] 0.768971591 2.397234e-01
#> [26,] 0.668077882 2.175368e-01
#> [27,] 0.565098006 1.919076e-01
#> [28,] 0.460552958 1.629000e-01
#> [29,] 0.354967516 1.306054e-01
#> [30,] 0.248867013 9.514180e-02
#> [31,] 0.142774127 5.665309e-02
#> [32,] 0.037205714 1.530830e-02
#> [33,] -0.067330294 -2.869960e-02
#> [34,] -0.170337914 -7.515502e-02
#> [35,] -0.271336030 -1.238212e-01
#> [36,] -0.369861189 -1.744418e-01
#> [37,] -0.465470258 -2.267429e-01
#> [38,] -0.557742931 -2.804348e-01
#> [39,] -0.646284052 -3.352141e-01
#> [40,] -0.730725763 -3.907659e-01
#> [41,] -0.810729446 -4.467664e-01
#> [42,] -0.885987455 -5.028847e-01
#> [43,] -0.956224631 -5.587860e-01
#> [44,] -1.021199583 -6.141335e-01
#> [45,] -1.080705734 -6.685911e-01
#> [46,] -1.134572132 -7.218262e-01
#> [47,] -1.182664007 -7.735120e-01
#> [48,] -1.224883089 -8.233298e-01
#> [49,] -1.261167679 -8.709722e-01
#> [50,] -1.291492475 -9.161445e-01
#> [51,] -1.315868158 -9.585680e-01
#> [52,] -1.334340742 -9.979815e-01
#> [53,] -1.346990699 -1.034144e+00
#> [54,] -1.353931855 -1.066836e+00
#> [55,] -1.355310091 -1.095861e+00
#> [56,] -1.351301824 -1.121050e+00
#> [57,] -1.342112322 -1.142259e+00
#> [58,] -1.327973830 -1.159374e+00
#> [59,] -1.309143542 -1.172307e+00
#> [60,] -1.285901437 -1.181003e+00
#> [61,] -1.258547976 -1.185439e+00
#> [62,] -1.227401702 -1.185620e+00
#> [63,] -1.192796736 -1.181585e+00
#> [64,] -1.155080214 -1.173405e+00
#> [65,] -1.114609658 -1.161182e+00
#> [66,] -1.071750318 -1.145048e+00
#> [67,] -1.026872492 -1.125169e+00
#> [68,] -0.980348856 -1.101738e+00
#> [69,] -0.932551808 -1.074978e+00
#> [70,] -0.883850853 -1.045140e+00
#> [71,] -0.834610045 -1.012499e+00
#> [72,] -0.785185507 -9.773576e-01
#> [73,] -0.735923035 -9.400395e-01
#> [74,] -0.687155814 -9.008896e-01
#> [75,] -0.639202253 -8.602716e-01
#> [76,] -0.592363952 -8.185658e-01
#> [77,] -0.546923828 -7.761666e-01
#> [78,] -0.503144381 -7.334802e-01
#> [79,] -0.461266153 -6.909220e-01
#> [80,] -0.421506341 -6.489138e-01
#> [81,] -0.384057618 -6.078815e-01
#> [82,] -0.349087128 -5.682521e-01
#> [83,] -0.316735691 -5.304513e-01
#> [84,] -0.287117196 -4.949001e-01
#> [85,] -0.260318209 -4.620131e-01
#> [86,] -0.236397770 -4.321948e-01
#> [87,] -0.215387399 -4.058378e-01
#> [88,] -0.197291295 -3.833199e-01
#> [89,] -0.182086736 -3.650017e-01
#> [90,] -0.169724662 -3.512240e-01
#> [91,] -0.160130437 -3.423062e-01
#> [92,] -0.153204801 -3.385435e-01
#> [93,] -0.148824966 -3.402057e-01
#> [94,] -0.146845886 -3.475346e-01
#> [95,] -0.147101663 -3.607429e-01
#> [96,] -0.149407085 -3.800129e-01
#> [97,] -0.153559284 -4.054947e-01
#> [98,] -0.159339508 -4.373057e-01
#> [99,] -0.166514974 -4.755294e-01
#> [100,] -0.174840806 -5.202150e-01
#> [101,] -0.184062034 -5.713767e-01
#> [102,] -0.193915645 -6.289938e-01
#> [103,] -0.204132658 -6.930105e-01
#> [104,] -0.214440225 -7.633361e-01
#> [105,] -0.224563732 -8.398455e-01
#> [106,] -0.234228883 -9.223798e-01
#> [107,] -0.243163763 -1.010747e+00
#> [108,] -0.251100856 -1.104724e+00
#> [109,] -0.257779007 -1.204055e+00
#> [110,] -0.262945319 -1.308456e+00
#> [111,] -0.266356964 -1.417616e+00
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#> [125,] -0.030420432 -3.221157e+00
#> [126,] 0.010550009 -3.351445e+00
#> [127,] 0.054768428 -3.479406e+00
#> [128,] 0.102148830 -3.604586e+00
#> [129,] 0.152584817 -3.726543e+00
#> [130,] 0.205950373 -3.844851e+00
#> [131,] 0.262100753 -3.959099e+00
#> [132,] 0.320873490 -4.068896e+00
#> [133,] 0.382089497 -4.173871e+00
#> [134,] 0.445554262 -4.273672e+00
#> [135,] 0.511059119 -4.367974e+00
#> [136,] 0.578382592 -4.456472e+00
#> [137,] 0.647291790 -4.538890e+00
#> [138,] 0.717543864 -4.614977e+00
#> [139,] 0.788887481 -4.684508e+00
#> [140,] 0.861064339 -4.747286e+00
#> [141,] 0.933810690 -4.803143e+00
#> [142,] 1.006858864 -4.851938e+00
#> [143,] 1.079938789 -4.893559e+00
#> [144,] 1.152779496 -4.927924e+00
#> [145,] 1.225110587 -4.954975e+00
#> [146,] 1.296663676 -4.974687e+00
#> [147,] 1.367173776 -4.987059e+00
#> [148,] 1.436380641 -4.992116e+00
#> [149,] 1.504030033 -4.989913e+00
#> [150,] 1.569874936 -4.980526e+00
#> [151,] 1.633676675 -4.964057e+00
#> [152,] 1.695205974 -4.940632e+00
#> [153,] 1.754243915 -4.910396e+00
#> [154,] 1.810582809 -4.873519e+00
#> [155,] 1.864026984 -4.830186e+00
#> [156,] 1.914393462 -4.780602e+00
#> [157,] 1.961512555 -4.724989e+00
#> [158,] 2.005228353 -4.663585e+00
#> [159,] 2.045399121 -4.596638e+00
#> [160,] 2.081897599 -4.524411e+00
#> [161,] 2.114611202 -4.447177e+00
#> [162,] 2.143442139 -4.365219e+00
#> [163,] 2.168307431 -4.278825e+00
#> [164,] 2.189138856 -4.188293e+00
#> [165,] 2.205882799 -4.093921e+00
#> [166,] 2.218500039 -3.996015e+00
#> [167,] 2.226965458 -3.894879e+00
#> [168,] 2.231267683 -3.790821e+00
#> [169,] 2.231408678 -3.684145e+00
#> [170,] 2.227403271 -3.575155e+00
#> [171,] 2.219278643 -3.464153e+00
#> [172,] 2.207073773 -3.351436e+00
#> [173,] 2.190838849 -3.237294e+00
#> [174,] 2.170634660 -3.122015e+00
#> [175,] 2.146531955 -3.005878e+00
#> [176,] 2.118610798 -2.889156e+00
#> [177,] 2.086959914 -2.772111e+00
#> [178,] 2.051676031 -2.655000e+00
#> [179,] 2.012863229 -2.538069e+00
#> [180,] 1.970632299 -2.421555e+00
#> [181,] 1.925100113 -2.305686e+00
#> [182,] 1.876389018 -2.190678e+00
#> [183,] 1.824626254 -2.076738e+00
#> [184,] 1.769943391 -1.964063e+00
#> [185,] 1.712475808 -1.852838e+00
#> [186,] 1.652362194 -1.743240e+00
#> [187,] 1.589744092 -1.635433e+00
#> [188,] 1.524765470 -1.529573e+00
#> [189,] 1.457572337 -1.425803e+00
#> [190,] 1.388312392 -1.324259e+00
#> [191,] 1.317134708 -1.225065e+00
#> [192,] 1.244189453 -1.128337e+00
#> [193,] 1.169627650 -1.034179e+00
#> [194,] 1.093600958 -9.426902e-01
#> [195,] 1.016261493 -8.539568e-01
#> [196,] 0.937761673 -7.680586e-01
#> [197,] 0.858254087 -6.850664e-01
#> [198,] 0.777891378 -6.050434e-01
#> [199,] 0.696826158 -5.280445e-01
#> [200,] 0.615210917 -4.541175e-01
#> [201,] 0.533197954 -3.833028e-01
#> [202,] 0.450939306 -3.156336e-01
#> [203,] 0.368586678 -2.511363e-01
#> [204,] 0.286291370 -1.898307e-01
#> [205,] 0.204204190 -1.317300e-01
#> [206,] 0.122475357 -7.684118e-02
#> [207,] 0.041254389 -2.516476e-02
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#> [363,] 0.054162721 3.483546e-01
#> [364,] 0.082400062 5.777995e-01
#> [365,] 0.103908242 8.006192e-01
#> [366,] 0.118883544 1.016086e+00
#> [367,] 0.127557749 1.223510e+00
#> [368,] 0.130196235 1.422238e+00
#> [369,] 0.127095856 1.611663e+00
#> [370,] 0.118582628 1.791221e+00
#> [371,] 0.105009233 1.960399e+00
#> [372,] 0.086752357 2.118732e+00
#> [373,] 0.064209882 2.265812e+00
#> [374,] 0.037797957 2.401282e+00
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#> [392,] -0.598129424 2.793791e+00
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#> [409,] -0.438789343 9.696125e-01
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#> [422,] 0.019930415 -2.985340e-02
#> [423,] 0.044609905 -6.503200e-02
#> [424,] 0.066221482 -9.397818e-02
#> [425,] 0.084530078 -1.168090e-01
#> [426,] 0.099327556 -1.336802e-01
#> [427,] 0.110434563 -1.447843e-01
#> [428,] 0.117702162 -1.503482e-01
#> [429,] 0.121013230 -1.506309e-01
#> [430,] 0.120283624 -1.459209e-01
#> [431,] 0.115463084 -1.365333e-01
#> [432,] 0.106535894 -1.228069e-01
#> [433,] 0.093521270 -1.051013e-01
#> [434,] 0.076473485 -8.379387e-02
#> [435,] 0.055481729 -5.927618e-02
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#> [468,] -0.893001888 3.806429e-01
#> [469,] -0.861325946 3.543928e-01
#> [470,] -0.823674712 3.268359e-01
#> [471,] -0.780126008 2.982420e-01
#> [472,] -0.730797716 2.688870e-01
#> [473,] -0.675847347 2.390508e-01
#> [474,] -0.615471334 2.090144e-01
#> [475,] -0.549904057 1.790575e-01
#> [476,] -0.479416605 1.494559e-01
#> [477,] -0.404315281 1.204793e-01
#> [478,] -0.324939864 9.238833e-02
#> [479,] -0.241661634 6.543297e-02
#> [480,] -0.154881175 3.984989e-02
#> [481,] -0.065025977 1.586054e-02
#> [482,] 0.027452159 -6.330751e-03
#> [483,] 0.122079879 -2.653856e-02
#> [484,] 0.218365202 -4.459794e-02
#> [485,] 0.315800564 -6.036582e-02
#> [486,] 0.413865986 -7.372225e-02
#> [487,] 0.512032331 -8.457138e-02
#> [488,] 0.609764629 -9.284224e-02
#> [489,] 0.706525451 -9.848941e-02
#> [490,] 0.801778304 -1.014933e-01
#> [491,] 0.894991034 -1.018604e-01
#> [492,] 0.985639194 -9.962302e-02
#> [493,] 1.073209382 -9.483934e-02
#> [494,] 1.157202500 -8.759258e-02
#> [495,] 1.237136931 -7.799045e-02
#> [496,] 1.312551595 -6.616421e-02
#> [497,] 1.383008885 -5.226756e-02
#> [498,] 1.448097447 -3.647530e-02
#> [499,] 1.507434781 -1.898195e-02
#> [500,] 1.560669671 -3.822538e-16
# Butterflies of the vignette' cover
panel(Out(a2l(replicate(100,
rfourier_shape(nb.h=6, alpha=0.4, nb.pts=200, plot=FALSE)))))
