Shape analysis deals with curve fitting, whether \(x(t)\) and \(y(t)\) positions along the curvilinear abscissa and/or radius/tangent angle variation. These functions are mainly intended for (self-)teaching of Fourier-based methods.
Usage
coo_oscillo(
coo,
method = c("efourier", "rfourier", "tfourier", "all")[4],
shape = TRUE,
nb.pts = 12
)Arguments
- coo
A list or a matrix of coordinates.
- method
character among
c('efourier', 'rfourier', 'tfourier', 'all').'all'by default- shape
logicalwhether to plot the original shape- nb.pts
integer. The number or reference points, sampled equidistantly along the curvilinear abscissa and added on the oscillo curves.
Examples
coo_oscillo(shapes[4])
#> [1] 0.00000000 4.70353942 3.90929170 3.90044215 3.89159259 4.66814120
#> [7] 3.87389348 3.07964576 6.21238885 6.20353930 6.19468974 6.18584018
#> [13] 6.17699063 5.38274291 6.15929151 6.15044196 6.14159240 5.34734468
#> [19] 6.12389329 5.32964557 5.32079601 4.52654829 5.30309689 4.50884917
#> [25] 4.49999962 4.49115006 3.69690234 4.47345095 3.67920323 2.88495551
#> [31] 3.66150411 2.86725639 2.85840684 2.84955728 2.84070772 2.83185817
#> [37] 2.82300861 2.81415905 2.80530950 3.58185810 2.78761038 2.77876083
#> [43] 2.76991127 2.76106171 2.75221216 2.74336260 2.73451304 2.72566349
#> [49] 2.71681393 2.70796437 2.69911482 2.69026526 2.68141570 2.67256614
#> [55] 2.66371659 2.65486703 2.64601747 1.85176975 3.41371652 1.83407064
#> [61] 2.61061925 2.60176969 2.59292013 2.58407058 2.57522102 2.56637146
#> [67] 2.55752191 2.54867235 2.53982279 2.53097324 2.52212368 2.51327412
#> [73] 2.50442457 2.49557501 2.48672545 2.47787590 2.46902634 2.46017678
#> [79] 2.45132723 2.44247767 2.43362811 2.42477856 2.41592900 2.40707944
#> [85] 2.39822988 2.38938033 2.38053077 2.37168121 2.36283166 1.56858394
#> [91] 2.34513254 2.33628299 2.32743343 3.88938020 3.88053064 3.87168109
#> [97] 3.07743337 3.85398197 3.84513242 3.83628286 3.82743330 3.81858375
#> [103] 4.59513235 3.80088463 3.79203508 4.56858368 4.55973413 3.76548641
#> [109] 4.54203501 4.53318546 5.30973406 4.51548634 4.50663679 5.28318539
#> [115] 4.48893767 5.26548628 4.47123856 5.24778717 5.23893761 4.44468989
#> [121] 5.22123849 5.21238894 4.41814122 5.19468982 5.18584027 5.17699071
#> [127] 5.16814115 4.37389343 5.15044204 5.14159248 5.13274293 5.12389337
#> [133] 5.11504381 5.10619426 5.09734470 5.08849514 4.29424742 5.07079603
#> [139] 5.06194647 5.05309692 5.04424736 5.03539780 5.02654825 5.80309685
#> [145] 5.00884913 4.99999958 4.99115002 4.98230046 4.97345091 4.96460135
#> [151] 4.95575179 5.73230040 4.93805268 4.92920312 4.92035356 4.91150401
#> [157] 4.90265445 5.67920306 4.88495534 4.87610578 4.86725622 4.85840667
#> [163] 4.84955711 4.84070755 4.83185800 4.82300844 4.81415888 4.80530933
#> [169] 4.79645977 4.00221205 3.99336249 3.19911477 2.40486705 2.39601750
#> [175] 1.60176978 2.37831838 1.58407066 2.36061927 1.56637155 2.34292016
#> [181] 1.54867243 1.53982288 2.31637148 1.52212376 1.51327421 2.28982281
#> [187] 1.49557509 1.48672554 2.26327414 1.46902642 1.46017687 1.45132731
#> [193] 2.22787592 1.43362820 1.42477864 1.41592908 2.19247769 1.39822997
#> [199] 0.60398225 2.16592902 1.37168130 1.36283174 1.35398219 1.34513263
#> [205] 1.33628307 1.32743352 1.31858396 1.30973440 1.30088485 1.29203529
#> [211] 1.28318573 1.27433617 1.26548662 1.25663706 1.24778750 1.23893795
#> [217] 1.23008839 1.22123883 1.21238928 0.41814156 1.19469016 1.18584061
#> [223] 1.17699105 1.16814149 0.37389377 1.15044238 1.14159282 0.34734510
#> [229] 1.12389371 1.11504415 0.32079643 1.09734504 0.30309732 1.07964593
#> [235] 0.28539821 1.06194681 0.26769909 0.25884954 1.03539814 0.24115042
#> [241] 0.23230087 0.22345131 0.21460175 0.20575219 0.19690264 0.18805308
#> [247] 5.67699067 0.17035397 5.65929155 0.15265485 5.64159244 0.13495574
#> [253] 5.62389333 5.61504377 0.10840707 5.59734466 5.58849510 5.57964554
#> [259] 5.57079599 5.56194643 5.55309687 5.54424732 5.53539776 5.52654820
#> [265] 5.51769865 5.50884909 5.49999953 4.70575181 5.48230042 5.47345086
#> [271] 4.67920314 5.45575175 5.44690219 4.65265447 5.42920308 5.42035352
#> [277] 4.62610580 4.61725625 5.39380485 5.38495529 5.37610574 4.58185802
#> [283] 5.35840662 6.13495523 4.55530935 5.33185795 5.32300840 5.31415884
#> [289] 5.30530928 6.08185789 4.50221201 6.06415878 5.26991106 5.26106150
#> [295] 5.25221194 5.24336239 6.01991099 4.44026511 6.00221188 5.20796416
#> [301] 5.19911460 5.19026505 5.18141549 5.17256593 5.16371638 5.94026498
#> [307] 5.14601726 4.35176954 5.12831815 5.11946859 5.89601720 5.10176948
#> [313] 5.09291992 5.08407036 5.07522081 5.06637125 5.05752169 5.04867214
#> [319] 5.03982258 5.03097302 5.02212347 5.01327391 5.00442435 4.99557480
#> [325] 4.98672524 4.97787568 4.96902613 4.96017657 4.95132701 4.94247746
#> [331] 4.93362790 4.13938018 4.91592879 5.69247739 4.11283151 4.88938012
#> [337] 4.88053056 4.87168100 4.86283145 4.06858373 4.84513233 4.83628278
#> [343] 4.04203506 4.81858366 4.80973410 4.01548638 4.79203499 3.99778727
#> [349] 4.77433588 3.98008816 4.75663676 3.96238904 4.73893765 3.94468993
#> [355] 4.72123854 3.92699082 4.70353942 3.90929170 4.68584031 3.89159259
#> [361] 4.66814120 3.87389348 4.65044208 3.85619436 3.84734481 3.83849525
#> [367] 4.61504386 3.82079614 3.81194658 4.58849519 3.79424747 3.78539791
#> [373] 3.77654835 3.76769880 3.75884924 3.74999968 3.74115012 3.73230057
#> [379] 3.72345101 3.71460145 2.92035373 3.69690234 2.90265462 3.67920323
#> [385] 2.88495551 2.87610595 3.65265456 2.85840684 2.84955728 3.62610589
#> [391] 2.83185817 2.82300861 3.59955722 3.59070766 2.79645994 3.57300855
#> [397] 2.77876083 3.55530943 3.54645988 2.75221216 3.52876076 3.51991121
#> [403] 3.51106165 3.50221209 3.49336254 3.48451298 3.47566342 4.25221203
#> [409] 3.45796431 3.44911475 4.22566336 3.43141564 4.20796424 3.41371652
#> [415] 4.19026513 4.18141557 4.17256602 4.16371646 4.15486690 4.14601735
#> [421] 4.92256595 3.34292007 4.11946868 4.11061912 4.10176956 3.30752184
#> [427] 4.08407045 4.07522089 3.28097317 4.05752178 3.26327406 4.03982267
#> [433] 4.03097311 3.23672539 3.22787583 4.00442444 3.21017672 3.98672533
#> [439] 3.19247761 3.18362805 3.17477849 3.16592893 3.15707938 2.36283166
#> [445] 3.13938026 3.13053071 2.33628299 3.11283159 2.31858387 3.09513248
#> [451] 3.08628292 3.07743337 3.85398197 3.84513242 3.05088470 3.82743330
#> [457] 3.03318558 3.80973419 3.01548647 3.00663691 3.78318552 2.98893780
#> [463] 2.98008824 3.75663685 2.96238913 2.95353957 2.15929185 2.93584046
#> [469] 2.14159274 1.34734502 1.33849546 1.32964590 0.53539818 0.52654863
#> [475] 0.51769907 1.29424768 5.99778710 0.49115040 0.48230084 1.25884945
#> [481] 0.46460173 0.45575217 0.44690262 0.43805306 0.42920350 0.42035395
#> [487] 0.41150439 0.40265483 0.39380528 1.95575205 1.94690249 1.15265477
#> [493] 1.92920338 1.92035382 1.12610610 1.90265471 1.10840699 1.88495559
#> [499] 1.09070787 1.86725648 1.07300876 0.27876104 1.05530964 1.04646009
#> [505] 0.25221237 1.02876097 1.01991142 1.01106186 1.78761047 1.77876091
#> [511] 0.98451319 1.76106180 0.96681408 0.95796452 0.16371680 0.94026541
#> [517] 0.14601769 5.63495527 0.12831857 0.11946902 5.60840660 0.10176990
#> [523] 0.09292035 5.58185793 5.57300838 5.56415882 5.55530926 5.54645971
#> [529] 5.53761015 5.52876059 4.73451287 5.51106148 5.50221192 4.70796420
#> [535] 5.48451281 5.47566325 6.25221186 6.24336230 6.23451274 6.22566319
#> [541] 6.21681363 6.20796407 6.19911452 0.69247782 5.39601724 0.67477870
#> [547] 6.16371629 6.15486673 6.14601718 6.13716762 0.63053092 5.33407034
#> [553] 0.61283181 6.10176939 6.09291984 6.08407028 6.07522072 6.06637117
#> [559] 6.05752161 0.55088491 5.25442433 6.03097294 6.02212338 6.01327383
#> [565] 6.00442427 0.49778757 5.20132699 5.97787560 5.96902604 5.96017649
#> [571] 5.95132693 5.94247737 5.93362781 5.92477826 5.13053054 5.90707914
#> [577] 5.89822959 5.10398187 5.88053047 5.87168092 5.07743320 5.85398180
#> [583] 5.05973408 5.05088453 5.82743313 5.03318541 5.02433586 5.80088446
#> [589] 5.00663674 4.99778719 5.77433579 4.98008807 4.97123852 5.74778712
#> [595] 5.73893757 4.94468985 4.93584029 5.71238890 5.70353934 4.90929162
#> [601] 5.68584023 5.67699067 5.66814111 4.87389339 5.65044200 5.64159244
#> [607] 5.63274288 5.62389333 4.82964561 5.60619421 5.59734466 5.58849510
#> [613] 5.57964554 5.57079599 5.56194643 5.55309687 5.54424732 5.53539776
#> [619] 5.52654820 5.51769865 5.50884909 5.49999953 5.49114998 5.48230042
#> [625] 5.47345086 5.46460131 5.45575175 5.44690219 5.43805264 5.42920308
#> [631] 5.42035352 5.41150397 5.40265441 5.39380485 5.38495529 5.37610574
#> [637] 5.36725618 5.35840662 5.34955707 5.34070751 5.33185795 5.32300840
#> [643] 6.09955700 5.30530928 5.29645973 5.28761017 5.27876061 5.26991106
#> [649] 5.26106150 6.03761011 0.53097341 6.01991099 0.51327429 0.50442474
#> [655] 0.49557518 5.98451277 0.47787607 0.46902651 5.95796410 5.16371638
#> [661] 5.94026498 4.36061910 5.13716771 4.34291999 4.33407043 4.32522087
#> [667] 5.88716764 4.30752176 5.86946853 4.28982264 4.28097309 4.27212353
#> [673] 3.47787581 4.25442442 3.46017670 3.45132714 3.44247758 3.43362803
#> [679] 3.42477847 3.41592891 3.40707936 3.39822980 3.38938024 2.59513252
#> [685] 3.37168113 2.57743341 2.56858385 2.55973430 2.55088474 2.54203518
#> [691] 2.53318563 1.73893791 2.51548651 2.50663696 1.71238924 2.48893784
#> [697] 1.69469012 2.47123873 1.67699101 2.45353961 1.65929189 1.65044234
#> [703] 2.42699094 1.63274322 1.62389367 3.18584044 4.74778721 4.73893765
#> [709] 4.73008809 3.93584037
coo_oscillo(shapes[4], 'efourier')
#> # A tibble: 710 × 2
#> dx dy
#> <dbl> <dbl>
#> 1 0 0
#> 2 0 -1
#> 3 -1 -2
#> 4 -2 -3
#> 5 -3 -4
#> 6 -3 -5
#> 7 -4 -6
#> 8 -5 -6
#> 9 -4 -6
#> 10 -3 -6
#> # ℹ 700 more rows
coo_oscillo(shapes[4], 'rfourier')
#> [1] 34.28884 35.22856 35.85539 36.52625 37.23875 38.21062 38.96933
#> [8] 38.77938 38.96933 39.18390 39.42267 39.68521 39.97105 41.22840
#> [15] 41.55177 41.89653 42.26213 43.56815 43.96536 45.28850 46.61700
#> [22] 47.52337 48.85250 49.75835 50.66774 51.58049 52.10667 53.03236
#> [29] 53.60027 53.25618 53.87744 53.57247 53.28452 53.01388 52.76080
#> [36] 52.52555 52.30835 52.10945 51.92905 52.75589 52.61573 52.49424
#> [43] 52.39157 52.30782 52.24307 52.19741 52.17088 52.16351 52.17531
#> [50] 52.20626 52.25633 52.32548 52.41361 52.52064 52.64645 52.79090
#> [57] 52.95385 52.15376 53.33453 52.57829 52.81768 53.07484 53.34950
#> [64] 53.64141 53.95027 54.27580 54.61770 54.97567 55.34939 55.73855
#> [71] 56.14283 56.56190 56.99543 57.44311 57.90459 58.37955 58.86768
#> [78] 59.36863 59.88210 60.40775 60.94528 61.49438 62.05473 62.62604
#> [85] 63.20800 63.80033 64.40274 65.01495 65.63669 65.49870 66.14613
#> [92] 66.80226 67.46682 68.21363 68.96685 69.72627 71.13586 71.90019
#> [99] 72.67024 73.44584 74.22680 75.01296 75.20000 76.00241 76.80946
#> [106] 77.04407 77.30385 78.13586 78.43027 78.74899 78.23153 78.58924
#> [113] 78.97065 78.49288 78.91279 78.46017 78.91827 78.49116 78.07453
#> [120] 78.58580 78.19525 77.81559 78.37960 78.02647 77.68461 77.35417
#> [127] 77.03530 77.68226 77.39058 77.11077 76.84296 76.58726 76.34381
#> [134] 76.11273 75.89411 75.68808 76.47732 76.29908 76.13356 75.98084
#> [141] 75.84100 75.71411 75.60023 74.50394 74.41509 74.33959 74.27748
#> [148] 74.22879 74.19355 74.17177 74.16347 73.16873 73.18765 73.22022
#> [155] 73.26643 73.32625 73.39964 72.49103 72.59283 72.70824 72.83719
#> [162] 72.97963 73.13546 73.30460 73.48696 73.68244 73.89094 74.11235
#> [169] 74.34655 75.56127 76.78281 77.74913 78.46964 79.20886 78.98907
#> [176] 79.76109 79.56797 80.37176 80.20506 81.03955 80.89895 80.77048
#> [183] 81.64820 81.54545 81.45484 82.37383 82.30844 82.25515 83.21339
#> [190] 83.18473 83.16808 83.16346 84.17077 84.18996 84.22102 84.26394
#> [197] 85.31688 85.38267 84.46363 85.54918 85.64983 85.76202 85.88571
#> [204] 86.02085 86.16738 86.32525 86.49439 86.67474 86.86623 87.06878
#> [211] 87.28232 87.50677 87.74204 87.98805 88.24470 88.51191 88.78958
#> [218] 89.07761 89.37590 88.73531 89.05721 89.38914 89.73098 90.08263
#> [225] 89.51415 89.88890 90.27317 89.75049 90.15753 90.57379 90.09726
#> [232] 90.53589 90.09246 90.55320 90.14314 90.62570 90.24922 89.89341
#> [239] 90.41049 90.08863 89.78789 89.50849 89.25062 89.01448 88.80024
#> [246] 88.60805 87.81833 87.65822 86.88289 86.75564 85.99543 85.90180
#> [253] 85.15746 84.41839 84.37043 83.64833 82.93200 82.22159 81.51725
#> [260] 80.81915 80.12746 79.44232 78.76392 78.09244 77.42804 76.77093
#> [267] 76.12127 74.71205 74.07134 73.43866 72.03249 71.40975 70.79566
#> [274] 69.39357 68.79056 68.19688 66.80013 65.40412 64.82571 64.25765
#> [281] 63.70023 62.31502 61.77244 62.09459 60.72216 60.21507 59.72041
#> [288] 59.23851 58.76967 59.20961 57.87245 58.35344 57.94651 57.55407
#> [295] 57.17643 56.81388 57.40838 56.13523 56.77207 56.47780 56.19977
#> [302] 55.93825 55.69346 55.46561 55.25493 56.04473 55.87204 54.72776
#> [309] 54.58755 54.46535 55.35682 55.27252 55.20620 55.15793 55.12777
#> [316] 55.11574 55.12184 55.14609 55.18844 55.24887 55.32730 55.42367
#> [323] 55.53789 55.66983 55.81938 55.98640 56.17072 56.37218 56.59060
#> [330] 56.82578 57.07752 56.38515 56.67414 57.92981 57.30013 57.63660
#> [337] 57.98837 58.35516 58.73668 58.21890 58.63543 59.06595 58.61935
#> [344] 59.08386 59.56152 59.18629 59.69666 59.37283 59.91499 59.64267
#> [351] 60.21563 59.99470 60.59734 60.42747 61.05860 60.93927 61.59763
#> [358] 61.52813 62.21241 62.19185 62.90071 62.92807 63.66015 63.73427
#> [365] 63.83964 63.97610 64.75812 64.93887 65.14982 65.96342 66.21642
#> [372] 66.49855 66.80942 67.14865 67.51580 67.91043 68.33204 68.78016
#> [379] 69.25426 69.75382 69.35679 69.89854 69.53111 70.11432 69.77669
#> [386] 69.45182 70.09278 69.79804 69.51644 70.21380 69.96247 69.72457
#> [393] 70.47665 71.24886 71.05751 71.86523 71.70342 72.54532 73.40480
#> [400] 73.28734 74.17868 75.08608 76.00895 76.94676 77.89895 78.86500
#> [407] 79.84441 80.84432 81.83670 82.84134 83.84129 84.85755 85.85730
#> [414] 86.88451 87.88397 88.88344 89.88292 90.88241 91.88191 92.88142
#> [421] 93.85554 94.88048 95.88002 96.87957 97.87913 98.91293 99.91216
#> [428] 100.91141 101.95369 102.95256 104.00323 105.00164 106.00008 107.05821
#> [435] 108.12447 109.12184 110.19536 111.19213 112.27258 113.36038 114.45531
#> [442] 115.55717 116.66577 116.78900 117.91146 119.04014 119.18609 120.32775
#> [449] 120.48874 121.64283 122.80236 123.96718 124.95013 125.93335 127.10095
#> [456] 128.08327 129.25466 130.23609 131.41112 132.59082 133.57020 134.75326
#> [463] 135.94073 136.91806 138.10864 139.30341 139.52852 140.73255 140.96957
#> [470] 140.24449 139.52997 138.82618 137.86237 136.89909 135.93634 135.25082
#> [477] 134.01247 133.05137 132.09086 131.41572 130.45849 129.50191 128.54599
#> [484] 127.59074 126.63619 125.68234 124.72922 123.77683 122.82521 123.13732
#> [491] 123.45675 122.84000 123.17644 123.52005 122.93616 123.29667 122.73616
#> [498] 123.11350 122.57662 122.97072 122.45772 121.54514 121.05088 120.57119
#> [505] 119.66929 119.20920 118.76418 118.33438 118.80149 119.27516 118.88086
#> [512] 119.37097 119.00220 118.64915 117.79197 117.46081 116.61205 115.23423
#> [519] 114.38642 113.54110 112.16122 111.31696 110.47530 109.09331 107.71215
#> [526] 106.33186 104.95248 103.57404 102.19657 100.82012 100.29919 98.92667
#> [533] 97.55533 97.04779 95.68088 94.31537 93.44900 92.58533 91.72442
#> [540] 90.86637 90.01124 89.15913 88.31012 88.00439 86.62177 86.33323
#> [547] 85.50294 84.67632 83.85348 83.03453 82.80597 81.40876 81.20026
#> [554] 80.40404 79.61241 78.82552 78.04351 77.26653 76.49472 76.37761
#> [561] 74.96730 74.21201 73.46257 72.71916 71.98197 71.94094 70.52699
#> [568] 69.80962 69.09928 68.39618 67.70055 67.01262 66.33263 65.66083
#> [575] 64.24875 63.58639 62.93294 61.52327 60.88054 60.24755 58.84152
#> [582] 58.22071 56.81733 55.41450 54.80961 53.41022 52.01162 51.42505
#> [589] 50.03093 48.63796 48.07263 46.68550 45.30004 44.75958 44.23513
#> [596] 42.86379 41.49533 41.00231 40.52797 39.18002 38.73500 38.31093
#> [603] 37.90850 36.60071 36.23449 35.89241 35.57516 35.28341 34.05109
#> [610] 33.80538 33.58765 33.39846 33.23829 33.10756 33.00662 32.93576
#> [617] 32.89515 32.88491 32.90508 32.95559 33.03631 33.14701 33.28740
#> [624] 33.45711 33.65568 33.88261 34.13735 34.41925 34.72768 35.06193
#> [631] 35.42126 35.80492 36.21214 36.64213 37.09410 37.56726 38.06082
#> [638] 38.57399 39.10600 39.65610 40.22354 40.80759 42.20611 42.80984
#> [645] 43.42821 44.06059 44.70640 45.36507 46.03603 47.44904 48.18901
#> [652] 49.60118 50.34924 51.10592 51.87084 53.27926 54.05043 54.82898
#> [659] 56.23445 56.86510 58.27294 58.15749 58.81854 58.75524 58.72594
#> [666] 58.73069 60.14474 60.18261 61.59580 61.66523 61.76697 61.90086
#> [673] 61.27762 61.46141 60.86654 60.28239 59.70928 59.14752 58.59744
#> [680] 58.05937 57.53366 57.02063 56.52065 55.15875 54.67832 53.32563
#> [687] 51.97622 50.63034 49.28829 47.95039 46.61700 45.71452 44.38155
#> [694] 43.05376 42.14616 40.81915 39.91086 38.58472 37.67564 36.35049
#> [701] 35.44054 34.53556 33.20556 32.29988 31.39993 30.97074 31.88281
#> [708] 32.80000 33.72190 34.28884
coo_oscillo(shapes[4], 'tfourier')
#> [1] 0.00000000 4.70353942 3.90929170 3.90044215 3.89159259 4.66814120
#> [7] 3.87389348 3.07964576 6.21238885 6.20353930 6.19468974 6.18584018
#> [13] 6.17699063 5.38274291 6.15929151 6.15044196 6.14159240 5.34734468
#> [19] 6.12389329 5.32964557 5.32079601 4.52654829 5.30309689 4.50884917
#> [25] 4.49999962 4.49115006 3.69690234 4.47345095 3.67920323 2.88495551
#> [31] 3.66150411 2.86725639 2.85840684 2.84955728 2.84070772 2.83185817
#> [37] 2.82300861 2.81415905 2.80530950 3.58185810 2.78761038 2.77876083
#> [43] 2.76991127 2.76106171 2.75221216 2.74336260 2.73451304 2.72566349
#> [49] 2.71681393 2.70796437 2.69911482 2.69026526 2.68141570 2.67256614
#> [55] 2.66371659 2.65486703 2.64601747 1.85176975 3.41371652 1.83407064
#> [61] 2.61061925 2.60176969 2.59292013 2.58407058 2.57522102 2.56637146
#> [67] 2.55752191 2.54867235 2.53982279 2.53097324 2.52212368 2.51327412
#> [73] 2.50442457 2.49557501 2.48672545 2.47787590 2.46902634 2.46017678
#> [79] 2.45132723 2.44247767 2.43362811 2.42477856 2.41592900 2.40707944
#> [85] 2.39822988 2.38938033 2.38053077 2.37168121 2.36283166 1.56858394
#> [91] 2.34513254 2.33628299 2.32743343 3.88938020 3.88053064 3.87168109
#> [97] 3.07743337 3.85398197 3.84513242 3.83628286 3.82743330 3.81858375
#> [103] 4.59513235 3.80088463 3.79203508 4.56858368 4.55973413 3.76548641
#> [109] 4.54203501 4.53318546 5.30973406 4.51548634 4.50663679 5.28318539
#> [115] 4.48893767 5.26548628 4.47123856 5.24778717 5.23893761 4.44468989
#> [121] 5.22123849 5.21238894 4.41814122 5.19468982 5.18584027 5.17699071
#> [127] 5.16814115 4.37389343 5.15044204 5.14159248 5.13274293 5.12389337
#> [133] 5.11504381 5.10619426 5.09734470 5.08849514 4.29424742 5.07079603
#> [139] 5.06194647 5.05309692 5.04424736 5.03539780 5.02654825 5.80309685
#> [145] 5.00884913 4.99999958 4.99115002 4.98230046 4.97345091 4.96460135
#> [151] 4.95575179 5.73230040 4.93805268 4.92920312 4.92035356 4.91150401
#> [157] 4.90265445 5.67920306 4.88495534 4.87610578 4.86725622 4.85840667
#> [163] 4.84955711 4.84070755 4.83185800 4.82300844 4.81415888 4.80530933
#> [169] 4.79645977 4.00221205 3.99336249 3.19911477 2.40486705 2.39601750
#> [175] 1.60176978 2.37831838 1.58407066 2.36061927 1.56637155 2.34292016
#> [181] 1.54867243 1.53982288 2.31637148 1.52212376 1.51327421 2.28982281
#> [187] 1.49557509 1.48672554 2.26327414 1.46902642 1.46017687 1.45132731
#> [193] 2.22787592 1.43362820 1.42477864 1.41592908 2.19247769 1.39822997
#> [199] 0.60398225 2.16592902 1.37168130 1.36283174 1.35398219 1.34513263
#> [205] 1.33628307 1.32743352 1.31858396 1.30973440 1.30088485 1.29203529
#> [211] 1.28318573 1.27433617 1.26548662 1.25663706 1.24778750 1.23893795
#> [217] 1.23008839 1.22123883 1.21238928 0.41814156 1.19469016 1.18584061
#> [223] 1.17699105 1.16814149 0.37389377 1.15044238 1.14159282 0.34734510
#> [229] 1.12389371 1.11504415 0.32079643 1.09734504 0.30309732 1.07964593
#> [235] 0.28539821 1.06194681 0.26769909 0.25884954 1.03539814 0.24115042
#> [241] 0.23230087 0.22345131 0.21460175 0.20575219 0.19690264 0.18805308
#> [247] 5.67699067 0.17035397 5.65929155 0.15265485 5.64159244 0.13495574
#> [253] 5.62389333 5.61504377 0.10840707 5.59734466 5.58849510 5.57964554
#> [259] 5.57079599 5.56194643 5.55309687 5.54424732 5.53539776 5.52654820
#> [265] 5.51769865 5.50884909 5.49999953 4.70575181 5.48230042 5.47345086
#> [271] 4.67920314 5.45575175 5.44690219 4.65265447 5.42920308 5.42035352
#> [277] 4.62610580 4.61725625 5.39380485 5.38495529 5.37610574 4.58185802
#> [283] 5.35840662 6.13495523 4.55530935 5.33185795 5.32300840 5.31415884
#> [289] 5.30530928 6.08185789 4.50221201 6.06415878 5.26991106 5.26106150
#> [295] 5.25221194 5.24336239 6.01991099 4.44026511 6.00221188 5.20796416
#> [301] 5.19911460 5.19026505 5.18141549 5.17256593 5.16371638 5.94026498
#> [307] 5.14601726 4.35176954 5.12831815 5.11946859 5.89601720 5.10176948
#> [313] 5.09291992 5.08407036 5.07522081 5.06637125 5.05752169 5.04867214
#> [319] 5.03982258 5.03097302 5.02212347 5.01327391 5.00442435 4.99557480
#> [325] 4.98672524 4.97787568 4.96902613 4.96017657 4.95132701 4.94247746
#> [331] 4.93362790 4.13938018 4.91592879 5.69247739 4.11283151 4.88938012
#> [337] 4.88053056 4.87168100 4.86283145 4.06858373 4.84513233 4.83628278
#> [343] 4.04203506 4.81858366 4.80973410 4.01548638 4.79203499 3.99778727
#> [349] 4.77433588 3.98008816 4.75663676 3.96238904 4.73893765 3.94468993
#> [355] 4.72123854 3.92699082 4.70353942 3.90929170 4.68584031 3.89159259
#> [361] 4.66814120 3.87389348 4.65044208 3.85619436 3.84734481 3.83849525
#> [367] 4.61504386 3.82079614 3.81194658 4.58849519 3.79424747 3.78539791
#> [373] 3.77654835 3.76769880 3.75884924 3.74999968 3.74115012 3.73230057
#> [379] 3.72345101 3.71460145 2.92035373 3.69690234 2.90265462 3.67920323
#> [385] 2.88495551 2.87610595 3.65265456 2.85840684 2.84955728 3.62610589
#> [391] 2.83185817 2.82300861 3.59955722 3.59070766 2.79645994 3.57300855
#> [397] 2.77876083 3.55530943 3.54645988 2.75221216 3.52876076 3.51991121
#> [403] 3.51106165 3.50221209 3.49336254 3.48451298 3.47566342 4.25221203
#> [409] 3.45796431 3.44911475 4.22566336 3.43141564 4.20796424 3.41371652
#> [415] 4.19026513 4.18141557 4.17256602 4.16371646 4.15486690 4.14601735
#> [421] 4.92256595 3.34292007 4.11946868 4.11061912 4.10176956 3.30752184
#> [427] 4.08407045 4.07522089 3.28097317 4.05752178 3.26327406 4.03982267
#> [433] 4.03097311 3.23672539 3.22787583 4.00442444 3.21017672 3.98672533
#> [439] 3.19247761 3.18362805 3.17477849 3.16592893 3.15707938 2.36283166
#> [445] 3.13938026 3.13053071 2.33628299 3.11283159 2.31858387 3.09513248
#> [451] 3.08628292 3.07743337 3.85398197 3.84513242 3.05088470 3.82743330
#> [457] 3.03318558 3.80973419 3.01548647 3.00663691 3.78318552 2.98893780
#> [463] 2.98008824 3.75663685 2.96238913 2.95353957 2.15929185 2.93584046
#> [469] 2.14159274 1.34734502 1.33849546 1.32964590 0.53539818 0.52654863
#> [475] 0.51769907 1.29424768 5.99778710 0.49115040 0.48230084 1.25884945
#> [481] 0.46460173 0.45575217 0.44690262 0.43805306 0.42920350 0.42035395
#> [487] 0.41150439 0.40265483 0.39380528 1.95575205 1.94690249 1.15265477
#> [493] 1.92920338 1.92035382 1.12610610 1.90265471 1.10840699 1.88495559
#> [499] 1.09070787 1.86725648 1.07300876 0.27876104 1.05530964 1.04646009
#> [505] 0.25221237 1.02876097 1.01991142 1.01106186 1.78761047 1.77876091
#> [511] 0.98451319 1.76106180 0.96681408 0.95796452 0.16371680 0.94026541
#> [517] 0.14601769 5.63495527 0.12831857 0.11946902 5.60840660 0.10176990
#> [523] 0.09292035 5.58185793 5.57300838 5.56415882 5.55530926 5.54645971
#> [529] 5.53761015 5.52876059 4.73451287 5.51106148 5.50221192 4.70796420
#> [535] 5.48451281 5.47566325 6.25221186 6.24336230 6.23451274 6.22566319
#> [541] 6.21681363 6.20796407 6.19911452 0.69247782 5.39601724 0.67477870
#> [547] 6.16371629 6.15486673 6.14601718 6.13716762 0.63053092 5.33407034
#> [553] 0.61283181 6.10176939 6.09291984 6.08407028 6.07522072 6.06637117
#> [559] 6.05752161 0.55088491 5.25442433 6.03097294 6.02212338 6.01327383
#> [565] 6.00442427 0.49778757 5.20132699 5.97787560 5.96902604 5.96017649
#> [571] 5.95132693 5.94247737 5.93362781 5.92477826 5.13053054 5.90707914
#> [577] 5.89822959 5.10398187 5.88053047 5.87168092 5.07743320 5.85398180
#> [583] 5.05973408 5.05088453 5.82743313 5.03318541 5.02433586 5.80088446
#> [589] 5.00663674 4.99778719 5.77433579 4.98008807 4.97123852 5.74778712
#> [595] 5.73893757 4.94468985 4.93584029 5.71238890 5.70353934 4.90929162
#> [601] 5.68584023 5.67699067 5.66814111 4.87389339 5.65044200 5.64159244
#> [607] 5.63274288 5.62389333 4.82964561 5.60619421 5.59734466 5.58849510
#> [613] 5.57964554 5.57079599 5.56194643 5.55309687 5.54424732 5.53539776
#> [619] 5.52654820 5.51769865 5.50884909 5.49999953 5.49114998 5.48230042
#> [625] 5.47345086 5.46460131 5.45575175 5.44690219 5.43805264 5.42920308
#> [631] 5.42035352 5.41150397 5.40265441 5.39380485 5.38495529 5.37610574
#> [637] 5.36725618 5.35840662 5.34955707 5.34070751 5.33185795 5.32300840
#> [643] 6.09955700 5.30530928 5.29645973 5.28761017 5.27876061 5.26991106
#> [649] 5.26106150 6.03761011 0.53097341 6.01991099 0.51327429 0.50442474
#> [655] 0.49557518 5.98451277 0.47787607 0.46902651 5.95796410 5.16371638
#> [661] 5.94026498 4.36061910 5.13716771 4.34291999 4.33407043 4.32522087
#> [667] 5.88716764 4.30752176 5.86946853 4.28982264 4.28097309 4.27212353
#> [673] 3.47787581 4.25442442 3.46017670 3.45132714 3.44247758 3.43362803
#> [679] 3.42477847 3.41592891 3.40707936 3.39822980 3.38938024 2.59513252
#> [685] 3.37168113 2.57743341 2.56858385 2.55973430 2.55088474 2.54203518
#> [691] 2.53318563 1.73893791 2.51548651 2.50663696 1.71238924 2.48893784
#> [697] 1.69469012 2.47123873 1.67699101 2.45353961 1.65929189 1.65044234
#> [703] 2.42699094 1.63274322 1.62389367 3.18584044 4.74778721 4.73893765
#> [709] 4.73008809 3.93584037
#tfourier is prone to high-frequency noise but smoothing can help
coo_oscillo(coo_smooth(shapes[4], 10), 'tfourier')
#> [1] 0.000000000 6.210281146 6.150339598 6.110870956 6.093957661 6.111051488
#> [7] 6.210841936 0.294826636 1.163080415 1.662325460 1.784906858 1.788459018
#> [13] 1.754364939 1.713694996 1.673686879 1.624391221 1.550688278 1.445544249
#> [19] 1.313650160 1.165054644 1.007403085 0.842241873 0.665533492 0.472501809
#> [25] 0.264958204 0.052746323 6.128257112 5.926985109 5.730762152 5.541624953
#> [31] 5.365867883 5.211467073 5.086389730 4.997097511 4.946510695 4.933000642
#> [37] 4.949742414 4.982955751 5.012460904 5.019029243 4.994585130 4.946466089
#> [43] 4.891849750 4.846153200 4.815140738 4.796127011 4.783744124 4.773987623
#> [49] 4.764958775 4.755946140 4.746333644 4.734694607 4.718307666 4.693917249
#> [55] 4.660156421 4.620031964 4.580677444 4.549991613 4.533287434 4.532292499
#> [61] 4.545279217 4.566934623 4.589359967 4.605421681 4.612112985 4.610800812
#> [67] 4.604740736 4.596653165 4.587948567 4.579116176 4.570267573 4.561418016
#> [73] 4.552568459 4.543718902 4.534869346 4.526019789 4.517170232 4.508320675
#> [79] 4.499471119 4.490620608 4.481752932 4.472741250 4.462985703 4.450603765
#> [85] 4.431608816 4.400770190 4.356068458 4.305424656 4.269520989 4.277135048
#> [91] 4.360538895 4.555194318 4.871254402 5.215038283 5.459664874 5.595213464
#> [97] 5.672103286 5.734294873 5.805171782 5.888871809 5.977816468 6.062603219
#> [103] 6.138686968 6.207147740 6.271367481 0.051070155 0.115529390 0.185002608
#> [109] 0.260266970 0.335648438 0.401580810 0.452499558 0.490752929 0.523002507
#> [115] 0.554570991 0.586753235 0.617247615 0.642073315 0.658350204 0.667047287
#> [121] 0.673606828 0.685132162 0.705052388 0.728633438 0.744734811 0.745801344
#> [127] 0.737404131 0.735346616 0.751874045 0.784845872 0.819132998 0.837128874
#> [133] 0.828297388 0.792765360 0.741689130 0.694623805 0.671233403 0.681431950
#> [139] 0.721943628 0.781107907 0.846153540 0.905318763 0.945847189 0.956185340
#> [145] 0.933520844 0.889053044 0.844590615 0.821054584 0.826911372 0.853852015
#> [151] 0.881659563 0.890921047 0.876241385 0.849987814 0.832106250 0.832287770
#> [157] 0.840824651 0.837648250 0.809803659 0.760803413 0.706008449 0.660112883
#> [163] 0.628012512 0.604377441 0.577183265 0.530156087 0.444950680 0.304766283
#> [169] 0.096072698 6.087754031 5.700461201 5.247258666 4.831451596 4.527523880
#> [175] 4.329498082 4.206491595 4.131062373 4.081089105 4.040449748 4.001478231
#> [181] 3.964579062 3.933656583 3.910945742 3.895211705 3.883184677 3.871266154
#> [187] 3.856146033 3.835553787 3.810038382 3.783889856 3.762402266 3.746921155
#> [193] 3.733416217 3.716285917 3.692075007 3.659767668 3.620829826 3.580502872
#> [199] 3.545836696 3.519458457 3.496862828 3.471910466 3.443688053 3.416538164
#> [205] 3.394773009 3.379129831 3.367634796 3.358040420 3.349046858 3.340179182
#> [211] 3.331310551 3.322298870 3.312543323 3.300160435 3.281145755 3.250115199
#> [217] 3.204257486 3.148748834 3.097182990 3.062798448 3.047139365 3.037836547
#> [223] 3.019070901 2.985270415 2.943990251 2.906371786 2.877162870 2.853033116
#> [229] 2.827294741 2.795605917 2.758775379 2.721017676 2.685491706 2.651638374
#> [235] 2.616756113 2.579249488 2.539266926 2.496642604 2.450285176 2.400599692
#> [241] 2.350909726 2.304563353 2.260820580 2.214420252 2.159471987 2.094718182
#> [247] 2.026085459 1.963248210 1.911995985 1.870137442 1.831022284 1.789478413
#> [253] 1.743510198 1.691608789 1.631150303 1.561569503 1.488650289 1.423172645
#> [259] 1.373787829 1.341690659 1.321606928 1.305654435 1.285571657 1.253491627
#> [265] 1.204250793 1.139519444 1.069263427 1.006648871 0.960120128 0.930025733
#> [271] 0.911026560 0.895946158 0.877978420 0.852313020 0.819389902 0.787791876
#> [277] 0.771357046 0.780349343 0.814054366 0.861526357 0.910083692 0.952417749
#> [283] 0.985608592 1.008800661 1.025873144 1.046448905 1.078707071 1.120695586
#> [289] 1.160889837 1.187477232 1.195902397 1.189182194 1.174564489 1.160112567
#> [295] 1.151279870 1.148175732 1.145840851 1.137610074 1.119048880 1.090947700
#> [301] 1.060659306 1.039140171 1.032285551 1.032745212 1.022979818 0.991476068
#> [307] 0.948086298 0.920008639 0.927148777 0.961284686 0.992101349 0.993873732
#> [313] 0.963915071 0.918406903 0.876060289 0.845934321 0.827081727 0.814716958
#> [319] 0.804962365 0.795950684 0.787083007 0.778231543 0.769363866 0.760353139
#> [325] 0.750614758 0.738375872 0.720105828 0.691716549 0.652608187 0.609790908
#> [331] 0.575970900 0.560292070 0.560253479 0.563707517 0.558656949 0.539780722
#> [337] 0.506825021 0.461757288 0.409794503 0.359637805 0.318856196 0.288830724
#> [343] 0.264555711 0.238816280 0.207252588 0.171067996 0.135611940 0.106165474
#> [349] 0.084689231 0.069773360 0.058688066 0.049228656 0.040263124 0.031399834
#> [355] 0.022548751 0.013684699 0.004705453 6.278316778 6.266646228 6.249714189
#> [361] 6.223378486 6.185711060 6.140814149 6.098429160 6.068030924 6.052616099
#> [367] 6.047041546 6.041070135 6.024843229 5.993927011 5.951419573 5.905757611
#> [373] 5.865459482 5.834682028 5.812125954 5.792458593 5.768502704 5.733457862
#> [379] 5.683206435 5.618467189 5.545329001 5.472432994 5.406413214 5.350205499
#> [385] 5.304888721 5.271062496 5.248378331 5.235801685 5.233541784 5.243796693
#> [391] 5.267701445 5.300728508 5.332712334 5.354453431 5.364377855 5.368534497
#> [397] 5.374741784 5.387390003 5.407383871 5.434201642 5.465689493 5.497519401
#> [403] 5.525769644 5.550355985 5.574942842 5.603203498 5.635133193 5.667217292
#> [409] 5.696503292 5.724011803 5.754170455 5.792492400 5.844118816 5.911952780
#> [415] 5.993258931 6.078066848 6.152989261 6.206858374 6.232226877 6.224754148
#> [421] 6.185255417 6.122244570 6.049372258 5.978525675 5.915552103 5.861307526
#> [427] 5.814628320 5.774712015 5.742004258 5.716275508 5.693379276 5.666055366
#> [433] 5.630481863 5.590829982 5.554144579 5.520973706 5.483347333 5.432738889
#> [439] 5.368764431 5.298373235 5.228480361 5.162317644 5.101305142 5.047172969
#> [445] 5.001770639 4.967325726 4.949028929 4.955822231 4.995559376 5.068649008
#> [451] 5.166128839 5.271169312 5.361943901 5.418816242 5.434261089 5.415787999
#> [457] 5.378749340 5.337253926 5.300066779 5.270326801 5.245798899 5.219095373
#> [463] 5.178948961 5.113005498 5.010509821 4.861906973 4.655872417 4.383607566
#> [469] 4.061035875 3.739006861 3.460013884 3.228975398 3.035724811 2.875726521
#> [475] 2.751418620 2.667347672 2.626605417 2.625083548 2.645200476 2.660136888
#> [481] 2.649921973 2.613646664 2.566698627 2.528381069 2.513356521 2.534150830
#> [487] 2.608723363 2.760815486 2.995303110 3.253844542 3.450019278 3.556829435
#> [493] 3.594254480 3.588553531 3.560325237 3.523018039 3.480988947 3.429095667
#> [499] 3.357730619 3.262973502 3.155419447 3.057566270 2.990178713 2.963327724
#> [505] 2.978269071 3.031263380 3.113254441 3.206490718 3.283579186 3.315652213
#> [511] 3.286439739 3.198490398 3.065780988 2.901072469 2.710327869 2.499825577
#> [517] 2.288736611 2.106853050 1.972716007 1.880608795 1.808217671 1.732016385
#> [523] 1.641441083 1.543848642 1.454766713 1.383471012 1.328109195 1.280445960
#> [529] 1.233298003 1.186051865 1.145835795 1.124395250 1.133998381 1.185203040
#> [535] 1.284655334 1.429095439 1.597639355 1.755997591 1.877909670 1.959627909
#> [541] 2.012852441 2.050062384 2.076448107 2.091254469 2.093166224 2.083874267
#> [547] 2.068528701 2.053935597 2.045086040 2.041980966 2.039645151 2.031397576
#> [553] 2.012695022 1.983859410 1.950961917 1.922825350 1.903874767 1.888886160
#> [559] 1.867115865 1.834104119 1.799091522 1.778085405 1.777842081 1.787473253
#> [565] 1.787246136 1.766366858 1.731953827 1.700820006 1.683021524 1.673232227
#> [571] 1.656126033 1.618934077 1.560828846 1.493152222 1.431106120 1.383899161
#> [577] 1.350760265 1.323321861 1.290847550 1.246070449 1.189727078 1.130361772
#> [583] 1.078468381 1.040047045 1.014823673 0.998771530 0.987568410 0.978706955
#> [589] 0.972097548 0.969825211 0.974911598 0.988572657 1.007325669 1.023813218
#> [595] 1.033242798 1.039315778 1.051423155 1.075752154 1.109940476 1.145106149
#> [601] 1.172013529 1.186848625 1.193363408 1.198926850 1.206369621 1.210402157
#> [607] 1.204972412 1.194030025 1.191273604 1.207820260 1.241670290 1.279478888
#> [613] 1.307637488 1.320968930 1.322284497 1.316968271 1.309024705 1.300337273
#> [619] 1.291505836 1.282657232 1.273807676 1.264958119 1.256108562 1.247259005
#> [625] 1.238409449 1.229559892 1.220710335 1.211860778 1.203011222 1.194161665
#> [631] 1.185312108 1.176462551 1.167613948 1.158782511 1.150095079 1.142151512
#> [637] 1.136835287 1.138149900 1.151463248 1.179461633 1.216397766 1.246996075
#> [643] 1.254805029 1.235032721 1.201996315 1.185517450 1.218031010 1.321091442
#> [649] 1.494393247 1.707858148 1.913968285 2.077528885 2.185390609 2.236504708
#> [655] 2.234154703 2.181616267 2.077397918 1.913965611 1.684446939 1.396172930
#> [661] 1.083379564 0.801165397 0.594838371 0.479858466 0.448502322 0.476558403
#> [667] 0.519940898 0.523261974 0.451098963 0.310029503 0.136270603 6.245725890
#> [673] 6.083883304 5.933308298 5.794794776 5.675631097 5.583900424 5.519806626
#> [679] 5.472922363 5.426039551 5.361978088 5.270595236 5.153649901 5.024269044
#> [685] 4.899718114 4.792550346 4.706581487 4.638154755 4.579941168 4.525357287
#> [691] 4.471842191 4.420780288 4.374056983 4.331365078 4.291374762 4.253868124
#> [697] 4.218994007 4.185218958 4.150165899 4.114424239 4.084166694 4.070249157
#> [703] 4.087829504 4.167359978 4.411768752 5.183594717 6.047475358 0.033827928
#> [709] 0.090954159 0.064865507