オロのロゴを数式で求めてみた
こんにちは、社長室の臼井です。
今回は、昨年末にオロ社内で展開されたアドベントカレンダーの中から、エンジニアの野田さんが書かれた記事を一つご紹介します。
普段、社内でどのような話題が広がっているのか、少し感じていただけると思いますっ！それではどうぞ！
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オロちゃんってかわいいですよね。
とても単純な図形で構成されてるのになんとも言えない味があって、
とてもいいなって思うんですよね。
単純だから書きやすいんですけど、
どうせならやっぱりきれいに書きたいなって思うので
ここらでオロちゃんの数式を求めておいたほうがいいと思いませんか？
というわけで、
最近趣味でJuliaを触ってるのでJuliaの勉強がてら、オロちゃんの数式を求めてみたいなと思います。
Juliaとは？
http://marui.hatenablog.com/entry/20120221/1329823079
簡単にいうとあらゆる言語のいいとこどりをしたい言語。
手順
・画像のエッジ抽出をする
・エッジ上の点をグルーピングする
・各点群に対してフーリエ変換を行い、数式にする
という感じとのこと。
参考：https://aomoriringo.hateblo.jp/entry/2013/11/30/074758
前半はPyCallモジュールからPython経由でopenCVを使って画像処理するのが手っ取り早い気がしますが(というかMathemathicaモジュールからリンクのコードをそのまま呼び出すのが最も楽。Mathematicaないとだめだけど）勉強なので出来るだけJuliaだけでいきたいと思います。
エッジ抽出
using Images
using FileIO
using ImageView
using ImageFeatures
using Colors
img = load("oro.jpg")
オロちゃんですね。
function edge(img)
gx, gy = ImageFiltering.imgradients(img,KernelFactors.ando3, "replicate")
mag, grad_angle = Images.magnitude_phase(gx,gy)
mag[mag .< 0.5] .= 0.0 # Threshold magnitude image
thinned = Images.thin_edges(mag, grad_angle)
mag #edgeといいつつmagを返している
end
edge_img = edge(Gray.(img) .> 0.5)
Gray.(edge_img)
オロちゃんの輪郭ですね。
ラベリング
エッジ上の点をグルーピングします。
Imagesモジュールに入ってなかったので適当に画像を左上から走査してぺぺっとラベル貼る感じ。
function labeling(img)
shape = size(img)
label_arr = zeros(Int,shape)
label::Int64 = 0
lookupTbl = Dict()
label_max = label
for i in 1:shape[1]
for j in 1:shape[2]
target = CartesianIndex(i,j)
candidates = CartesianIndex.([(i-1,j-1) (i-1,j) (i-1,j+1) (i,j-1) ])
candidates = filter(x-> 1 ≤ x[1] ≤ shape[1] && 1 ≤ x[2] ≤ shape[2], candidates)
iszero(img[target]) && continue
if all(iszero,label_arr[candidates])
label = label_max + 1
label_max = label
else
label = minimum(filter(x->x>0, label_arr[candidates]))
filter(x-> x > label, label_arr[candidates]) .|> x-> lookupTbl[x] = label
end
label_arr[target] = label
end
end
while true
rep_label_arr = replace(x->haskey(lookupTbl,x) ? lookupTbl[x] : x,label_arr)
rep_label_arr == label_arr && break
label_arr = rep_label_arr
end
label_arr
end
function show_label(label_arr)
# color_imgs = [zeros(RGB{Normed{UInt8,8}},size(label_arr)) for l in Set(label_arr) if l > 0]
color_imgs = zeros(RGB{Normed{UInt8,8}},size(label_arr))
labels = [l for l in Set(label_arr) if l > 0]
colors = collect(Colors.color_names)
for (num, kv) in enumerate(rand(colors,length(labels)))
n,c = kv
color_imgs[findall(l->l==labels[num],label_arr)] .= color(n)
end
color_imgs
end
show_label(labeling(edge_img))
ラベルごとに色付けしたオロちゃん(うーん、かわいくはない気がする)
結果
juliaのfft周りを調べてたらこのあたりで寝落ちしたので、
翌朝、参考リンクのコードを流してMathematicaから出力した出来立てほやほや新鮮な式だけ貼っておきます。
{9633/23-(3297 Cos(t))/52-402/13 Cos(2t)-23644/213 Cos(3t)+6439/24 Cos(4t)+1988/25 Cos(5t)
+73/19 Cos(6t)+497/17 Cos(7t)-3 Cos(8t)+1101/100 Cos(9t)-43/20 Cos(10t)
+37/19 Cos(11t)-1/6 Cos(12t)+121/12 Cos(13t)-13/14 Cos(14t)+199/34 Cos(15t)
-21/26 Cos(16t)+109/27 Cos(17t)-5/8 Cos(18t)+164/47 Cos(19t)+69/55 Cos(20t)
+45/26 Cos(21t)-11/27 Cos(22t)+17/19 Cos(23t)-19/22 Cos(24t)+25/23 Cos(25t)
-29/24 Cos(26t)+7/8 Cos(27t)+3/4 Cos(28t)+34/25 Cos(29t)-2/5 Cos(30t)
+22/27 Cos(31t)-10/17 Cos(32t)+20/27 Cos(33t)-4/5 Cos(34t)+8/17 Cos(35t)
-5/11 Cos(36t)+1/2 Cos(37t)-7/13 Cos(38t)+3/8 Cos(39t)-6/13 Cos(40t)
+26/79 Cos(41t)-7/17 Cos(42t)+6/17 Cos(43t)-5/18 Cos(44t)+3/16 Cos(45t)
-5/17 Cos(46t)+1/55 Cos(47t)-23/40 Cos(48t)+1/44 Cos(49t)-25/76 Cos(50t)
+2/15 Cos(51t)-9/23 Cos(52t)+1/35 Cos(53t)-4/15 Cos(54t)+1/20 Cos(55t)
-4/11 Cos(56t)-1/45 Cos(57t)-5/22 Cos(58t)+1/39 Cos(59t)-6/23 Cos(60t)
-1/105 Cos(61t)-4/25 Cos(62t)-1/11 Cos(63t)-6/17 Cos(64t)-1/17 Cos(65t)
-3/22 Cos(66t)+1/19 Cos(67t)-1/3 Cos(68t)-1/28 Cos(69t)-12/47 Cos(70t)
+1/224 Cos(71t)-5/16 Cos(72t)-1/17 Cos(73t)-2/11 Cos(74t)-1/129 Cos(75t)
-8/41 Cos(76t)-1/91 Cos(77t)-4/15 Cos(78t)-3/28 Cos(79t)-3/19 Cos(80t)
-1/28 Cos(81t)-2/11 Cos(82t)-1/41 Cos(83t)-2/11 Cos(84t)+1/36 Cos(85t)
-3/14 Cos(86t)-1/12 Cos(87t)-2/13 Cos(88t)+1/77 Cos(89t)-2/9 Cos(90t)
+1/276 Cos(91t)-3/23 Cos(92t)+1/111 Cos(93t)-3/22 Cos(94t)-1/56 Cos(95t)
-2/23 Cos(96t)+1/103 Cos(97t)-3/25 Cos(98t)-2/23 Cos(100t)
+1/42 Cos(101t)-3/29 Cos(102t)+1/38 Cos(103t)-1/22 Cos(104t)+1/21 Cos(105t)
-1/17 Cos(106t)+1/24 Cos(107t)-1/24 Cos(108t)+1/363 Cos(109t)-1/15 Cos(110t)
+1/348 Cos(111t)-1/38 Cos(112t)+1/24 Cos(113t)+1/34 Cos(114t)+1/22 Cos(115t)
+1/22 Cos(116t)+1/364 Cos(117t)-1/38 Cos(118t)+1/21 Cos(119t)-1/41 Cos(120t)
-1/199 Cos(121t)+1/30 Cos(122t)+1/16 Cos(123t)+1/118 Cos(124t)+1/19 Cos(125t)
-1/181 Cos(126t)+2/27 Cos(127t)-1/98 Cos(128t)+1/37 Cos(129t)+1/37 Cos(130t)
+1/14 Cos(131t)-1/65 Cos(132t)+1/13 Cos(133t)+2/27 Cos(135t)
-1/49 Cos(136t)+1/19 Cos(137t)+1/38 Cos(138t)+1/17 Cos(139t)-1/39 Cos(140t)
+2/19 Cos(141t)+1/44 Cos(142t)+1/22 Cos(143t)+1/170 Cos(144t)+1/17 Cos(145t)
+1/43 Cos(146t)+1/18 Cos(147t)-1/79 Cos(148t)+1/20 Cos(149t)+1/161 Cos(150t)
+1/44 Cos(151t)+1/104 Cos(152t)+1/18 Cos(153t)+1/36 Cos(154t)+1/24 Cos(155t)
+1/35 Cos(156t)+1/21 Cos(157t)+1/35 Cos(158t)+1/39 Cos(160t)
+1/27 Cos(161t)+1/196 Cos(162t)+1/63 Cos(163t)+1/43 Cos(164t)+1/32 Cos(165t)
+1/107 Cos(166t)+1/423 Cos(167t)+1/61 Cos(168t)+1/17 Cos(169t)-1/60 Cos(170t)
+1/55 Cos(171t)+1/399 Cos(172t)+1/22 Cos(173t)-1/58 Cos(174t)+1/32 Cos(175t)
-1/214 Cos(176t)+1/31 Cos(177t)-1/27 Cos(178t)+1/30 Cos(179t)+1/91 Cos(180t)
+1/133 Cos(181t)-1/22 Cos(182t)+1/21 Cos(183t)+1/105 Cos(184t)-1/56 Cos(186t)
+1/69 Cos(187t)+1/80 Cos(188t)-1/207 Cos(189t)-1/20 Cos(190t)
+1/26 Cos(191t)-1/106 Cos(192t)-1/261 Cos(193t)-1/28 Cos(194t)+1/22 Cos(195t)
-1/41 Cos(196t)-1/131 Cos(197t)-1/22 Cos(198t)+1/24 Cos(199t)-1/49 Cos(200t)
+(47 Sin(t))/20+25/24 Sin(2t)+73/14 Sin(3t)+245/17 Sin(4t)+63/5 Sin(5t)
+160/23 Sin(6t)+168/23 Sin(7t)+51/10 Sin(8t)+29/12 Sin(9t)+33/17 Sin(10t)
+7/19 Sin(11t)+26/35 Sin(12t)+25/14 Sin(13t)+63/38 Sin(14t)+11/6 Sin(15t)
+3/2 Sin(16t)+37/25 Sin(17t)+27/17 Sin(18t)+24/23 Sin(19t)+17/12 Sin(20t)
+19/14 Sin(21t)+13/11 Sin(22t)+27/29 Sin(23t)+26/35 Sin(24t)+14/19 Sin(25t)
+10/19 Sin(26t)+4/13 Sin(27t)+8/9 Sin(28t)+38/37 Sin(29t)+31/35 Sin(30t)
+18/23 Sin(31t)+22/27 Sin(32t)+13/16 Sin(33t)+11/29 Sin(34t)+5/22 Sin(35t)
+4/7 Sin(36t)+17/35 Sin(37t)+4/11 Sin(38t)+11/24 Sin(39t)+13/22 Sin(40t)
+13/25 Sin(41t)+5/17 Sin(42t)+3/10 Sin(43t)+11/24 Sin(44t)+6/17 Sin(45t)
+6/23 Sin(46t)+5/17 Sin(47t)+4/19 Sin(48t)+7/34 Sin(49t)+3/32 Sin(50t)
+5/23 Sin(51t)+4/19 Sin(52t)+3/22 Sin(53t)+3/13 Sin(54t)+6/25 Sin(55t)
+4/17 Sin(56t)+3/28 Sin(57t)+1/10 Sin(58t)+1/8 Sin(59t)+2/21 Sin(60t)
+1/14 Sin(62t)+2/15 Sin(63t)-1/48 Sin(64t)-1/46 Sin(65t)
+1/25 Sin(66t)+1/7 Sin(67t)+1/74 Sin(68t)-1/21 Sin(69t)+1/16 Sin(70t)
+6/41 Sin(71t)+1/20 Sin(72t)-1/10 Sin(73t)+1/44 Sin(74t)+1/35 Sin(75t)
-1/20 Sin(76t)-1/11 Sin(77t)+1/12 Sin(78t)+1/19 Sin(79t)-1/41 Sin(80t)
-1/19 Sin(81t)+1/76 Sin(82t)+1/38 Sin(83t)-1/8 Sin(84t)-1/16 Sin(85t)
+1/37 Sin(86t)-1/19 Sin(87t)-1/16 Sin(88t)-1/49 Sin(89t)+1/91 Sin(90t)
-2/21 Sin(91t)-2/21 Sin(92t)+1/499 Sin(93t)+1/38 Sin(94t)-3/22 Sin(95t)
-1/13 Sin(96t)+1/389 Sin(97t)+1/118 Sin(98t)-2/23 Sin(99t)-1/13 Sin(100t)
+1/47 Sin(101t)-1/43 Sin(102t)-5/34 Sin(103t)-1/14 Sin(104t)+1/41 Sin(105t)
-1/17 Sin(106t)-3/29 Sin(107t)-1/156 Sin(108t)+1/56 Sin(109t)-1/29 Sin(110t)
-1/14 Sin(111t)-1/32 Sin(112t)+1/222 Sin(113t)-1/19 Sin(114t)-2/21 Sin(115t)
-1/74 Sin(116t)-2/25 Sin(118t)-1/26 Sin(119t)-1/37 Sin(121t)-1/18 Sin(122t)
-1/23 Sin(123t)+1/137 Sin(124t)-1/63 Sin(125t)
-1/11 Sin(126t)-1/76 Sin(127t)+1/101 Sin(128t)-1/17 Sin(129t)-1/23 Sin(130t)
-1/24 Sin(131t)+1/55 Sin(132t)-1/47 Sin(133t)-1/17 Sin(134t)-1/429 Sin(135t)
+1/53 Sin(136t)-1/13 Sin(137t)-1/92 Sin(138t)+1/39 Sin(139t)-1/71 Sin(140t)
-1/21 Sin(141t)-1/23 Sin(142t)+1/51 Sin(143t)+1/45 Sin(144t)-1/17 Sin(145t)
-1/45 Sin(146t)+1/25 Sin(147t)-1/250 Sin(148t)-1/22 Sin(149t)+1/158 Sin(150t)
-1/125 Sin(153t)+1/35 Sin(154t)+1/21 Sin(155t)
-1/26 Sin(156t)-1/50 Sin(157t)+1/20 Sin(158t)+1/117 Sin(159t)-1/43 Sin(160t)
-1/69 Sin(161t)+1/65 Sin(162t)+1/17 Sin(163t)-1/39 Sin(164t)-1/89 Sin(165t)
+1/15 Sin(166t)+1/313 Sin(167t)-1/67 Sin(168t)+1/21 Sin(169t)+1/144 Sin(170t)
+1/43 Sin(171t)+1/106 Sin(172t)+1/139 Sin(173t)+1/16 Sin(174t)+1/92 Sin(175t)
-1/29 Sin(176t)+1/18 Sin(177t)+1/27 Sin(178t)-1/24 Sin(179t)+1/25 Sin(180t)
+1/35 Sin(181t)+1/32 Sin(182t)+1/49 Sin(183t)-1/205 Sin(184t)+1/14 Sin(185t)
+1/19 Sin(186t)-1/20 Sin(187t)-1/126 Sin(188t)+1/16 Sin(189t)+1/268 Sin(190t)
-1/81 Sin(191t)+1/67 Sin(192t)+1/19 Sin(193t)+1/22 Sin(194t)-1/73 Sin(195t)
+1/147 Sin(196t)+1/20 Sin(197t)+1/49 Sin(198t)-1/47 Sin(199t)+1/38 Sin(200t),
-(9255/22)+(1118 Cos(t))/19+438/25 Cos(2t)+4099/24 Cos(3t)+2744/23 Cos(4t)-2915/26 Cos(5t)
+70/9 Cos(6t)-813/22 Cos(7t)-28/23 Cos(8t)-200/13 Cos(9t)-49/19 Cos(10t)
-314/29 Cos(11t)+198/13 Cos(12t)-31/5 Cos(13t)+13/15 Cos(14t)-169/34 Cos(15t)
+31/21 Cos(16t)-11/13 Cos(17t)-2/9 Cos(18t)-20/9 Cos(19t)+6/13 Cos(20t)
-65/31 Cos(21t)-40/29 Cos(22t)-50/27 Cos(23t)+39/29 Cos(24t)-25/26 Cos(25t)
-5/27 Cos(26t)-3/25 Cos(27t)+47/33 Cos(28t)-29/26 Cos(29t)-1/8 Cos(30t)
-11/18 Cos(31t)+11/12 Cos(32t)-4/5 Cos(33t)-5/26 Cos(34t)-6/43 Cos(35t)
+10/17 Cos(36t)-11/14 Cos(37t)+1/29 Cos(38t)+3/20 Cos(39t)+14/23 Cos(40t)
-21/43 Cos(41t)+11/45 Cos(42t)+11/32 Cos(43t)+7/17 Cos(44t)-13/18 Cos(45t)
+3/22 Cos(46t)+4/15 Cos(47t)+7/20 Cos(48t)-7/16 Cos(49t)+6/17 Cos(50t)
+2/7 Cos(51t)+3/19 Cos(52t)-7/17 Cos(53t)+10/23 Cos(54t)+5/16 Cos(55t)
+5/31 Cos(56t)-7/24 Cos(57t)+5/12 Cos(58t)+1/6 Cos(59t)+1/15 Cos(60t)
-2/9 Cos(61t)+13/25 Cos(62t)+3/23 Cos(63t)-1/13 Cos(64t)-2/19 Cos(65t)
+26/51 Cos(66t)+1/22 Cos(67t)-1/13 Cos(68t)-1/12 Cos(69t)+11/24 Cos(70t)
+1/20 Cos(71t)+1/93 Cos(72t)+1/18 Cos(73t)+4/9 Cos(74t)-1/28 Cos(75t)
-1/16 Cos(76t)+2/15 Cos(77t)+7/19 Cos(78t)+1/35 Cos(79t)-1/98 Cos(80t)
+4/29 Cos(81t)+6/23 Cos(82t)-2/13 Cos(83t)+1/19 Cos(84t)+2/15 Cos(85t)
+3/11 Cos(86t)-5/28 Cos(87t)+1/131 Cos(88t)+3/19 Cos(89t)+1/16 Cos(90t)
-1/7 Cos(91t)-1/28 Cos(92t)+1/10 Cos(93t)+1/15 Cos(94t)-3/19 Cos(95t)
+3/29 Cos(96t)+3/23 Cos(97t)+1/12 Cos(98t)-7/41 Cos(99t)+5/36 Cos(100t)
+2/15 Cos(101t)-1/263 Cos(102t)-3/31 Cos(103t)+3/22 Cos(104t)+1/12 Cos(105t)
-1/30 Cos(106t)-1/11 Cos(107t)+1/9 Cos(108t)-1/233 Cos(109t)-1/22 Cos(110t)
-1/16 Cos(111t)+5/27 Cos(112t)-1/252 Cos(113t)-2/21 Cos(114t)-1/14 Cos(115t)
+2/17 Cos(116t)-1/22 Cos(117t)-1/17 Cos(118t)-1/57 Cos(119t)+1/11 Cos(120t)
-2/21 Cos(121t)-1/19 Cos(122t)-1/228 Cos(123t)+1/13 Cos(124t)-1/16 Cos(125t)
-1/19 Cos(126t)+1/60 Cos(127t)+2/27 Cos(128t)-1/8 Cos(129t)-1/18 Cos(130t)
+1/103 Cos(131t)+1/23 Cos(132t)-3/25 Cos(133t)-1/23 Cos(134t)+1/48 Cos(135t)
+1/37 Cos(136t)-2/17 Cos(137t)+1/74 Cos(138t)-1/31 Cos(139t)-1/99 Cos(140t)
-1/9 Cos(141t)+1/158 Cos(142t)-1/16 Cos(144t)-1/12 Cos(145t)
-1/200 Cos(146t)-1/52 Cos(147t)-1/14 Cos(148t)-1/13 Cos(149t)+1/32 Cos(150t)
+1/72 Cos(151t)-1/28 Cos(152t)-1/21 Cos(153t)+1/21 Cos(154t)-1/42 Cos(155t)
-1/120 Cos(156t)-1/20 Cos(157t)+1/20 Cos(158t)-1/56 Cos(159t)-1/20 Cos(160t)
-1/403 Cos(162t)-2/27 Cos(163t)-1/34 Cos(164t)-1/26 Cos(165t)
+1/103 Cos(166t)-1/16 Cos(167t)-1/20 Cos(168t)+1/41 Cos(169t)-1/60 Cos(170t)
-1/24 Cos(171t)-1/29 Cos(172t)-1/358 Cos(173t)+1/38 Cos(174t)-1/13 Cos(175t)
+1/91 Cos(176t)-1/31 Cos(177t)-1/165 Cos(178t)-1/26 Cos(179t)-1/80 Cos(180t)
+1/244 Cos(181t)-1/48 Cos(182t)-1/120 Cos(183t)+1/25 Cos(184t)-1/27 Cos(187t)
+1/23 Cos(188t)-1/124 Cos(189t)-1/47 Cos(190t)
+1/70 Cos(191t)+1/96 Cos(192t)+1/124 Cos(193t)-1/34 Cos(194t)-1/473 Cos(195t)
+1/32 Cos(196t)-1/41 Cos(197t)+1/55 Cos(198t)+1/66 Cos(199t)+1/41 Cos(200t)
+(55 Sin(t))/21+81/20 Sin(2t)+66/7 Sin(3t)+132/23 Sin(4t)-116/41 Sin(5t)
-31/9 Sin(6t)-87/25 Sin(7t)-144/31 Sin(8t)-103/36 Sin(9t)-63/20 Sin(10t)
-10/11 Sin(11t)+13/18 Sin(12t)-5/22 Sin(13t)-14/11 Sin(14t)-10/9 Sin(15t)
-27/22 Sin(16t)-11/17 Sin(17t)-17/15 Sin(18t)-7/12 Sin(19t)-15/46 Sin(20t)
-22/29 Sin(21t)-8/7 Sin(22t)-38/37 Sin(23t)-7/9 Sin(24t)-15/17 Sin(25t)
-20/27 Sin(26t)-1/14 Sin(27t)+1/30 Sin(28t)-5/11 Sin(29t)-10/23 Sin(30t)
-5/12 Sin(31t)-9/22 Sin(32t)-10/13 Sin(33t)-5/8 Sin(34t)-5/23 Sin(35t)
-5/22 Sin(36t)-11/20 Sin(37t)-12/35 Sin(38t)-7/43 Sin(39t)-3/13 Sin(40t)
-7/16 Sin(41t)-5/26 Sin(42t)+1/31 Sin(43t)-7/36 Sin(44t)-8/19 Sin(45t)
-5/17 Sin(46t)-2/13 Sin(47t)-37/110 Sin(48t)-8/19 Sin(49t)-3/28 Sin(50t)
+1/227 Sin(51t)-1/4 Sin(52t)-11/45 Sin(53t)+1/33 Sin(54t)+1/177 Sin(55t)
-7/31 Sin(56t)-4/15 Sin(57t)+1/24 Sin(58t)+1/58 Sin(59t)-5/22 Sin(60t)
-4/23 Sin(61t)+1/16 Sin(62t)-1/41 Sin(63t)-5/18 Sin(64t)-2/23 Sin(65t)
+5/27 Sin(66t)+1/19 Sin(67t)-3/19 Sin(68t)+1/35 Sin(69t)+3/32 Sin(70t)
-1/13 Sin(71t)-5/29 Sin(72t)+1/56 Sin(73t)+4/33 Sin(74t)-1/10 Sin(75t)
-3/19 Sin(76t)+1/9 Sin(77t)+3/20 Sin(78t)-1/13 Sin(79t)-2/19 Sin(80t)
+3/23 Sin(81t)+1/14 Sin(82t)-1/13 Sin(83t)-1/86 Sin(84t)+3/16 Sin(85t)
+1/37 Sin(86t)-2/17 Sin(87t)-1/17 Sin(88t)+5/36 Sin(89t)+1/63 Sin(90t)
-2/23 Sin(91t)+1/18 Sin(92t)+1/6 Sin(93t)-1/61 Sin(94t)-1/11 Sin(95t)
+1/14 Sin(96t)+3/19 Sin(97t)-1/87 Sin(98t)-3/31 Sin(99t)+3/29 Sin(100t)
+5/28 Sin(101t)-1/25 Sin(102t)-1/17 Sin(103t)+3/22 Sin(104t)+2/15 Sin(105t)
-1/35 Sin(106t)+1/177 Sin(107t)+2/15 Sin(108t)+1/20 Sin(109t)-1/11 Sin(110t)
+1/35 Sin(111t)+4/21 Sin(112t)+1/24 Sin(113t)-3/20 Sin(114t)-1/42 Sin(115t)
+2/13 Sin(116t)+1/23 Sin(117t)-1/14 Sin(118t)+1/16 Sin(119t)+3/29 Sin(120t)
-1/35 Sin(121t)-1/18 Sin(122t)+1/14 Sin(123t)+3/25 Sin(124t)+1/157 Sin(125t)
-1/16 Sin(126t)+1/16 Sin(127t)+1/14 Sin(128t)-1/12 Sin(129t)-1/17 Sin(130t)
+3/22 Sin(131t)+3/26 Sin(132t)-1/11 Sin(133t)-1/19 Sin(134t)+5/36 Sin(135t)
+1/24 Sin(136t)-1/14 Sin(137t)+1/27 Sin(138t)+1/8 Sin(139t)+1/69 Sin(140t)
-1/16 Sin(141t)+1/196 Sin(142t)+1/10 Sin(143t)-1/29 Sin(144t)-1/20 Sin(145t)
+1/17 Sin(146t)+1/14 Sin(147t)-1/32 Sin(148t)-1/16 Sin(149t)+1/22 Sin(150t)
+2/19 Sin(151t)-1/21 Sin(152t)-1/10 Sin(153t)+1/16 Sin(154t)+1/19 Sin(155t)
-1/9 Sin(156t)-2/23 Sin(157t)+1/11 Sin(158t)+1/84 Sin(159t)-2/17 Sin(160t)
+1/45 Sin(161t)+1/14 Sin(162t)-1/17 Sin(163t)-1/12 Sin(164t)+1/26 Sin(165t)
+2/27 Sin(166t)-1/27 Sin(167t)-2/19 Sin(168t)+1/27 Sin(170t)
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+1/359 Cos(157t)-1/198 Cos(158t)+1/127 Cos(160t)
-1/75 Cos(161t)+1/408 Cos(165t)
+1/220 Cos(166t)-1/182 Cos(168t)+1/401 Cos(169t)-1/293 Cos(170t)
+1/310 Cos(172t)-1/268 Cos(177t)+1/231 Cos(178t)-1/463 Cos(192t)-1/425 Cos(199t)
+(7 Sin(t))/19+4/13 Sin(2t)-69/28 Sin(3t)-46/21 Sin(4t)+3/26 Sin(5t)
-6/19 Sin(6t)-5/12 Sin(7t)-2/17 Sin(8t)-1/67 Sin(9t)-5/19 Sin(10t)
-2/13 Sin(11t)+4/27 Sin(12t)-7/19 Sin(13t)-1/19 Sin(14t)+12/49 Sin(15t)
-42/85 Sin(16t)+1/11 Sin(17t)+2/25 Sin(18t)-10/21 Sin(19t)+4/21 Sin(20t)
+1/27 Sin(21t)-5/17 Sin(22t)+4/29 Sin(23t)-1/37 Sin(24t)-3/11 Sin(25t)
+1/75 Sin(26t)-1/57 Sin(27t)-2/11 Sin(28t)+1/25 Sin(29t)+1/27 Sin(30t)
-1/7 Sin(31t)-1/54 Sin(32t)+1/19 Sin(33t)-2/21 Sin(34t)-3/28 Sin(35t)
+1/31 Sin(36t)-1/31 Sin(37t)-2/17 Sin(38t)+1/19 Sin(39t)-1/58 Sin(40t)
-1/7 Sin(41t)+1/33 Sin(42t)-1/34 Sin(43t)-1/13 Sin(44t)+1/17 Sin(45t)
-1/23 Sin(46t)-3/25 Sin(47t)+1/77 Sin(48t)-1/74 Sin(49t)-1/16 Sin(50t)
+1/244 Sin(51t)-1/41 Sin(52t)-1/12 Sin(53t)-1/17 Sin(54t)+1/148 Sin(55t)
+1/25 Sin(56t)-1/54 Sin(57t)-1/21 Sin(58t)-1/18 Sin(59t)+1/135 Sin(60t)
+1/18 Sin(61t)-1/58 Sin(62t)+1/34 Sin(63t)+1/35 Sin(64t)-1/7 Sin(65t)
-1/20 Sin(66t)+1/16 Sin(67t)-1/49 Sin(68t)+1/19 Sin(70t)
+1/55 Sin(71t)-1/46 Sin(72t)-1/34 Sin(73t)-1/30 Sin(74t)-1/28 Sin(75t)
-1/63 Sin(76t)+1/26 Sin(77t)+1/28 Sin(78t)-1/39 Sin(79t)-1/29 Sin(80t)
-1/68 Sin(82t)-1/34 Sin(83t)+1/20 Sin(85t)
-1/176 Sin(86t)-1/19 Sin(87t)+1/72 Sin(88t)+1/98 Sin(89t)-1/24 Sin(90t)
+1/51 Sin(91t)+1/35 Sin(92t)-1/46 Sin(93t)-1/48 Sin(94t)-1/205 Sin(95t)
+1/173 Sin(96t)+1/71 Sin(97t)-1/154 Sin(98t)-1/45 Sin(99t)-1/162 Sin(100t)
-1/196 Sin(101t)+1/63 Sin(102t)+1/54 Sin(103t)+1/108 Sin(104t)-1/52 Sin(105t)
-1/60 Sin(106t)-1/190 Sin(107t)-1/295 Sin(108t)+1/163 Sin(109t)+1/54 Sin(110t)
-1/222 Sin(111t)-1/119 Sin(112t)+1/210 Sin(113t)-1/126 Sin(114t)+1/388 Sin(115t)
+1/149 Sin(116t)-1/190 Sin(118t)-1/216 Sin(121t)+1/272 Sin(122t)
+1/290 Sin(123t)+1/374 Sin(124t)+1/228 Sin(125t)
-1/356 Sin(127t)-1/234 Sin(128t)-1/363 Sin(129t)+1/312 Sin(131t)
+1/259 Sin(132t)+1/154 Sin(133t)-1/327 Sin(136t)-1/198 Sin(137t)
-1/183 Sin(138t)+1/195 Sin(139t)+1/271 Sin(140t)
-1/213 Sin(141t)+1/250 Sin(142t)-1/221 Sin(144t)+1/408 Sin(146t)
-1/214 Sin(147t)-1/199 Sin(148t)+1/362 Sin(149t)+1/286 Sin(150t)
+1/232 Sin(151t)+1/171 Sin(152t)-1/269 Sin(154t)+1/295 Sin(155t)
-1/200 Sin(156t)-1/238 Sin(157t)+1/161 Sin(158t)-1/196 Sin(159t)
+1/106 Sin(161t)+1/144 Sin(162t)-1/362 Sin(163t)+1/321 Sin(164t)-1/152 Sin(165t)
-1/90 Sin(166t)+1/203 Sin(168t)+1/499 Sin(169t)+1/160 Sin(170t)
+1/480 Sin(171t)-1/114 Sin(172t)+1/283 Sin(174t)-1/197 Sin(175t)
+1/152 Sin(177t)-1/173 Sin(178t)+1/109 Sin(180t)
-1/309 Sin(182t)-1/196 Sin(184t)+1/250 Sin(186t)-1/346 Sin(191t)
+1/368 Sin(192t)-1/208 Sin(194t)+1/304 Sin(195t)
-1/199 Sin(197t)+1/395 Sin(198t)+1/330 Sin(199t)-1/254 Sin(200t)
,-(7268/21)-(356 Cos(t))/29-197/6 Cos(2t)-124/9 Cos(3t)+43/19 Cos(4t)+566/29 Cos(5t)
-47/10 Cos(6t)+82/33 Cos(7t)+411/77 Cos(8t)-95/33 Cos(9t)+58/19 Cos(10t)
+1/16 Cos(11t)+22/25 Cos(12t)-17/45 Cos(13t)+39/28 Cos(14t)-7/26 Cos(15t)
+12/19 Cos(16t)+7/27 Cos(17t)+5/8 Cos(18t)-15/59 Cos(19t)+17/28 Cos(20t)
+2/11 Cos(21t)+1/17 Cos(22t)+2/23 Cos(23t)+9/25 Cos(24t)-8/31 Cos(25t)
+5/23 Cos(26t)+2/13 Cos(27t)-3/28 Cos(28t)+1/31 Cos(29t)+1/4 Cos(30t)
-5/22 Cos(31t)+3/19 Cos(32t)+1/13 Cos(33t)+1/34 Cos(34t)+1/16 Cos(35t)
+4/23 Cos(36t)-1/17 Cos(37t)+2/25 Cos(38t)+3/23 Cos(39t)-1/22 Cos(40t)
+1/44 Cos(41t)+1/21 Cos(42t)-1/60 Cos(43t)+1/374 Cos(44t)+1/25 Cos(45t)
-1/27 Cos(46t)-1/230 Cos(47t)+1/56 Cos(48t)-1/128 Cos(49t)+1/48 Cos(50t)
+1/23 Cos(52t)-1/18 Cos(53t)+1/13 Cos(54t)-2/25 Cos(55t)
+2/23 Cos(56t)-2/23 Cos(57t)+1/10 Cos(58t)-2/23 Cos(59t)+1/15 Cos(60t)
-1/20 Cos(61t)+1/30 Cos(62t)-1/23 Cos(63t)+1/27 Cos(64t)-1/20 Cos(65t)
+1/28 Cos(66t)-1/21 Cos(67t)+1/43 Cos(68t)-1/50 Cos(70t)
+1/40 Cos(71t)-1/29 Cos(72t)+1/102 Cos(73t)-1/103 Cos(75t)
+1/67 Cos(76t)-1/40 Cos(77t)+1/344 Cos(78t)-1/26 Cos(79t)+1/39 Cos(80t)
+1/64 Cos(81t)-1/28 Cos(82t)-1/23 Cos(83t)+1/44 Cos(84t)-1/152 Cos(85t)
+1/38 Cos(86t)-1/12 Cos(87t)+1/36 Cos(88t)-1/35 Cos(89t)+1/24 Cos(90t)
-1/20 Cos(91t)-1/352 Cos(92t)+1/95 Cos(94t)-1/30 Cos(95t)
+1/103 Cos(96t)-1/28 Cos(97t)-1/101 Cos(99t)+1/40 Cos(100t)
+1/74 Cos(102t)-1/86 Cos(103t)-1/38 Cos(104t)+1/49 Cos(105t)
+1/181 Cos(106t)-1/23 Cos(107t)-1/79 Cos(108t)-1/26 Cos(109t)-1/63 Cos(110t)
-1/36 Cos(111t)-1/53 Cos(112t)-1/28 Cos(113t)-1/472 Cos(114t)-1/95 Cos(115t)
-1/125 Cos(116t)-1/43 Cos(117t)+1/69 Cos(118t)-1/66 Cos(119t)-1/284 Cos(120t)
-1/42 Cos(121t)-1/26 Cos(122t)-1/249 Cos(124t)+1/219 Cos(125t)
-1/62 Cos(126t)+1/46 Cos(127t)+1/57 Cos(128t)+1/50 Cos(129t)+1/131 Cos(130t)
+1/171 Cos(131t)-1/78 Cos(132t)+1/80 Cos(133t)-1/63 Cos(134t)-1/95 Cos(135t)
-1/94 Cos(136t)-1/92 Cos(137t)-1/49 Cos(138t)+1/101 Cos(140t)
-1/50 Cos(141t)-1/299 Cos(142t)-1/78 Cos(143t)-1/109 Cos(145t)
-1/142 Cos(146t)-1/30 Cos(147t)-1/58 Cos(149t)-1/58 Cos(151t)
+1/162 Cos(152t)-1/70 Cos(153t)+1/106 Cos(154t)-1/331 Cos(155t)
+1/104 Cos(156t)-1/105 Cos(157t)+1/130 Cos(158t)-1/93 Cos(159t)+1/294 Cos(160t)
-1/276 Cos(161t)-1/156 Cos(163t)+1/261 Cos(164t)-1/313 Cos(165t)
+1/278 Cos(168t)-1/168 Cos(169t)-1/404 Cos(172t)-1/205 Cos(175t)
+1/374 Cos(176t)-1/293 Cos(177t)-1/294 Cos(179t)+1/390 Cos(180t)
+1/431 Cos(186t)-1/266 Cos(187t)+1/301 Cos(188t)+1/394 Cos(196t)+1/290 Cos(198t)+1/297 Cos(200t)
+(28 Sin(t))/47+11/9 Sin(2t)+22/13 Sin(3t)-23/27 Sin(4t)-29/15 Sin(5t)
+8/25 Sin(6t)-4/11 Sin(7t)-35/36 Sin(8t)+6/19 Sin(9t)-11/34 Sin(10t)
-11/23 Sin(11t)+2/11 Sin(12t)-7/31 Sin(13t)-7/27 Sin(14t)-1/18 Sin(15t)
-5/28 Sin(16t)-7/36 Sin(17t)-5/22 Sin(18t)+1/28 Sin(19t)-5/24 Sin(20t)
-6/25 Sin(21t)+1/10 Sin(22t)-4/23 Sin(23t)-1/6 Sin(24t)+4/31 Sin(25t)
-4/31 Sin(26t)-1/7 Sin(27t)+4/33 Sin(28t)-2/23 Sin(29t)-1/7 Sin(30t)
+2/19 Sin(31t)-1/15 Sin(32t)-5/28 Sin(33t)+1/30 Sin(34t)-1/8 Sin(35t)
-4/21 Sin(36t)+1/14 Sin(37t)-3/26 Sin(38t)-4/21 Sin(39t)+1/20 Sin(40t)
-1/34 Sin(41t)-2/23 Sin(42t)+1/32 Sin(43t)-1/156 Sin(44t)-1/17 Sin(45t)
+1/15 Sin(46t)+1/79 Sin(47t)-1/30 Sin(48t)-1/38 Sin(50t)
-1/17 Sin(51t)-1/34 Sin(52t)+1/92 Sin(53t)-1/20 Sin(54t)-1/32 Sin(55t)
+1/41 Sin(56t)-1/13 Sin(57t)-1/14 Sin(58t)+3/28 Sin(59t)-1/412 Sin(60t)
-2/23 Sin(61t)-1/13 Sin(62t)-1/12 Sin(63t)-1/63 Sin(65t)
-2/23 Sin(66t)-3/29 Sin(67t)-1/107 Sin(68t)+1/19 Sin(69t)-1/25 Sin(70t)
-1/297 Sin(71t)-1/15 Sin(73t)+1/25 Sin(74t)-1/85 Sin(75t)
-1/23 Sin(76t)+1/28 Sin(77t)-1/13 Sin(78t)-1/24 Sin(79t)+1/17 Sin(80t)
+1/74 Sin(81t)-1/23 Sin(82t)-1/11 Sin(83t)+1/56 Sin(84t)+1/26 Sin(85t)
-1/26 Sin(86t)-1/78 Sin(87t)-1/26 Sin(88t)+1/42 Sin(89t)+1/64 Sin(90t)
-1/22 Sin(91t)-1/261 Sin(92t)-1/44 Sin(96t)+1/94 Sin(97t)-1/39 Sin(98t)+1/143 Sin(99t)+1/64 Sin(100t)
-1/49 Sin(101t)+1/36 Sin(102t)-1/49 Sin(103t)-1/84 Sin(104t)+1/46 Sin(105t)
-1/77 Sin(106t)-1/211 Sin(107t)-1/53 Sin(108t)-1/101 Sin(109t)-1/67 Sin(111t)
+1/222 Sin(112t)-1/79 Sin(113t)-1/239 Sin(114t)+1/143 Sin(115t)
-1/52 Sin(116t)+1/136 Sin(117t)-1/284 Sin(118t)-1/346 Sin(119t)+1/95 Sin(120t)
-1/108 Sin(121t)+1/112 Sin(122t)-1/256 Sin(123t)+1/158 Sin(125t)
-1/128 Sin(126t)+1/373 Sin(127t)-1/217 Sin(128t)-1/186 Sin(129t)+1/159 Sin(130t)
-1/105 Sin(131t)+1/133 Sin(132t)-1/363 Sin(133t)+1/107 Sin(135t)
+1/115 Sin(137t)+1/149 Sin(138t)-1/442 Sin(139t)+1/188 Sin(142t)+1/216 Sin(143t)+1/134 Sin(145t)
+1/138 Sin(146t)+1/50 Sin(147t)+1/123 Sin(148t)+1/285 Sin(149t)+1/93 Sin(150t)
+1/184 Sin(151t)+1/284 Sin(153t)-1/279 Sin(154t)-1/227 Sin(156t)
+1/331 Sin(157t)+1/341 Sin(158t)+1/253 Sin(159t)+1/187 Sin(160t)
+1/197 Sin(162t)+1/143 Sin(163t)-1/264 Sin(164t)+1/248 Sin(165t)
+1/268 Sin(166t)-1/266 Sin(167t)+1/166 Sin(169t)+1/154 Sin(170t)
+1/130 Sin(172t)+1/203 Sin(173t)+1/130 Sin(174t)+1/104 Sin(175t)
+1/425 Sin(177t)+1/110 Sin(178t)+1/161 Sin(181t)+1/291 Sin(182t)+1/204 Sin(184t)+1/135 Sin(185t)
+1/254 Sin(186t)+1/197 Sin(187t)+1/124 Sin(190t)
+1/242 Sin(191t)+1/222 Sin(194t)+1/254 Sin(195t)
+1/441 Sin(196t)+1/211 Sin(197t)+1/159 Sin(200t)
}
（-pi<=t<=pi）
※参考リンクの方法だと3つの点群に分けられて3つ分の曲線の式が求まりました
あんなに単純だったオロちゃんがこんなになってしまうなんて…
(もっと適当なとこで近似を打ち切ればいいだけでは)
というわけで
かわいいオロちゃんをきれいに書くために必要な式が求まりましたとさ。
感想
JuliaではREPLやJupyter上でTexっぽく変数宣言すると変換して表示してくれたり、定数*変数をそのまま数式っぽく2xみたいにかけるので複雑な数式書くのに楽かなーと思って今回はオロちゃんの近似式を求めようとしたんですが、最後結局自力で書けなかったのが残念です。
近似されたオロちゃんをプロットしたものはロゴの改変に当たるのかどうかちょっと気になりますが、まあ、大丈夫でしょう。（fin）
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