matlab怎麼把圓周率按照這種方式環形排列？

01-08

----更新----

關於存矢量圖已經找到原因, 在 export setup &> Fonts 下可以設置導出字型大小的最小值.

故下文中代碼有更新

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這個不難, 比較繁瑣的是參數的選取. 先上圖. (不知道圖片是不是掛了, 順便給個鏈接)

http://images2015.cnblogs.com/blog/524505/201604/524505-20160414133259488-727525125.png假設如下:

0. 字元位置由半徑 radius 和轉角 theta 確定1. 字型大小(fontsize)線性變化

2. 每個近似圓周上排布的字元數目(no)需要根據字型大小確定

3. 每兩個相鄰字元的轉角變化(theta)根據 no 確定

4. 每兩個字元間的半徑變化也要根據 no 確定

5. 單個字元的旋轉角度 rotate 由轉角決定

剩下的事情就是調參數

close all; clear all; clc; a = [... "3.14159265358979323846264338327950288419716939937510",... "58209749445923078164062862089986280348253421170679",... "82148086513282306647093844609550582231725359408128",... "48111745028410270193852110555964462294895493038196",... "44288109756659334461284756482337867831652712019091",... "45648566923460348610454326648213393607260249141273",... "72458700660631558817488152092096282925409171536436",... "78925903600113305305488204665213841469519415116094",... "33057270365759591953092186117381932611793105118548",... "07446237996274956735188575272489122793818301194912",... "98336733624406566430860213949463952247371907021798",... "60943702770539217176293176752384674818467669405132",... "00056812714526356082778577134275778960917363717872",... "14684409012249534301465495853710507922796892589235",... "42019956112129021960864034418159813629774771309960",... "51870721134999999837297804995105973173281609631859",... "50244594553469083026425223082533446850352619311881",... "71010003137838752886587533208381420617177669147303",... "59825349042875546873115956286388235378759375195778",... "18577805321712268066130019278766111959092164201989",... "38095257201065485863278865936153381827968230301952",... "03530185296899577362259941389124972177528347913151",... "55748572424541506959508295331168617278558890750983",... "81754637464939319255060400927701671139009848824012",... "85836160356370766010471018194295559619894676783744",... "94482553797747268471040475346462080466842590694912",... "93313677028989152104752162056966024058038150193511",... "25338243003558764024749647326391419927260426992279",... "67823547816360093417216412199245863150302861829745",... "55706749838505494588586926995690927210797509302955",... "32116534498720275596023648066549911988183479775356",... "63698074265425278625518184175746728909777727938000",... "81647060016145249192173217214772350141441973568548",... "16136115735255213347574184946843852332390739414333",... "45477624168625189835694855620992192221842725502542",... "56887671790494601653466804988627232791786085784383",... "82796797668145410095388378636095068006422512520511",... "73929848960841284886269456042419652850222106611863",... "06744278622039194945047123713786960956364371917287",... "46776465757396241389086583264599581339047802759009",... "94657640789512694683983525957098258226205224894077",... "26719478268482601476990902640136394437455305068203",... "49625245174939965143142980919065925093722169646151",... "57098583874105978859597729754989301617539284681382",... "68683868942774155991855925245953959431049972524680",... "84598727364469584865383673622262609912460805124388",... "43904512441365497627807977156914359977001296160894",... "41694868555848406353422072225828488648158456028506",... "01684273945226746767889525213852254995466672782398",... "64565961163548862305774564980355936345681743241125",... "15076069479451096596094025228879710893145669136867",... "22874894056010150330861792868092087476091782493858",... "90097149096759852613655497818931297848216829989487",... "22658804857564014270477555132379641451523746234364",... "54285844479526586782105114135473573952311342716610",... "21359695362314429524849371871101457654035902799344",... "03742007310578539062198387447808478489683321445713",... "86875194350643021845319104848100537061468067491927",... "81911979399520614196634287544406437451237181921799",... "98391015919561814675142691239748940907186494231961",... "56794520809514655022523160388193014209376213785595",... "66389377870830390697920773467221825625996615014215",... "03068038447734549202605414665925201497442850732518",... "66600213243408819071048633173464965145390579626856",... "10055081066587969981635747363840525714591028970641",... "40110971206280439039759515677157700420337869936007",... "23055876317635942187312514712053292819182618612586",... "73215791984148488291644706095752706957220917567116",... "72291098169091528017350671274858322287183520935396",... "57251210835791513698820914442100675103346711031412",... "67111369908658516398315019701651511685171437657618",... "35155650884909989859982387345528331635507647918535",... "89322618548963213293308985706420467525907091548141",... "65498594616371802709819943099244889575712828905923",... "23326097299712084433573265489382391193259746366730",... "58360414281388303203824903758985243744170291327656",... "18093773444030707469211201913020330380197621101100",... "44929321516084244485963766983895228684783123552658",... "21314495768572624334418930396864262434107732269780",... "28073189154411010446823252716201052652272111660396",... "66557309254711055785376346682065310989652691862056",... "47693125705863566201855810072936065987648611791045",... "33488503461136576867532494416680396265797877185560",... "84552965412665408530614344431858676975145661406800",... "70023787765913440171274947042056223053899456131407",... "11270004078547332699390814546646458807972708266830",... "63432858785698305235808933065757406795457163775254",... "20211495576158140025012622859413021647155097925923",... "09907965473761255176567513575178296664547791745011",... "29961489030463994713296210734043751895735961458901",... "93897131117904297828564750320319869151402870808599",... "04801094121472213179476477726224142548545403321571",... "85306142288137585043063321751829798662237172159160",... "77166925474873898665494945011465406284336639379003",... "97692656721463853067360965712091807638327166416274",... "88880078692560290228472104031721186082041900042296",... "61711963779213375751149595015660496318629472654736",... "42523081770367515906735023507283540567040386743513",... "62222477158915049530984448933309634087807693259939",... "78054193414473774418426312986080998886874132604721"]; a = a(1:1400); figure(1); hold on; N = length(a); fontsize_all = linspace(20,2,N); x = zeros(N,1); y = x; rotate = x; radius = 5000; theta = pi/2; for ii = 1:N; fontsize = fontsize_all(ii); rotate(ii) = -90+180*theta/pi; x(ii) = radius*cos(theta); y(ii) = radius*sin(theta); no = (2*pi*radius)/fontsize; radius = radius - 350*(fontsize/no) - 0.3; theta = theta - 15*(2*pi/no); end h = text(x(:),y(:),a(:),"fontname","Arial","Margin",0.001,... "Interpreter","none","HorizontalAlignment","center"); set(h,{"fontsize"},num2cell(fontsize_all)",{"rotation"},num2cell(rotate) );

set(gcf,"position",[50,50,600,600],"color","w"); axis equal; axis(5000*[-1,1,-1,1]); axis off;

實際使用了小數點後近1400位數據

可惜的是 Matlab 渲染效果還是不好, 保存為矢量圖後和 figure 中顯示不一樣, 因此只能截圖了, 清晰度上還有差距.

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在我的電腦上存為矢量圖或者 PDF 時字型大小小於 8 時存儲字型大小會重新設置為8. 我也不知道這是matlab的問題還是我自己系統的問題. @Falccm 提醒說可以用 print, 也是提高點陣圖清晰度一個辦法. 但目前我還沒找到小字型大小前提下出矢量圖的辦法. (已經解決)

借花獻佛一下：

graphics - How to make the digits of Pi go around in a spiral like this?

Answer of Martin Büttner :

numbers = Translate[#, {-4.5, -10}] /@ First[First[ ImportString[ExportString[ Style[#, FontSize -&> 24, FontFamily -&> "Arial"], "PDF"], "PDF", "TextMode" -&> "Outlines"] ]] /@ {"."}~Join~CharacterRange["0", "9"];

With[{fontsize = 0.0655, digits = 10000}, Graphics[ MapIndexed[ With[{angle = (-(#2[[1]] - 2) + Switch[#2[[1]], 1, -0.1, 2, 0, _, 0.6]) fontsize}, With[{scale = (1 - 1.5 fontsize)^(-angle/(2 Pi))}, GeometricTransformation[ numbers[[# + 2]], RightComposition[ ScalingTransform[{1, 1} 0.1 fontsize*scale], TranslationTransform[{0, scale}], RotationTransform[Pi/4 + angle] ] ] ] ] , Insert[First@RealDigits[Pi, 10, digits], -1, 2] ], PlotRange -&> {{-1.1, 1.1}, {-1.1, 1.1}} ] ]

Answer of Dr. belisarius

ClearAll[height, nbr, width, nextt, w, angles, list, f, digits]; f = 50; digits = 3000; s = -5/4 Pi; nbrSpacing = 12/10; list = First@RealDigits[Pi, 10, digits];


w[nbr_] := w[nbr] = Cases[First[First[ImportString[ExportString[

       Style[ToString@nbr, FontFamily -&> "Courier", FontSize -&> 10], "PDF"],

       "TextMode" -&> "Outlines"]]],

            FilledCurve[a__] :&> {EdgeForm[Black], FilledCurve[a]}, Infinity]
parmsFont = {Min@#, Max@#}  /@ Transpose[w[1][[1, 2, 2, 1]]];

{aspectRatio, center, origHeight} = {Divide @@ (Subtract @@@ #), Mean[#[[1]]],

                                    -Subtract @@ (#[[2]])} @parmsFont;
height[t_] := E^(t/f) - E^((t - 2 Pi)/f) // N
nbr[n_, t_] := {GeometricTransformation[w[n],

   Composition[TranslationTransform[E^(t/f) {Cos[t], Sin[t]}],

               ScalingTransform[height[t]/origHeight {1, 1}],

               RotationTransform[t - Pi/2]]]}
width[t_] := aspectRatio height[t]

nextt[t_] := nextt[t] = (t - nbrSpacing  width[t] E^(s/f)/E^(t/f))

angles = NestList[nextt, s, digits - 1] // N;

Graphics@MapThread[nbr, {list, angles}]

f = 80 時

f = 25 時

還有其他一些答案，不過都沒有這兩個效果好！

居然被舉報了，現在才知道討論mma和題主居然是「不宜公開討論的政治內容」，就問你們怕不怕？我反正是怕了

以下是修改的答案，懇請大人物手下留情啊：

你們mma有個好，MATLAB問題來得比誰都快，就不懂一個道理，那什麼大財才是Best！

而且提問用的圖的風格怎麼好像graphics - How to make the digits of ?€ go around in a spiral like this?最佳答案改了改參數生成的嘛，一定是我眼花了，一看還是匿名提問，嗯懂了啊，肯定是我眼花了啊

Something along the line..

varPi = vpa(pi,360); piStr = char(varPi); initialR = 10; ax = axes; ax.XLim = [-10,10]; ax.YLim = [-10,10]; for i = 1:numel(piStr) theta = deg2rad(mod(i,360))*10; rho = initialR - log(i)*1.1; [x,y] = pol2cart(theta,rho); hold on; text(x,y,piStr(i),"rotation",rad2deg(theta)-90,"FontSize",rho*2); end hold off;

較短的mathematica代碼

numbers = ImportString[ExportString[Style[#,20,FontFamily-&>"Arial"],"PDF"] ][[1,1,2,1,1]] /@Characters@".0123456789";

Graphics@MapIndexed[(s=0.07; t=(2-Tr@#2)s; MapAt[Map[(1-1.5s)^(-t/(2π))(0.1s RotationMatrix@t.#+{-Sin@t,Cos@t}),#,{2}] , #,{2}]), numbers[[Insert[RealDigits[π,10,1000][[1]],-1,2]+2]]]