{"id":77343,"date":"2026-02-24T13:42:02","date_gmt":"2026-02-24T05:42:02","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/77343.html"},"modified":"2026-02-24T13:42:02","modified_gmt":"2026-02-24T05:42:02","slug":"flutter-for-harmony-%e8%b7%a8%e5%b9%b3%e5%8f%b0%e5%bc%80%e5%8f%91%e5%ae%9e%e6%88%98%ef%bc%9a%e8%9e%ba%e6%97%8b%e4%b8%8e%e9%bb%84%e9%87%91%e5%88%86%e5%89%b2-%e8%87%aa%e7%84%b6%e7%95%8c","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/77343.html","title":{"rendered":"Flutter for Harmony \u8de8\u5e73\u53f0\u5f00\u53d1\u5b9e\u6218\uff1a\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272\u2014\u2014\u81ea\u7136\u754c\u7684\u97f5\u5f8b\u5bc6\u7801"},"content":{"rendered":"

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u6b22\u8fce\u52a0\u5165\u5f00\u6e90\u9e3f\u8499\u8de8\u5e73\u53f0\u793e\u533a：https:\/\/openharmonycrossplatform.csdn.net<\/p>\n

\n

🌀 \u4e00\u3001\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272：\u6570\u5b66\u4e4b\u7f8e<\/h3>\n

📚 1.1 \u9ec4\u91d1\u6bd4\u4f8b\u7684\u53d1\u73b0<\/h4>\n

\u9ec4\u91d1\u6bd4\u4f8b（Golden Ratio），\u53c8\u79f0\u9ec4\u91d1\u5206\u5272，\u662f\u4e00\u4e2a\u65e0\u7406\u6570，\u901a\u5e38\u7528\u5e0c\u814a\u5b57\u6bcd \u03c6（phi）\u8868\u793a，\u5176\u503c\u7ea6\u4e3a 1.618033988749\u2026<\/p>\n

\u6570\u5b66\u5b9a\u4e49：<\/p>\n

\u9ec4\u91d1\u6bd4\u4f8b \u03c6 = (1 + \u221a5) \/ 2 \u2248 1.618<\/p>\n

\u6ee1\u8db3\u65b9\u7a0b：\u03c6\u00b2 = \u03c6 + 1<\/p>\n

\u51e0\u4f55\u610f\u4e49：<\/p>\n

\u5c06\u7ebf\u6bb5\u5206\u4e3a\u4e24\u90e8\u5206，\u4f7f\u5f97\u6574\u4f53\u4e0e\u8f83\u5927\u90e8\u5206\u4e4b\u6bd4
\n\u7b49\u4e8e\u8f83\u5927\u90e8\u5206\u4e0e\u8f83\u5c0f\u90e8\u5206\u4e4b\u6bd4<\/p>\n

A\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500B\u2500\u2500\u2500\u2500\u2500C
\n |<\u2500\u2500\u2500 a \u2500\u2500\u2500\u2500\u2500>|<- b->|<\/p>\n

(a + b) \/ a = a \/ b = \u03c6<\/p>\n

\u5386\u53f2\u6e0a\u6e90：<\/p>\n

\u516c\u5143\u524d300\u5e74：\u6b27\u51e0\u91cc\u5f97\u5728\u300a\u51e0\u4f55\u539f\u672c\u300b\u4e2d\u9996\u6b21\u63cf\u8ff0
\n\u516c\u5143\u524d5\u4e16\u7eaa：\u53e4\u5e0c\u814a\u5efa\u7b51\u5e15\u7279\u519c\u795e\u5e99\u8fd0\u7528\u6b64\u6bd4\u4f8b
\n1509\u5e74：\u5362\u5361\u00b7\u5e15\u4e54\u5229\u8457\u300a\u795e\u5723\u6bd4\u4f8b\u300b
\n19\u4e16\u7eaa：\u5fb7\u56fd\u6570\u5b66\u5bb6\u9a6c\u4e01\u00b7\u6b27\u59c6\u6b63\u5f0f\u547d\u540d"\u9ec4\u91d1\u5206\u5272"<\/p>\n

\n

📐 1.2 \u6590\u6ce2\u90a3\u5951\u6570\u5217\u4e0e\u9ec4\u91d1\u6bd4\u4f8b<\/h4>\n

\u6590\u6ce2\u90a3\u5951\u6570\u5217\u4e0e\u9ec4\u91d1\u6bd4\u4f8b\u6709\u7740\u6df1\u523b\u7684\u6570\u5b66\u8054\u7cfb：<\/p>\n

\u6590\u6ce2\u90a3\u5951\u6570\u5217\u5b9a\u4e49：<\/p>\n

F(n) = F(n-1) + F(n-2)
\nF(0) = 0, F(1) = 1<\/p>\n

\u6570\u5217：0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…<\/p>\n

\u9ec4\u91d1\u6bd4\u4f8b\u6536\u655b：<\/p>\n

\u76f8\u90bb\u4e24\u9879\u4e4b\u6bd4\u8d8b\u8fd1\u4e8e\u9ec4\u91d1\u6bd4\u4f8b：
\n1\/1 = 1
\n2\/1 = 2
\n3\/2 = 1.5
\n5\/3 \u2248 1.667
\n8\/5 = 1.6
\n13\/8 = 1.625
\n21\/13 \u2248 1.615
\n34\/21 \u2248 1.619
\n55\/34 \u2248 1.618 \u2190 \u8d8b\u8fd1 \u03c6<\/p>\n

\u901a\u9879\u516c\u5f0f（\u6bd4\u5185\u516c\u5f0f）：
\nF(n) = (\u03c6\u207f – (-\u03c6)\u207b\u207f) \/ \u221a5<\/p>\n

\u6590\u6ce2\u90a3\u5951\u77e9\u5f62：<\/p>\n

\u7528\u6590\u6ce2\u90a3\u5951\u6570\u5217\u6784\u5efa\u7684\u77e9\u5f62：<\/p>\n

\u250c\u2500\u252c\u2500\u252c\u2500\u2500\u2500\u252c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510
\n\u25021\u25021\u2502 2 \u2502 3 \u2502
\n\u251c\u2500\u2534\u2500\u253c\u2500\u2500\u2500\u2524 \u2502
\n\u2502 \u2502 \u2502 \u2502
\n\u2502 1 \u2502 \u251c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2524
\n\u2502 \u2502 \u2502 5 \u2502
\n\u2514\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2534\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518<\/p>\n

\u6bcf\u4e2a\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u90fd\u662f\u6590\u6ce2\u90a3\u5951\u6570<\/p>\n

\n

🔬 1.3 \u87ba\u65cb\u66f2\u7ebf\u5bb6\u65cf<\/h4>\n

\u87ba\u65cb\u662f\u81ea\u7136\u754c\u4e2d\u6700\u4f18\u7f8e\u7684\u66f2\u7ebf\u5f62\u6001\u4e4b\u4e00：<\/p>\n\n\u87ba\u65cb\u7c7b\u578b\u6781\u5750\u6807\u65b9\u7a0b\u7279\u70b9<\/tr>\n\n\n\n\n\n\n
🌀 \u963f\u57fa\u7c73\u5fb7\u87ba\u65cb<\/td>\nr = a + b\u03b8<\/td>\n\u7b49\u8ddd\u87ba\u65cb，\u76f8\u90bb\u5708\u95f4\u8ddd\u76f8\u7b49<\/td>\n<\/tr>\n
🌻 \u9ec4\u91d1\u87ba\u65cb<\/td>\nr = a\u00b7e^(b\u03b8)，b = ln(\u03c6)\/(\u03c0\/2)<\/td>\n\u589e\u957f\u6bd4\u4f8b\u7b26\u5408\u9ec4\u91d1\u5206\u5272<\/td>\n<\/tr>\n
📡 \u53cc\u66f2\u87ba\u65cb<\/td>\nr = a\/\u03b8<\/td>\n\u5411\u4e2d\u5fc3\u65e0\u9650\u903c\u8fd1<\/td>\n<\/tr>\n
\u269b\ufe0f \u8d39\u9a6c\u87ba\u65cb<\/td>\nr\u00b2 = a\u00b2\u03b8<\/td>\n\u7b49\u9762\u79ef\u87ba\u65cb<\/td>\n<\/tr>\n
🔭 \u5bf9\u6570\u87ba\u65cb<\/td>\nr = a\u00b7e^(b\u03b8)<\/td>\n\u81ea\u7136\u754c\u6700\u5e38\u89c1\u7684\u87ba\u65cb<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u87ba\u65cb\u5bf9\u6bd4\u793a\u610f：<\/p>\n

\u963f\u57fa\u7c73\u5fb7\u87ba\u65cb： \u9ec4\u91d1\u87ba\u65cb： \u8d39\u9a6c\u87ba\u65cb：
\n \u256d\u2500\u2500\u2500\u256e \u256d\u2500\u2500\u2500\u2500\u256e \u256d\u2500\u2500\u2500\u2500\u256e
\n \u256d\u256f \u2570\u256e \u256d\u256f \u2570\u256e \u256d\u256f \u2b24 \u2570\u256e
\n \u256d\u256f \u2570\u256e \u256d\u256f \u2b24 \u2570\u256e \u256d\u256f \u2570\u256e
\n \u256d\u256f \u2570\u256e \u256d\u256f \u2570\u256e \u256d\u256f \u2b24 \u2570\u256e
\n\u256d\u256f \u2570\u256e \u256d\u256f \u2570\u256e \u256d\u256f \u2570\u256e
\n\u2570\u256e \u256d\u256f \u2570\u256e \u256d\u256f \u2570\u256e \u2b24 \u256d\u256f
\n \u2570\u256e \u256d\u256f \u2570\u256e \u256d\u256f \u2570\u256e \u256d\u256f
\n \u2570\u256e \u256d\u256f \u2570\u256e \u2b24 \u256d\u256f \u2570\u256e \u2b24 \u256d\u256f
\n \u2570\u256e \u256d\u256f \u2570\u256e \u256d\u256f \u2570\u2500\u2500\u2500\u2500\u256f
\n \u2570\u2500\u2500\u2500\u256f \u2570\u2500\u2500\u2500\u2500\u256f<\/p>\n

\u7b49\u95f4\u8ddd\u6269\u5c55 \u6309\u9ec4\u91d1\u6bd4\u4f8b\u6269\u5c55 \u7b49\u9762\u79ef\u6269\u5c55<\/p>\n

\n

🎯 1.4 \u9ec4\u91d1\u89d2\u5ea6\u4e0e\u81ea\u7136\u6392\u5217<\/h4>\n

\u9ec4\u91d1\u89d2\u5ea6：<\/p>\n

\u9ec4\u91d1\u89d2\u5ea6 = 360\u00b0 \u00d7 (1 – 1\/\u03c6) \u2248 137.507764\u00b0<\/p>\n

\u8fd9\u662f\u5411\u65e5\u8475\u79cd\u5b50\u3001\u677e\u679c\u9cde\u7247\u7684\u6392\u5217\u89d2\u5ea6
\n\u786e\u4fdd\u6bcf\u4e2a\u65b0\u5143\u7d20\u90fd\u4e0d\u4f1a\u4e0e\u4e4b\u524d\u7684\u5b8c\u5168\u91cd\u53e0
\n\u6700\u5927\u5316\u5229\u7528\u7a7a\u95f4<\/p>\n

\u5411\u65e5\u8475\u79cd\u5b50\u6392\u5217：<\/p>\n

\u00b7 \u00b7 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u2b24 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7 \u00b7
\n \u00b7 \u00b7 \u00b7 \u00b7 \u00b7<\/p>\n

\u6bcf\u9897\u79cd\u5b50\u95f4\u9694 137.5\u00b0
\n\u5f62\u6210\u8d39\u9a6c\u87ba\u65cb\u56fe\u6848<\/p>\n

\u81ea\u7136\u754c\u4e2d\u7684\u6590\u6ce2\u90a3\u5951\u6570：<\/p>\n\n\u751f\u7269\u6590\u6ce2\u90a3\u5951\u6570\u73b0\u8c61<\/tr>\n\n\n\n\n\n\n
🌻 \u5411\u65e5\u8475<\/td>\n34, 55, 89<\/td>\n\u79cd\u5b50\u87ba\u65cb\u6570<\/td>\n<\/tr>\n
🌲 \u677e\u679c<\/td>\n8, 13<\/td>\n\u9cde\u7247\u87ba\u65cb<\/td>\n<\/tr>\n
🌸 \u82b1\u74e3<\/td>\n3, 5, 8, 13<\/td>\n\u82b1\u74e3\u6570\u91cf<\/td>\n<\/tr>\n
🐚 \u9e66\u9e49\u87ba<\/td>\n\u8fde\u7eed<\/td>\n\u58f3\u5ba4\u751f\u957f<\/td>\n<\/tr>\n
🌀 \u94f6\u6cb3\u7cfb<\/td>\n\u8fd1\u4f3c<\/td>\n\u65cb\u81c2\u7ed3\u6784<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n

🔧 \u4e8c\u3001\u87ba\u65cb\u66f2\u7ebf\u7684 Dart \u5b9e\u73b0<\/h3>\n

🧮 2.1 \u9ec4\u91d1\u6bd4\u4f8b\u5e38\u91cf\u4e0e\u5de5\u5177\u7c7b<\/h4>\n

import<\/span> 'dart:math'<\/span><\/span>;<\/span>
\nimport<\/span> 'dart:typed_data'<\/span><\/span>;<\/span><\/p>\n

\/\/\/ \u9ec4\u91d1\u6bd4\u4f8b\u5e38\u91cf<\/span>
\nconst<\/span> double phi =<\/span> (<\/span>1<\/span> +<\/span> sqrt5)<\/span> \/<\/span> 2<\/span>;<\/span>
\nconst<\/span> double sqrt5 =<\/span> 2.23606797749979<\/span>;<\/span>
\nconst<\/span> double goldenAngle =<\/span> 2<\/span> *<\/span> pi *<\/span> (<\/span>1<\/span> –<\/span> 1<\/span> \/<\/span> phi)<\/span>;<\/span>
\nconst<\/span> double goldenAngleDeg =<\/span> 360<\/span> *<\/span> (<\/span>1<\/span> –<\/span> 1<\/span> \/<\/span> phi)<\/span>;<\/span><\/p>\n

\/\/\/ \u9ec4\u91d1\u6bd4\u4f8b\u8ba1\u7b97\u5668<\/span>
\nclass<\/span> GoldenRatio<\/span> {<\/span>
\n \/\/\/ \u9ec4\u91d1\u6bd4\u4f8b\u503c<\/span>
\n static<\/span> const<\/span> double value =<\/span> phi;<\/span><\/p>\n

\/\/\/ \u9ec4\u91d1\u6bd4\u4f8b\u5171\u8f6d<\/span>
\n static<\/span> const<\/span> double conjugate =<\/span> 1<\/span> \/<\/span> phi;<\/span><\/p>\n

\/\/\/ \u8ba1\u7b97\u9ec4\u91d1\u5206\u5272\u70b9<\/span>
\n static<\/span> double goldenSection<\/span>(<\/span>double total)<\/span> {<\/span>
\n return<\/span> total *<\/span> conjugate;<\/span>
\n }<\/span><\/p>\n

\/\/\/ \u751f\u6210\u6590\u6ce2\u90a3\u5951\u6570\u5217<\/span>
\n static<\/span> List<\/span><<\/span>int><\/span><\/span> fibonacci<\/span>(<\/span>int n)<\/span> {<\/span>
\n if<\/span> (<\/span>n <=<\/span> 0<\/span>)<\/span> return<\/span> [<\/span>]<\/span>;<\/span>
\n if<\/span> (<\/span>n ==<\/span> 1<\/span>)<\/span> return<\/span> [<\/span>1<\/span>]<\/span>;<\/span>
\n if<\/span> (<\/span>n ==<\/span> 2<\/span>)<\/span> return<\/span> [<\/span>1<\/span>,<\/span> 1<\/span>]<\/span>;<\/span><\/p>\n

final<\/span> result =<\/span> [<\/span>1<\/span>,<\/span> 1<\/span>]<\/span>;<\/span>
\n for<\/span> (<\/span>int i =<\/span> 2<\/span>;<\/span> i <<\/span> n;<\/span> i++<\/span>)<\/span> {<\/span>
\n result.<\/span>add<\/span>(<\/span>result[<\/span>i –<\/span> 1<\/span>]<\/span> +<\/span> result[<\/span>i –<\/span> 2<\/span>]<\/span>)<\/span>;<\/span>
\n }<\/span>
\n return<\/span> result;<\/span>
\n }<\/span><\/p>\n

\/\/\/ \u8ba1\u7b97\u7b2c n \u4e2a\u6590\u6ce2\u90a3\u5951\u6570（\u6bd4\u5185\u516c\u5f0f）<\/span>
\n static<\/span> double fibonacciAt<\/span>(<\/span>int n)<\/span> {<\/span>
\n return<\/span> (<\/span>pow<\/span>(<\/span>phi,<\/span> n)<\/span> –<\/span> pow<\/span>(<\/span>–<\/span>phi,<\/span> –<\/span>n)<\/span>)<\/span> \/<\/span> sqrt5;<\/span>
\n }<\/span><\/p>\n

\/\/\/ \u5411\u65e5\u8475\u79cd\u5b50\u6392\u5217<\/span>
\n static<\/span> List<\/span><<\/span>Offset<\/span>><\/span><\/span> sunflowerSeeds<\/span>(<\/span>{<\/span>
\n required Offset<\/span> center,<\/span>
\n required int count,<\/span>
\n required double maxRadius,<\/span>
\n }<\/span>)<\/span> {<\/span>
\n final<\/span> seeds =<\/span> <<\/span>Offset<\/span>><\/span><\/span>[<\/span>]<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> count;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> theta =<\/span> i *<\/span> goldenAngle;<\/span>
\n final<\/span> r =<\/span> maxRadius *<\/span> sqrt<\/span>(<\/span>i \/<\/span> count)<\/span>;<\/span><\/p>\n

seeds.<\/span>add<\/span>(<\/span>Offset<\/span>(<\/span>
\n center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta)<\/span>,<\/span>
\n center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta)<\/span>,<\/span>
\n )<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> seeds;<\/span>
\n }<\/span><\/p>\n

\/\/\/ \u751f\u6210\u9ec4\u91d1\u77e9\u5f62\u5e8f\u5217<\/span>
\n static<\/span> List<\/span><<\/span>Rect<\/span>><\/span><\/span> goldenRectangles<\/span>(<\/span>{<\/span>
\n required Size<\/span> initialSize,<\/span>
\n required int count,<\/span>
\n }<\/span>)<\/span> {<\/span>
\n final<\/span> rects =<\/span> <<\/span>Rect<\/span>><\/span><\/span>[<\/span>]<\/span>;<\/span>
\n double width =<\/span> initialSize.<\/span>width;<\/span>
\n double height =<\/span> initialSize.<\/span>height;<\/span>
\n double x =<\/span> 0<\/span>,<\/span> y =<\/span> 0<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> count;<\/span> i++<\/span>)<\/span> {<\/span>
\n rects.<\/span>add<\/span>(<\/span>Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>x,<\/span> y,<\/span> width,<\/span> height)<\/span>)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>width ><\/span> height)<\/span> {<\/span>
\n x +=<\/span> height;<\/span>
\n width -=<\/span> height;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n y +=<\/span> width;<\/span>
\n height -=<\/span> width;<\/span>
\n }<\/span><\/p>\n

if<\/span> (<\/span>width <<\/span> 1<\/span> ||<\/span> height <<\/span> 1<\/span>)<\/span> break<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> rects;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\n

\u26a1 2.2 \u87ba\u65cb\u66f2\u7ebf\u751f\u6210\u5668<\/h4>\n

\/\/\/ \u87ba\u65cb\u70b9<\/span>
\nclass<\/span> SpiralPoint<\/span> {<\/span>
\n final<\/span> double r;<\/span>
\n final<\/span> double theta;<\/span>
\n final<\/span> int index;<\/span><\/p>\n

const<\/span> SpiralPoint<\/span>(<\/span>this<\/span>.<\/span>r,<\/span> this<\/span>.<\/span>theta,<\/span> this<\/span>.<\/span>index)<\/span>;<\/span><\/p>\n

\/\/\/ \u8f6c\u6362\u4e3a\u7b1b\u5361\u5c14\u5750\u6807<\/span>
\n Offset<\/span> toOffset<\/span>(<\/span>Offset<\/span> center,<\/span> {<\/span>double scale =<\/span> 1.0<\/span>}<\/span>)<\/span> {<\/span>
\n return<\/span> Offset<\/span>(<\/span>
\n center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta)<\/span> *<\/span> scale,<\/span>
\n center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta)<\/span> *<\/span> scale,<\/span>
\n )<\/span>;<\/span>
\n }<\/span><\/p>\n

\/\/\/ \u65cb\u8f6c<\/span>
\n SpiralPoint<\/span> rotate<\/span>(<\/span>double angle)<\/span> =<\/span>><\/span> SpiralPoint<\/span>(<\/span>r,<\/span> theta +<\/span> angle,<\/span> index)<\/span>;<\/span><\/p>\n

\/\/\/ \u7f29\u653e<\/span>
\n SpiralPoint<\/span> scale<\/span>(<\/span>double factor)<\/span> =<\/span>><\/span> SpiralPoint<\/span>(<\/span>r *<\/span> factor,<\/span> theta,<\/span> index)<\/span>;<\/span>
\n}<\/span><\/p>\n

\/\/\/ \u87ba\u65cb\u751f\u6210\u5668\u57fa\u7c7b<\/span>
\nabstract<\/span> class<\/span> SpiralGenerator<\/span> {<\/span>
\n final<\/span> double a;<\/span>
\n final<\/span> double b;<\/span><\/p>\n

const<\/span> SpiralGenerator<\/span>(<\/span>{<\/span>this<\/span>.<\/span>a =<\/span> 1.0<\/span>,<\/span> this<\/span>.<\/span>b =<\/span> 1.0<\/span>}<\/span>)<\/span>;<\/span><\/p>\n

\/\/\/ \u8ba1\u7b97\u7ed9\u5b9a\u89d2\u5ea6\u7684\u534a\u5f84<\/span>
\n double radius<\/span>(<\/span>double theta)<\/span>;<\/span><\/p>\n

\/\/\/ \u751f\u6210\u87ba\u65cb\u70b9\u5e8f\u5217<\/span>
\n List<\/span><<\/span>SpiralPoint<\/span>><\/span><\/span> generate<\/span>(<\/span>{<\/span>
\n required double startAngle,<\/span>
\n required double endAngle,<\/span>
\n required double angleStep,<\/span>
\n }<\/span>)<\/span> {<\/span>
\n final<\/span> points =<\/span> <<\/span>SpiralPoint<\/span>><\/span><\/span>[<\/span>]<\/span>;<\/span>
\n int index =<\/span> 0<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>double theta =<\/span> startAngle;<\/span> theta <=<\/span> endAngle;<\/span> theta +=<\/span> angleStep)<\/span> {<\/span>
\n final<\/span> r =<\/span> radius<\/span>(<\/span>theta)<\/span>;<\/span>
\n points.<\/span>add<\/span>(<\/span>SpiralPoint<\/span>(<\/span>r,<\/span> theta,<\/span> index++<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> points;<\/span>
\n }<\/span><\/p>\n

\/\/\/ \u751f\u6210\u8def\u5f84<\/span>
\n Path<\/span> toPath<\/span>(<\/span>List<\/span><<\/span>SpiralPoint<\/span>><\/span><\/span> points,<\/span> Offset<\/span> center,<\/span> {<\/span>double scale =<\/span> 1.0<\/span>}<\/span>)<\/span> {<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> points.<\/span>length;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> offset =<\/span> points[<\/span>i]<\/span>.<\/span>toOffset<\/span>(<\/span>center,<\/span> scale:<\/span> scale)<\/span>;<\/span>
\n if<\/span> (<\/span>i ==<\/span> 0<\/span>)<\/span> {<\/span>
\n path.<\/span>moveTo<\/span>(<\/span>offset.<\/span>dx,<\/span> offset.<\/span>dy)<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n path.<\/span>lineTo<\/span>(<\/span>offset.<\/span>dx,<\/span> offset.<\/span>dy)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

return<\/span> path;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\/\/\/ \u963f\u57fa\u7c73\u5fb7\u87ba\u65cb<\/span>
\nclass<\/span> ArchimedeanSpiral<\/span> extends<\/span> SpiralGenerator<\/span> {<\/span>
\n const<\/span> ArchimedeanSpiral<\/span>(<\/span>{<\/span>super<\/span>.<\/span>a,<\/span> super<\/span>.<\/span>b}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n double radius<\/span>(<\/span>double theta)<\/span> =<\/span>><\/span> a +<\/span> b *<\/span> theta;<\/span>
\n}<\/span><\/p>\n

\/\/\/ \u9ec4\u91d1\u87ba\u65cb<\/span>
\nclass<\/span> GoldenSpiral<\/span> extends<\/span> SpiralGenerator<\/span> {<\/span>
\n final<\/span> double growthFactor;<\/span><\/p>\n

const<\/span> GoldenSpiral<\/span>(<\/span>{<\/span>
\n super<\/span>.<\/span>a =<\/span> 1.0<\/span>,<\/span>
\n this<\/span>.<\/span>growthFactor =<\/span> 0.306349<\/span>,<\/span>
\n }<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n double radius<\/span>(<\/span>double theta)<\/span> =<\/span>><\/span> a *<\/span> exp<\/span>(<\/span>growthFactor *<\/span> theta)<\/span>;<\/span>
\n}<\/span><\/p>\n

\/\/\/ \u5bf9\u6570\u87ba\u65cb<\/span>
\nclass<\/span> LogarithmicSpiral<\/span> extends<\/span> SpiralGenerator<\/span> {<\/span>
\n final<\/span> double k;<\/span><\/p>\n

const<\/span> LogarithmicSpiral<\/span>(<\/span>{<\/span>
\n super<\/span>.<\/span>a =<\/span> 1.0<\/span>,<\/span>
\n this<\/span>.<\/span>k =<\/span> 0.1<\/span>,<\/span>
\n }<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n double radius<\/span>(<\/span>double theta)<\/span> =<\/span>><\/span> a *<\/span> exp<\/span>(<\/span>k *<\/span> theta)<\/span>;<\/span>
\n}<\/span><\/p>\n

\/\/\/ \u8d39\u9a6c\u87ba\u65cb<\/span>
\nclass<\/span> FermatSpiral<\/span> extends<\/span> SpiralGenerator<\/span> {<\/span>
\n const<\/span> FermatSpiral<\/span>(<\/span>{<\/span>super<\/span>.<\/span>a =<\/span> 1.0<\/span>}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n double radius<\/span>(<\/span>double theta)<\/span> =<\/span>><\/span> a *<\/span> sqrt<\/span>(<\/span>theta.<\/span>abs<\/span>(<\/span>)<\/span>)<\/span>;<\/span><\/p>\n

\/\/\/ \u751f\u6210\u53cc\u5206\u652f\u8d39\u9a6c\u87ba\u65cb<\/span>
\n List<\/span><<\/span>SpiralPoint<\/span>><\/span><\/span> generateDouble<\/span>(<\/span>{<\/span>
\n required double maxTheta,<\/span>
\n required double angleStep,<\/span>
\n }<\/span>)<\/span> {<\/span>
\n final<\/span> points =<\/span> <<\/span>SpiralPoint<\/span>><\/span><\/span>[<\/span>]<\/span>;<\/span>
\n int index =<\/span> 0<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>double theta =<\/span> 0<\/span>;<\/span> theta <=<\/span> maxTheta;<\/span> theta +=<\/span> angleStep)<\/span> {<\/span>
\n points.<\/span>add<\/span>(<\/span>SpiralPoint<\/span>(<\/span>radius<\/span>(<\/span>theta)<\/span>,<\/span> theta,<\/span> index++<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

for<\/span> (<\/span>double theta =<\/span> angleStep;<\/span> theta <=<\/span> maxTheta;<\/span> theta +=<\/span> angleStep)<\/span> {<\/span>
\n points.<\/span>add<\/span>(<\/span>SpiralPoint<\/span>(<\/span>radius<\/span>(<\/span>theta)<\/span>,<\/span> theta +<\/span> pi,<\/span> index++<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> points;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\/\/\/ \u53cc\u66f2\u87ba\u65cb<\/span>
\nclass<\/span> HyperbolicSpiral<\/span> extends<\/span> SpiralGenerator<\/span> {<\/span>
\n const<\/span> HyperbolicSpiral<\/span>(<\/span>{<\/span>super<\/span>.<\/span>a =<\/span> 1.0<\/span>}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n double radius<\/span>(<\/span>double theta)<\/span> =<\/span>><\/span> theta ><\/span> 0.01<\/span> ?<\/span> a \/<\/span> theta :<\/span> a \/<\/span> 0.01<\/span>;<\/span>
\n}<\/span><\/p>\n

\n

🎨 2.3 \u9ec4\u91d1\u77e9\u5f62\u4e0e\u87ba\u65cb\u6784\u9020<\/h4>\n

import<\/span> 'package:flutter\/material.dart'<\/span><\/span>;<\/span><\/p>\n

\/\/\/ \u9ec4\u91d1\u77e9\u5f62<\/span>
\nclass<\/span> GoldenRectangle<\/span> {<\/span>
\n final<\/span> double width;<\/span>
\n final<\/span> double height;<\/span>
\n final<\/span> Offset<\/span> origin;<\/span><\/p>\n

GoldenRectangle<\/span>(<\/span>{<\/span>
\n required this<\/span>.<\/span>width,<\/span>
\n this<\/span>.<\/span>height =<\/span> 0<\/span>,<\/span>
\n this<\/span>.<\/span>origin =<\/span> Offset<\/span>.<\/span>zero,<\/span>
\n }<\/span>)<\/span> :<\/span> height =<\/span> height ==<\/span> 0<\/span> ?<\/span> width \/<\/span> phi :<\/span> height;<\/span><\/p>\n

\/\/\/ \u662f\u5426\u4e3a\u9ec4\u91d1\u77e9\u5f62<\/span>
\n bool get<\/span> isGolden =<\/span>><\/span> (<\/span>width \/<\/span> height –<\/span> phi)<\/span>.<\/span>abs<\/span>(<\/span>)<\/span> <<\/span> 0.001<\/span>;<\/span><\/p>\n

\/\/\/ \u9ec4\u91d1\u6bd4\u4f8b<\/span>
\n double get<\/span> ratio =<\/span>><\/span> width \/<\/span> height;<\/span><\/p>\n

\/\/\/ \u5206\u5272\u51fa\u6b63\u65b9\u5f62<\/span>
\n Rect<\/span> get<\/span> square =<\/span>><\/span> Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>origin.<\/span>dx,<\/span> origin.<\/span>dy,<\/span> height,<\/span> height)<\/span>;<\/span><\/p>\n

\/\/\/ \u5206\u5272\u540e\u5269\u4f59\u7684\u77e9\u5f62<\/span>
\n GoldenRectangle<\/span> get<\/span> remainder =<\/span>><\/span> GoldenRectangle<\/span>(<\/span>
\n width:<\/span> width –<\/span> height,<\/span>
\n height:<\/span> height,<\/span>
\n origin:<\/span> Offset<\/span>(<\/span>origin.<\/span>dx +<\/span> height,<\/span> origin.<\/span>dy)<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

\/\/\/ \u751f\u6210\u9012\u5f52\u5206\u5272\u5e8f\u5217<\/span>
\n List<\/span><<\/span>GoldenRectangle<\/span>><\/span><\/span> subdivide<\/span>(<\/span>int depth)<\/span> {<\/span>
\n final<\/span> result =<\/span> <<\/span>GoldenRectangle<\/span>><\/span><\/span>[<\/span>this<\/span>]<\/span>;<\/span>
\n var<\/span> current =<\/span> this<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> depth;<\/span> i++<\/span>)<\/span> {<\/span>
\n if<\/span> (<\/span>current.<\/span>width <<\/span> 1<\/span> ||<\/span> current.<\/span>height <<\/span> 1<\/span>)<\/span> break<\/span>;<\/span>
\n current =<\/span> current.<\/span>remainder;<\/span>
\n result.<\/span>add<\/span>(<\/span>current)<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> result;<\/span>
\n }<\/span><\/p>\n

\/\/\/ \u751f\u6210\u9ec4\u91d1\u87ba\u65cb\u8def\u5f84<\/span>
\n Path<\/span> generateSpiralPath<\/span>(<\/span>int depth)<\/span> {<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span>
\n var<\/span> current =<\/span> this<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> depth;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> square =<\/span> current.<\/span>square;<\/span><\/p>\n

\/\/ \u6839\u636e\u65b9\u5411\u7ed8\u5236\u56db\u5206\u4e4b\u4e00\u5706\u5f27<\/span>
\n final<\/span> startAngle =<\/span> i *<\/span> pi \/<\/span> 2<\/span>;<\/span>
\n path.<\/span>arcTo<\/span>(<\/span>
\n square,<\/span>
\n startAngle,<\/span>
\n –<\/span>pi \/<\/span> 2<\/span>,<\/span>
\n false<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>current.<\/span>width <<\/span> 1<\/span> ||<\/span> current.<\/span>height <<\/span> 1<\/span>)<\/span> break<\/span>;<\/span>
\n current =<\/span> current.<\/span>remainder;<\/span>
\n }<\/span><\/p>\n

return<\/span> path;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\/\/\/ \u87ba\u65cb\u53ef\u89c6\u5316\u63a7\u5236\u5668<\/span>
\nclass<\/span> SpiralVisualizationController<\/span> extends<\/span> ChangeNotifier<\/span> {<\/span>
\n double _time =<\/span> 0<\/span>;<\/span>
\n double _rotation =<\/span> 0<\/span>;<\/span>
\n double _scale =<\/span> 1.0<\/span>;<\/span>
\n double _growthRate =<\/span> 0.306349<\/span>;<\/span>
\n int _turns =<\/span> 5<\/span>;<\/span>
\n int _seedCount =<\/span> 200<\/span>;<\/span>
\n double _animationSpeed =<\/span> 1.0<\/span>;<\/span><\/p>\n

SpiralType<\/span> _type =<\/span> SpiralType<\/span>.<\/span>golden;<\/span>
\n Color<\/span> _primaryColor =<\/span> Colors<\/span>.<\/span>amber;<\/span>
\n Color<\/span> _secondaryColor =<\/span> Colors<\/span>.<\/span>purple;<\/span>
\n bool _showGrid =<\/span> true<\/span>;<\/span>
\n bool _showSeeds =<\/span> false<\/span>;<\/span><\/p>\n

double get<\/span> time =<\/span>><\/span> _time;<\/span>
\n double get<\/span> rotation =<\/span>><\/span> _rotation;<\/span>
\n double get<\/span> scale =<\/span>><\/span> _scale;<\/span>
\n double get<\/span> growthRate =<\/span>><\/span> _growthRate;<\/span>
\n int get<\/span> turns =<\/span>><\/span> _turns;<\/span>
\n int get<\/span> seedCount =<\/span>><\/span> _seedCount;<\/span>
\n double get<\/span> animationSpeed =<\/span>><\/span> _animationSpeed;<\/span>
\n SpiralType<\/span> get<\/span> type =<\/span>><\/span> _type;<\/span>
\n Color<\/span> get<\/span> primaryColor =<\/span>><\/span> _primaryColor;<\/span>
\n Color<\/span> get<\/span> secondaryColor =<\/span>><\/span> _secondaryColor;<\/span>
\n bool get<\/span> showGrid =<\/span>><\/span> _showGrid;<\/span>
\n bool get<\/span> showSeeds =<\/span>><\/span> _showSeeds;<\/span><\/p>\n

void<\/span> update<\/span>(<\/span>double dt)<\/span> {<\/span>
\n _time +=<\/span> dt *<\/span> _animationSpeed;<\/span>
\n _rotation +=<\/span> dt *<\/span> 0.5<\/span> *<\/span> _animationSpeed;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> setSpiralType<\/span>(<\/span>SpiralType<\/span> type)<\/span> {<\/span>
\n _type =<\/span> type;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> setTurns<\/span>(<\/span>int turns)<\/span> {<\/span>
\n _turns =<\/span> turns.<\/span>clamp<\/span>(<\/span>1<\/span>,<\/span> 20<\/span>)<\/span>;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> setSeedCount<\/span>(<\/span>int count)<\/span> {<\/span>
\n _seedCount =<\/span> count.<\/span>clamp<\/span>(<\/span>10<\/span>,<\/span> 500<\/span>)<\/span>;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> setGrowthRate<\/span>(<\/span>double rate)<\/span> {<\/span>
\n _growthRate =<\/span> rate.<\/span>clamp<\/span>(<\/span>0.01<\/span>,<\/span> 1.0<\/span>)<\/span>;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> setAnimationSpeed<\/span>(<\/span>double speed)<\/span> {<\/span>
\n _animationSpeed =<\/span> speed.<\/span>clamp<\/span>(<\/span>0.1<\/span>,<\/span> 3.0<\/span>)<\/span>;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> toggleGrid<\/span>(<\/span>)<\/span> {<\/span>
\n _showGrid =<\/span> !<\/span>_showGrid;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> toggleSeeds<\/span>(<\/span>)<\/span> {<\/span>
\n _showSeeds =<\/span> !<\/span>_showSeeds;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> reset<\/span>(<\/span>)<\/span> {<\/span>
\n _time =<\/span> 0<\/span>;<\/span>
\n _rotation =<\/span> 0<\/span>;<\/span>
\n _scale =<\/span> 1.0<\/span>;<\/span>
\n notifyListeners<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

enum<\/span> SpiralType<\/span> {<\/span>
\n archimedean,<\/span>
\n golden,<\/span>
\n logarithmic,<\/span>
\n fermat,<\/span>
\n hyperbolic,<\/span>
\n}<\/span><\/p>\n

\n

📦 \u4e09\u3001\u5b8c\u6574\u793a\u4f8b\u4ee3\u7801<\/h3>\n

\u4ee5\u4e0b\u662f\u5b8c\u6574\u7684\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272\u53ef\u89c6\u5316\u793a\u4f8b\u4ee3\u7801：<\/p>\n

import<\/span> 'package:flutter\/material.dart'<\/span><\/span>;<\/span>
\nimport<\/span> 'dart:math'<\/span><\/span>;<\/span><\/p>\n

void<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
\n runApp<\/span>(<\/span>const<\/span> SpiralApp<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> SpiralApp<\/span> extends<\/span> StatelessWidget<\/span> {<\/span>
\n const<\/span> SpiralApp<\/span>(<\/span>{<\/span>super<\/span>.<\/span>key}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n Widget<\/span> build<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n return<\/span> MaterialApp<\/span>(<\/span>
\n title:<\/span> '\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272'<\/span><\/span>,<\/span>
\n theme:<\/span> ThemeData<\/span>(<\/span>
\n colorScheme:<\/span> ColorScheme<\/span>.<\/span>fromSeed<\/span>(<\/span>seedColor:<\/span> Colors<\/span>.<\/span>amber,<\/span> brightness:<\/span> Brightness<\/span>.<\/span>dark)<\/span>,<\/span>
\n useMaterial3:<\/span> true<\/span>,<\/span>
\n )<\/span>,<\/span>
\n home:<\/span> const<\/span> SpiralHomePage<\/span>(<\/span>)<\/span>,<\/span>
\n debugShowCheckedModeBanner:<\/span> false<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

class<\/span> SpiralHomePage<\/span> extends<\/span> StatelessWidget<\/span> {<\/span>
\n const<\/span> SpiralHomePage<\/span>(<\/span>{<\/span>super<\/span>.<\/span>key}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n Widget<\/span> build<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n return<\/span> Scaffold<\/span>(<\/span>
\n appBar:<\/span> AppBar<\/span>(<\/span>
\n title:<\/span> const<\/span> Text<\/span>(<\/span>'🌀 \u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272'<\/span><\/span>)<\/span>,<\/span>
\n backgroundColor:<\/span> Theme<\/span>.<\/span>of<\/span>(<\/span>context)<\/span>.<\/span>colorScheme.<\/span>inversePrimary,<\/span>
\n )<\/span>,<\/span>
\n body:<\/span> ListView<\/span>(<\/span>
\n padding:<\/span> const<\/span> EdgeInsets<\/span>.<\/span>all<\/span>(<\/span>16<\/span>)<\/span>,<\/span>
\n children:<\/span> [<\/span>
\n _buildCard<\/span>(<\/span>
\n context,<\/span>
\n title:<\/span> '\u9ec4\u91d1\u87ba\u65cb'<\/span><\/span>,<\/span>
\n description:<\/span> '\u81ea\u7136\u754c\u6700\u4f18\u7f8e\u7684\u66f2\u7ebf'<\/span><\/span>,<\/span>
\n icon:<\/span> Icons<\/span>.<\/span>all_inclusive,<\/span>
\n color:<\/span> Colors<\/span>.<\/span>amber,<\/span>
\n onTap:<\/span> (<\/span>)<\/span> =<\/span>><\/span> Navigator<\/span>.<\/span>push<\/span>(<\/span>
\n context,<\/span>
\n MaterialPageRoute<\/span>(<\/span>builder:<\/span> (<\/span>_)<\/span> =<\/span>><\/span> const<\/span> GoldenSpiralDemo<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n _buildCard<\/span>(<\/span>
\n context,<\/span>
\n title:<\/span> '\u87ba\u65cb\u5bb6\u65cf'<\/span><\/span>,<\/span>
\n description:<\/span> '\u4e94\u79cd\u7ecf\u5178\u87ba\u65cb\u5bf9\u6bd4'<\/span><\/span>,<\/span>
\n icon:<\/span> Icons<\/span>.<\/span>show_chart,<\/span>
\n color:<\/span> Colors<\/span>.<\/span>purple,<\/span>
\n onTap:<\/span> (<\/span>)<\/span> =<\/span>><\/span> Navigator<\/span>.<\/span>push<\/span>(<\/span>
\n context,<\/span>
\n MaterialPageRoute<\/span>(<\/span>builder:<\/span> (<\/span>_)<\/span> =<\/span>><\/span> const<\/span> SpiralFamilyDemo<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n _buildCard<\/span>(<\/span>
\n context,<\/span>
\n title:<\/span> '\u5411\u65e5\u8475\u79cd\u5b50'<\/span><\/span>,<\/span>
\n description:<\/span> '\u9ec4\u91d1\u89d2\u5ea6\u7684\u7a7a\u95f4\u6392\u5217'<\/span><\/span>,<\/span>
\n icon:<\/span> Icons<\/span>.<\/span>local_florist,<\/span>
\n color:<\/span> Colors<\/span>.<\/span>orange,<\/span>
\n onTap:<\/span> (<\/span>)<\/span> =<\/span>><\/span> Navigator<\/span>.<\/span>push<\/span>(<\/span>
\n context,<\/span>
\n MaterialPageRoute<\/span>(<\/span>builder:<\/span> (<\/span>_)<\/span> =<\/span>><\/span> const<\/span> SunflowerDemo<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n _buildCard<\/span>(<\/span>
\n context,<\/span>
\n title:<\/span> '\u9ec4\u91d1\u77e9\u5f62'<\/span><\/span>,<\/span>
\n description:<\/span> '\u9012\u5f52\u5206\u5272\u4e0e\u87ba\u65cb\u6784\u9020'<\/span><\/span>,<\/span>
\n icon:<\/span> Icons<\/span>.<\/span>crop_square,<\/span>
\n color:<\/span> Colors<\/span>.<\/span>teal,<\/span>
\n onTap:<\/span> (<\/span>)<\/span> =<\/span>><\/span> Navigator<\/span>.<\/span>push<\/span>(<\/span>
\n context,<\/span>
\n MaterialPageRoute<\/span>(<\/span>builder:<\/span> (<\/span>_)<\/span> =<\/span>><\/span> const<\/span> GoldenRectangleDemo<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n _buildCard<\/span>(<\/span>
\n context,<\/span>
\n title:<\/span> '\u6590\u6ce2\u90a3\u5951\u52a8\u753b'<\/span><\/span>,<\/span>
\n description:<\/span> '\u6570\u5217\u7684\u53ef\u89c6\u5316\u751f\u957f'<\/span><\/span>,<\/span>
\n icon:<\/span> Icons<\/span>.<\/span>animation,<\/span>
\n color:<\/span> Colors<\/span>.<\/span>indigo,<\/span>
\n onTap:<\/span> (<\/span>)<\/span> =<\/span>><\/span> Navigator<\/span>.<\/span>push<\/span>(<\/span>
\n context,<\/span>
\n MaterialPageRoute<\/span>(<\/span>builder:<\/span> (<\/span>_)<\/span> =<\/span>><\/span> const<\/span> FibonacciDemo<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span><\/p>\n

Widget<\/span> _buildCard<\/span>(<\/span>
\n BuildContext<\/span> context,<\/span> {<\/span>
\n required String<\/span> title,<\/span>
\n required String<\/span> description,<\/span>
\n required IconData<\/span> icon,<\/span>
\n required Color<\/span> color,<\/span>
\n required VoidCallback<\/span> onTap,<\/span>
\n }<\/span>)<\/span> {<\/span>
\n return<\/span> Card<\/span>(<\/span>
\n margin:<\/span> const<\/span> EdgeInsets<\/span>.<\/span>only<\/span>(<\/span>bottom:<\/span> 12<\/span>)<\/span>,<\/span>
\n shape:<\/span> RoundedRectangleBorder<\/span>(<\/span>borderRadius:<\/span> BorderRadius<\/span>.<\/span>circular<\/span>(<\/span>16<\/span>)<\/span>)<\/span>,<\/span>
\n child:<\/span> InkWell<\/span>(<\/span>
\n onTap:<\/span> onTap,<\/span>
\n borderRadius:<\/span> BorderRadius<\/span>.<\/span>circular<\/span>(<\/span>16<\/span>)<\/span>,<\/span>
\n child:<\/span> Padding<\/span>(<\/span>
\n padding:<\/span> const<\/span> EdgeInsets<\/span>.<\/span>all<\/span>(<\/span>16<\/span>)<\/span>,<\/span>
\n child:<\/span> Row<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n Container<\/span>(<\/span>
\n width:<\/span> 56<\/span>,<\/span>
\n height:<\/span> 56<\/span>,<\/span>
\n decoration:<\/span> BoxDecoration<\/span>(<\/span>
\n color:<\/span> color.<\/span>withOpacity<\/span>(<\/span>0.1<\/span>)<\/span>,<\/span>
\n borderRadius:<\/span> BorderRadius<\/span>.<\/span>circular<\/span>(<\/span>12<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n child:<\/span> Icon<\/span>(<\/span>icon,<\/span> color:<\/span> color,<\/span> size:<\/span> 28<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n const<\/span> SizedBox<\/span>(<\/span>width:<\/span> 16<\/span>)<\/span>,<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> Column<\/span>(<\/span>
\n crossAxisAlignment:<\/span> CrossAxisAlignment<\/span>.<\/span>start,<\/span>
\n children:<\/span> [<\/span>
\n Text<\/span>(<\/span>
\n title,<\/span>
\n style:<\/span> const<\/span> TextStyle<\/span>(<\/span>
\n fontSize:<\/span> 16<\/span>,<\/span>
\n fontWeight:<\/span> FontWeight<\/span>.<\/span>bold,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n const<\/span> SizedBox<\/span>(<\/span>height:<\/span> 4<\/span>)<\/span>,<\/span>
\n Text<\/span>(<\/span>
\n description,<\/span>
\n style:<\/span> TextStyle<\/span>(<\/span>color:<\/span> Colors<\/span>.<\/span>grey[<\/span>600<\/span>]<\/span>,<\/span> fontSize:<\/span> 14<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Icon<\/span>(<\/span>Icons<\/span>.<\/span>chevron_right,<\/span> color:<\/span> Colors<\/span>.<\/span>grey[<\/span>400<\/span>]<\/span>)<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

const<\/span> double phi =<\/span> (<\/span>1<\/span> +<\/span> sqrt5)<\/span> \/<\/span> 2<\/span>;<\/span>
\nconst<\/span> double sqrt5 =<\/span> 2.23606797749979<\/span>;<\/span>
\nconst<\/span> double goldenAngle =<\/span> 2<\/span> *<\/span> pi *<\/span> (<\/span>1<\/span> –<\/span> 1<\/span> \/<\/span> phi)<\/span>;<\/span><\/p>\n

class<\/span> GoldenSpiralDemo<\/span> extends<\/span> StatefulWidget<\/span> {<\/span>
\n const<\/span> GoldenSpiralDemo<\/span>(<\/span>{<\/span>super<\/span>.<\/span>key}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n State<\/span><<\/span>GoldenSpiralDemo<\/span>><\/span><\/span> createState<\/span>(<\/span>)<\/span> =<\/span>><\/span> _GoldenSpiralDemoState<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> _GoldenSpiralDemoState extends<\/span> State<\/span><<\/span>GoldenSpiralDemo<\/span>><\/span><\/span>
\n with<\/span> SingleTickerProviderStateMixin<\/span> {<\/span>
\n late AnimationController<\/span> _controller;<\/span>
\n double _time =<\/span> 0<\/span>;<\/span>
\n int _turns =<\/span> 6<\/span>;<\/span>
\n double _growthRate =<\/span> 0.306349<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> initState<\/span>(<\/span>)<\/span> {<\/span>
\n super<\/span>.<\/span>initState<\/span>(<\/span>)<\/span>;<\/span>
\n _controller =<\/span> AnimationController<\/span>(<\/span>
\n vsync:<\/span> this<\/span>,<\/span>
\n duration:<\/span> const<\/span> Duration<\/span>(<\/span>milliseconds:<\/span> 16<\/span>)<\/span>,<\/span>
\n )<\/span>.<\/span>.<\/span>repeat<\/span>(<\/span>)<\/span>;<\/span>
\n _controller.<\/span>addListener<\/span>(<\/span>(<\/span>)<\/span> {<\/span>
\n _time +=<\/span> 0.016<\/span>;<\/span>
\n setState<\/span>(<\/span>(<\/span>)<\/span> {<\/span>}<\/span>)<\/span>;<\/span>
\n }<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n void<\/span> dispose<\/span>(<\/span>)<\/span> {<\/span>
\n _controller.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n super<\/span>.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n Widget<\/span> build<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n return<\/span> Scaffold<\/span>(<\/span>
\n appBar:<\/span> AppBar<\/span>(<\/span>title:<\/span> const<\/span> Text<\/span>(<\/span>'\u9ec4\u91d1\u87ba\u65cb'<\/span><\/span>)<\/span>)<\/span>,<\/span>
\n body:<\/span> Column<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> CustomPaint<\/span>(<\/span>
\n painter:<\/span> GoldenSpiralPainter<\/span>(<\/span>_time,<\/span> _turns,<\/span> _growthRate)<\/span>,<\/span>
\n size:<\/span> Size<\/span>.<\/span>infinite,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n _buildControls<\/span>(<\/span>)<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span><\/p>\n

Widget<\/span> _buildControls<\/span>(<\/span>)<\/span> {<\/span>
\n return<\/span> Container<\/span>(<\/span>
\n padding:<\/span> const<\/span> EdgeInsets<\/span>.<\/span>all<\/span>(<\/span>16<\/span>)<\/span>,<\/span>
\n decoration:<\/span> BoxDecoration<\/span>(<\/span>
\n color:<\/span> Colors<\/span>.<\/span>grey[<\/span>900<\/span>]<\/span>,<\/span>
\n borderRadius:<\/span> const<\/span> BorderRadius<\/span>.<\/span>vertical<\/span>(<\/span>top:<\/span> Radius<\/span>.<\/span>circular<\/span>(<\/span>20<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n child:<\/span> Column<\/span>(<\/span>
\n mainAxisSize:<\/span> MainAxisSize<\/span>.<\/span>min,<\/span>
\n children:<\/span> [<\/span>
\n Row<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n const<\/span> Text<\/span>(<\/span>'\u5708\u6570: '<\/span><\/span>,<\/span> style:<\/span> TextStyle<\/span>(<\/span>color:<\/span> Colors<\/span>.<\/span>white70)<\/span>)<\/span>,<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> Slider<\/span>(<\/span>
\n value:<\/span> _turns.<\/span>toDouble<\/span>(<\/span>)<\/span>,<\/span>
\n min:<\/span> 2<\/span>,<\/span>
\n max:<\/span> 12<\/span>,<\/span>
\n divisions:<\/span> 10<\/span>,<\/span>
\n onChanged:<\/span> (<\/span>v)<\/span> =<\/span>><\/span> setState<\/span>(<\/span>(<\/span>)<\/span> =<\/span>><\/span> _turns =<\/span> v.<\/span>toInt<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Text<\/span>(<\/span>'<\/span>$<\/span>_turns<\/span><\/span>'<\/span><\/span>,<\/span> style:<\/span> const<\/span> TextStyle<\/span>(<\/span>color:<\/span> Colors<\/span>.<\/span>amber)<\/span>)<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Row<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n const<\/span> Text<\/span>(<\/span>'\u589e\u957f\u7387: '<\/span><\/span>,<\/span> style:<\/span> TextStyle<\/span>(<\/span>color:<\/span> Colors<\/span>.<\/span>white70)<\/span>)<\/span>,<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> Slider<\/span>(<\/span>
\n value:<\/span> _growthRate,<\/span>
\n min:<\/span> 0.1<\/span>,<\/span>
\n max:<\/span> 0.5<\/span>,<\/span>
\n onChanged:<\/span> (<\/span>v)<\/span> =<\/span>><\/span> setState<\/span>(<\/span>(<\/span>)<\/span> =<\/span>><\/span> _growthRate =<\/span> v)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Text<\/span>(<\/span>_growthRate.<\/span>toStringAsFixed<\/span>(<\/span>3<\/span>)<\/span>,<\/span>
\n style:<\/span> const<\/span> TextStyle<\/span>(<\/span>color:<\/span> Colors<\/span>.<\/span>amber)<\/span>)<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

class<\/span> GoldenSpiralPainter<\/span> extends<\/span> CustomPainter<\/span> {<\/span>
\n final<\/span> double time;<\/span>
\n final<\/span> int turns;<\/span>
\n final<\/span> double growthRate;<\/span><\/p>\n

GoldenSpiralPainter<\/span>(<\/span>this<\/span>.<\/span>time,<\/span> this<\/span>.<\/span>turns,<\/span> this<\/span>.<\/span>growthRate)<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> paint<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Size<\/span> size)<\/span> {<\/span>
\n final<\/span> center =<\/span> Offset<\/span>(<\/span>size.<\/span>width \/<\/span> 2<\/span>,<\/span> size.<\/span>height \/<\/span> 2<\/span>)<\/span>;<\/span>
\n final<\/span> maxR =<\/span> min<\/span>(<\/span>size.<\/span>width,<\/span> size.<\/span>height)<\/span> \/<\/span> 2<\/span> –<\/span> 40<\/span>;<\/span><\/p>\n

canvas.<\/span>drawRect<\/span>(<\/span>
\n Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> size.<\/span>width,<\/span> size.<\/span>height)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> const<\/span> Color<\/span>(<\/span>0xFF0a0a15<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

_drawGrid<\/span>(<\/span>canvas,<\/span> center,<\/span> maxR)<\/span>;<\/span>
\n _drawGoldenSpiral<\/span>(<\/span>canvas,<\/span> center,<\/span> maxR)<\/span>;<\/span>
\n _drawParticles<\/span>(<\/span>canvas,<\/span> center,<\/span> maxR)<\/span>;<\/span><\/p>\n

canvas.<\/span>drawCircle<\/span>(<\/span>center,<\/span> 4<\/span>,<\/span> Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> Colors<\/span>.<\/span>amber)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> _drawGrid<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Offset<\/span> center,<\/span> double maxR)<\/span> {<\/span>
\n final<\/span> gridPaint =<\/span> Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> Colors<\/span>.<\/span>white10
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>stroke;<\/span><\/p>\n

for<\/span> (<\/span>int r =<\/span> 20<\/span>;<\/span> r <=<\/span> maxR;<\/span> r +=<\/span> 40<\/span>)<\/span> {<\/span>
\n canvas.<\/span>drawCircle<\/span>(<\/span>center,<\/span> r.<\/span>toDouble<\/span>(<\/span>)<\/span>,<\/span> gridPaint)<\/span>;<\/span>
\n }<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> 12<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> angle =<\/span> i *<\/span> pi \/<\/span> 6<\/span> +<\/span> time *<\/span> 0.1<\/span>;<\/span>
\n canvas.<\/span>drawLine<\/span>(<\/span>
\n center,<\/span>
\n Offset<\/span>(<\/span>center.<\/span>dx +<\/span> maxR *<\/span> cos<\/span>(<\/span>angle)<\/span>,<\/span> center.<\/span>dy +<\/span> maxR *<\/span> sin<\/span>(<\/span>angle)<\/span>)<\/span>,<\/span>
\n gridPaint,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

void<\/span> _drawGoldenSpiral<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Offset<\/span> center,<\/span> double maxR)<\/span> {<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span>
\n final<\/span> spiralPaint =<\/span> Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>stroke
\n .<\/span>.<\/span>strokeWidth =<\/span> 2<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>double theta =<\/span> 0<\/span>;<\/span> theta <=<\/span> turns *<\/span> 2<\/span> *<\/span> pi;<\/span> theta +=<\/span> 0.02<\/span>)<\/span> {<\/span>
\n final<\/span> r =<\/span> maxR *<\/span> 0.1<\/span> *<\/span> exp<\/span>(<\/span>growthRate *<\/span> theta)<\/span>;<\/span>
\n if<\/span> (<\/span>r ><\/span> maxR)<\/span> break<\/span>;<\/span><\/p>\n

final<\/span> x =<\/span> center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta +<\/span> time)<\/span>;<\/span>
\n final<\/span> y =<\/span> center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta +<\/span> time)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>theta ==<\/span> 0<\/span>)<\/span> {<\/span>
\n path.<\/span>moveTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n path.<\/span>lineTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

spiralPaint.<\/span>shader =<\/span> LinearGradient<\/span>(<\/span>
\n colors:<\/span> [<\/span>Colors<\/span>.<\/span>amber,<\/span> Colors<\/span>.<\/span>orange,<\/span> Colors<\/span>.<\/span>red]<\/span>,<\/span>
\n )<\/span>.<\/span>createShader<\/span>(<\/span>Rect<\/span>.<\/span>fromCircle<\/span>(<\/span>center:<\/span> center,<\/span> radius:<\/span> maxR)<\/span>)<\/span>;<\/span><\/p>\n

canvas.<\/span>drawPath<\/span>(<\/span>path,<\/span> spiralPaint)<\/span>;<\/span><\/p>\n

final<\/span> mirrorPath =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>double theta =<\/span> 0<\/span>;<\/span> theta <=<\/span> turns *<\/span> 2<\/span> *<\/span> pi;<\/span> theta +=<\/span> 0.02<\/span>)<\/span> {<\/span>
\n final<\/span> r =<\/span> maxR *<\/span> 0.1<\/span> *<\/span> exp<\/span>(<\/span>growthRate *<\/span> theta)<\/span>;<\/span>
\n if<\/span> (<\/span>r ><\/span> maxR)<\/span> break<\/span>;<\/span><\/p>\n

final<\/span> x =<\/span> center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>–<\/span>theta +<\/span> time)<\/span>;<\/span>
\n final<\/span> y =<\/span> center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>–<\/span>theta +<\/span> time)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>theta ==<\/span> 0<\/span>)<\/span> {<\/span>
\n mirrorPath.<\/span>moveTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n mirrorPath.<\/span>lineTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

spiralPaint.<\/span>shader =<\/span> LinearGradient<\/span>(<\/span>
\n colors:<\/span> [<\/span>Colors<\/span>.<\/span>purple,<\/span> Colors<\/span>.<\/span>indigo,<\/span> Colors<\/span>.<\/span>blue]<\/span>,<\/span>
\n )<\/span>.<\/span>createShader<\/span>(<\/span>Rect<\/span>.<\/span>fromCircle<\/span>(<\/span>center:<\/span> center,<\/span> radius:<\/span> maxR)<\/span>)<\/span>;<\/span><\/p>\n

canvas.<\/span>drawPath<\/span>(<\/span>mirrorPath,<\/span> spiralPaint)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> _drawParticles<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Offset<\/span> center,<\/span> double maxR)<\/span> {<\/span>
\n for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> 30<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> theta =<\/span> i *<\/span> goldenAngle +<\/span> time *<\/span> 0.5<\/span>;<\/span>
\n final<\/span> r =<\/span> maxR *<\/span> 0.8<\/span> *<\/span> sqrt<\/span>(<\/span>i \/<\/span> 30<\/span>)<\/span>;<\/span>
\n final<\/span> x =<\/span> center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta)<\/span>;<\/span>
\n final<\/span> y =<\/span> center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta)<\/span>;<\/span><\/p>\n

final<\/span> hue =<\/span> (<\/span>i *<\/span> 12<\/span> +<\/span> time *<\/span> 30<\/span>)<\/span> %<\/span> 360<\/span>;<\/span>
\n canvas.<\/span>drawCircle<\/span>(<\/span>
\n Offset<\/span>(<\/span>x,<\/span> y)<\/span>,<\/span>
\n 3<\/span> +<\/span> 2<\/span> *<\/span> sin<\/span>(<\/span>time *<\/span> 2<\/span> +<\/span> i)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> HSVColor<\/span>.<\/span>fromAHSV<\/span>(<\/span>1<\/span>,<\/span> hue,<\/span> 0.8<\/span>,<\/span> 1<\/span>)<\/span>.<\/span>toColor<\/span>(<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n bool shouldRepaint<\/span>(<\/span>covariant<\/span> GoldenSpiralPainter<\/span> old)<\/span> =<\/span>><\/span> true<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> SpiralFamilyDemo<\/span> extends<\/span> StatefulWidget<\/span> {<\/span>
\n const<\/span> SpiralFamilyDemo<\/span>(<\/span>{<\/span>super<\/span>.<\/span>key}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n State<\/span><<\/span>SpiralFamilyDemo<\/span>><\/span><\/span> createState<\/span>(<\/span>)<\/span> =<\/span>><\/span> _SpiralFamilyDemoState<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> _SpiralFamilyDemoState extends<\/span> State<\/span><<\/span>SpiralFamilyDemo<\/span>><\/span><\/span>
\n with<\/span> SingleTickerProviderStateMixin<\/span> {<\/span>
\n late AnimationController<\/span> _controller;<\/span>
\n double _time =<\/span> 0<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> initState<\/span>(<\/span>)<\/span> {<\/span>
\n super<\/span>.<\/span>initState<\/span>(<\/span>)<\/span>;<\/span>
\n _controller =<\/span> AnimationController<\/span>(<\/span>
\n vsync:<\/span> this<\/span>,<\/span>
\n duration:<\/span> const<\/span> Duration<\/span>(<\/span>milliseconds:<\/span> 16<\/span>)<\/span>,<\/span>
\n )<\/span>.<\/span>.<\/span>repeat<\/span>(<\/span>)<\/span>;<\/span>
\n _controller.<\/span>addListener<\/span>(<\/span>(<\/span>)<\/span> {<\/span>
\n _time +=<\/span> 0.016<\/span>;<\/span>
\n setState<\/span>(<\/span>(<\/span>)<\/span> {<\/span>}<\/span>)<\/span>;<\/span>
\n }<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n void<\/span> dispose<\/span>(<\/span>)<\/span> {<\/span>
\n _controller.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n super<\/span>.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n Widget<\/span> build<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n return<\/span> Scaffold<\/span>(<\/span>
\n appBar:<\/span> AppBar<\/span>(<\/span>title:<\/span> const<\/span> Text<\/span>(<\/span>'\u87ba\u65cb\u5bb6\u65cf'<\/span><\/span>)<\/span>)<\/span>,<\/span>
\n body:<\/span> CustomPaint<\/span>(<\/span>
\n painter:<\/span> SpiralFamilyPainter<\/span>(<\/span>_time)<\/span>,<\/span>
\n size:<\/span> Size<\/span>.<\/span>infinite,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

class<\/span> SpiralFamilyPainter<\/span> extends<\/span> CustomPainter<\/span> {<\/span>
\n final<\/span> double time;<\/span><\/p>\n

SpiralFamilyPainter<\/span>(<\/span>this<\/span>.<\/span>time)<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> paint<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Size<\/span> size)<\/span> {<\/span>
\n canvas.<\/span>drawRect<\/span>(<\/span>
\n Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> size.<\/span>width,<\/span> size.<\/span>height)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> const<\/span> Color<\/span>(<\/span>0xFF0a0a15<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

final<\/span> positions =<\/span> [<\/span>
\n Offset<\/span>(<\/span>size.<\/span>width *<\/span> 0.25<\/span>,<\/span> size.<\/span>height *<\/span> 0.25<\/span>)<\/span>,<\/span>
\n Offset<\/span>(<\/span>size.<\/span>width *<\/span> 0.75<\/span>,<\/span> size.<\/span>height *<\/span> 0.25<\/span>)<\/span>,<\/span>
\n Offset<\/span>(<\/span>size.<\/span>width *<\/span> 0.25<\/span>,<\/span> size.<\/span>height *<\/span> 0.75<\/span>)<\/span>,<\/span>
\n Offset<\/span>(<\/span>size.<\/span>width *<\/span> 0.75<\/span>,<\/span> size.<\/span>height *<\/span> 0.75<\/span>)<\/span>,<\/span>
\n ]<\/span>;<\/span><\/p>\n

final<\/span> labels =<\/span> [<\/span>'\u963f\u57fa\u7c73\u5fb7'<\/span><\/span>,<\/span> '\u9ec4\u91d1\u87ba\u65cb'<\/span><\/span>,<\/span> '\u8d39\u9a6c\u87ba\u65cb'<\/span><\/span>,<\/span> '\u53cc\u66f2\u87ba\u65cb'<\/span><\/span>]<\/span>;<\/span>
\n final<\/span> colors =<\/span> [<\/span>Colors<\/span>.<\/span>amber,<\/span> Colors<\/span>.<\/span>purple,<\/span> Colors<\/span>.<\/span>teal,<\/span> Colors<\/span>.<\/span>orange]<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> 4<\/span>;<\/span> i++<\/span>)<\/span> {<\/span>
\n _drawSpiral<\/span>(<\/span>canvas,<\/span> positions[<\/span>i]<\/span>,<\/span> i,<\/span> colors[<\/span>i]<\/span>,<\/span> labels[<\/span>i]<\/span>)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

void<\/span> _drawSpiral<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Offset<\/span> center,<\/span> int type,<\/span> Color<\/span> color,<\/span> String<\/span> label)<\/span> {<\/span>
\n final<\/span> maxR =<\/span> 60.0<\/span>;<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>double theta =<\/span> 0<\/span>;<\/span> theta <=<\/span> 6<\/span> *<\/span> pi;<\/span> theta +=<\/span> 0.05<\/span>)<\/span> {<\/span>
\n double r;<\/span>
\n switch<\/span> (<\/span>type)<\/span> {<\/span>
\n case<\/span> 0<\/span>:<\/span>
\n r =<\/span> 5<\/span> +<\/span> theta *<\/span> 8<\/span>;<\/span>
\n break<\/span>;<\/span>
\n case<\/span> 1<\/span>:<\/span>
\n r =<\/span> 5<\/span> *<\/span> exp<\/span>(<\/span>0.1<\/span> *<\/span> theta)<\/span>;<\/span>
\n break<\/span>;<\/span>
\n case<\/span> 2<\/span>:<\/span>
\n r =<\/span> 15<\/span> *<\/span> sqrt<\/span>(<\/span>theta)<\/span>;<\/span>
\n break<\/span>;<\/span>
\n case<\/span> 3<\/span>:<\/span>
\n r =<\/span> theta ><\/span> 0.1<\/span> ?<\/span> 150<\/span> \/<\/span> theta :<\/span> 150<\/span>;<\/span>
\n break<\/span>;<\/span>
\n default<\/span>:<\/span>
\n r =<\/span> theta;<\/span>
\n }<\/span><\/p>\n

if<\/span> (<\/span>r ><\/span> maxR)<\/span> break<\/span>;<\/span><\/p>\n

final<\/span> x =<\/span> center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta +<\/span> time)<\/span>;<\/span>
\n final<\/span> y =<\/span> center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta +<\/span> time)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>theta ==<\/span> 0<\/span>)<\/span> {<\/span>
\n path.<\/span>moveTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n path.<\/span>lineTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

canvas.<\/span>drawPath<\/span>(<\/span>
\n path,<\/span>
\n Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> color
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>stroke
\n .<\/span>.<\/span>strokeWidth =<\/span> 2<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

final<\/span> textPainter =<\/span> TextPainter<\/span>(<\/span>
\n text:<\/span> TextSpan<\/span>(<\/span>
\n text:<\/span> label,<\/span>
\n style:<\/span> TextStyle<\/span>(<\/span>color:<\/span> color,<\/span> fontSize:<\/span> 12<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n textDirection:<\/span> TextDirection<\/span>.<\/span>ltr,<\/span>
\n )<\/span>.<\/span>.<\/span>layout<\/span>(<\/span>)<\/span>;<\/span>
\n textPainter.<\/span>paint<\/span>(<\/span>canvas,<\/span> Offset<\/span>(<\/span>center.<\/span>dx –<\/span> 30<\/span>,<\/span> center.<\/span>dy +<\/span> maxR +<\/span> 10<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n bool shouldRepaint<\/span>(<\/span>covariant<\/span> SpiralFamilyPainter<\/span> old)<\/span> =<\/span>><\/span> true<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> SunflowerDemo<\/span> extends<\/span> StatefulWidget<\/span> {<\/span>
\n const<\/span> SunflowerDemo<\/span>(<\/span>{<\/span>super<\/span>.<\/span>key}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n State<\/span><<\/span>SunflowerDemo<\/span>><\/span><\/span> createState<\/span>(<\/span>)<\/span> =<\/span>><\/span> _SunflowerDemoState<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> _SunflowerDemoState extends<\/span> State<\/span><<\/span>SunflowerDemo<\/span>><\/span><\/span>
\n with<\/span> SingleTickerProviderStateMixin<\/span> {<\/span>
\n late AnimationController<\/span> _controller;<\/span>
\n double _time =<\/span> 0<\/span>;<\/span>
\n int _seedCount =<\/span> 200<\/span>;<\/span>
\n bool _animate =<\/span> true<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> initState<\/span>(<\/span>)<\/span> {<\/span>
\n super<\/span>.<\/span>initState<\/span>(<\/span>)<\/span>;<\/span>
\n _controller =<\/span> AnimationController<\/span>(<\/span>
\n vsync:<\/span> this<\/span>,<\/span>
\n duration:<\/span> const<\/span> Duration<\/span>(<\/span>milliseconds:<\/span> 16<\/span>)<\/span>,<\/span>
\n )<\/span>.<\/span>.<\/span>repeat<\/span>(<\/span>)<\/span>;<\/span>
\n _controller.<\/span>addListener<\/span>(<\/span>(<\/span>)<\/span> {<\/span>
\n if<\/span> (<\/span>_animate)<\/span> {<\/span>
\n _time +=<\/span> 0.016<\/span>;<\/span>
\n setState<\/span>(<\/span>(<\/span>)<\/span> {<\/span>}<\/span>)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n void<\/span> dispose<\/span>(<\/span>)<\/span> {<\/span>
\n _controller.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n super<\/span>.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n Widget<\/span> build<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n return<\/span> Scaffold<\/span>(<\/span>
\n appBar:<\/span> AppBar<\/span>(<\/span>title:<\/span> const<\/span> Text<\/span>(<\/span>'\u5411\u65e5\u8475\u79cd\u5b50\u6392\u5217'<\/span><\/span>)<\/span>)<\/span>,<\/span>
\n body:<\/span> Column<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> CustomPaint<\/span>(<\/span>
\n painter:<\/span> SunflowerPainter<\/span>(<\/span>_time,<\/span> _seedCount)<\/span>,<\/span>
\n size:<\/span> Size<\/span>.<\/span>infinite,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n _buildControls<\/span>(<\/span>)<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span><\/p>\n

Widget<\/span> _buildControls<\/span>(<\/span>)<\/span> {<\/span>
\n return<\/span> Container<\/span>(<\/span>
\n padding:<\/span> const<\/span> EdgeInsets<\/span>.<\/span>all<\/span>(<\/span>16<\/span>)<\/span>,<\/span>
\n decoration:<\/span> BoxDecoration<\/span>(<\/span>
\n color:<\/span> Colors<\/span>.<\/span>grey[<\/span>900<\/span>]<\/span>,<\/span>
\n borderRadius:<\/span> const<\/span> BorderRadius<\/span>.<\/span>vertical<\/span>(<\/span>top:<\/span> Radius<\/span>.<\/span>circular<\/span>(<\/span>20<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n child:<\/span> Column<\/span>(<\/span>
\n mainAxisSize:<\/span> MainAxisSize<\/span>.<\/span>min,<\/span>
\n children:<\/span> [<\/span>
\n Row<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n const<\/span> Text<\/span>(<\/span>'\u79cd\u5b50\u6570: '<\/span><\/span>,<\/span> style:<\/span> TextStyle<\/span>(<\/span>color:<\/span> Colors<\/span>.<\/span>white70)<\/span>)<\/span>,<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> Slider<\/span>(<\/span>
\n value:<\/span> _seedCount.<\/span>toDouble<\/span>(<\/span>)<\/span>,<\/span>
\n min:<\/span> 50<\/span>,<\/span>
\n max:<\/span> 500<\/span>,<\/span>
\n divisions:<\/span> 45<\/span>,<\/span>
\n onChanged:<\/span> (<\/span>v)<\/span> =<\/span>><\/span> setState<\/span>(<\/span>(<\/span>)<\/span> =<\/span>><\/span> _seedCount =<\/span> v.<\/span>toInt<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Text<\/span>(<\/span>'<\/span>$<\/span>_seedCount<\/span><\/span>'<\/span><\/span>,<\/span> style:<\/span> const<\/span> TextStyle<\/span>(<\/span>color:<\/span> Colors<\/span>.<\/span>orange)<\/span>)<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Row<\/span>(<\/span>
\n mainAxisAlignment:<\/span> MainAxisAlignment<\/span>.<\/span>center,<\/span>
\n children:<\/span> [<\/span>
\n ElevatedButton<\/span>(<\/span>
\n onPressed:<\/span> (<\/span>)<\/span> =<\/span>><\/span> setState<\/span>(<\/span>(<\/span>)<\/span> =<\/span>><\/span> _animate =<\/span> !<\/span>_animate)<\/span>,<\/span>
\n child:<\/span> Text<\/span>(<\/span>_animate ?<\/span> '\u6682\u505c'<\/span><\/span> :<\/span> '\u64ad\u653e'<\/span><\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n const<\/span> SizedBox<\/span>(<\/span>width:<\/span> 16<\/span>)<\/span>,<\/span>
\n ElevatedButton<\/span>(<\/span>
\n onPressed:<\/span> (<\/span>)<\/span> =<\/span>><\/span> setState<\/span>(<\/span>(<\/span>)<\/span> =<\/span>><\/span> _time =<\/span> 0<\/span>)<\/span>,<\/span>
\n child:<\/span> const<\/span> Text<\/span>(<\/span>'\u91cd\u7f6e'<\/span><\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

class<\/span> SunflowerPainter<\/span> extends<\/span> CustomPainter<\/span> {<\/span>
\n final<\/span> double time;<\/span>
\n final<\/span> int seedCount;<\/span><\/p>\n

SunflowerPainter<\/span>(<\/span>this<\/span>.<\/span>time,<\/span> this<\/span>.<\/span>seedCount)<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> paint<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Size<\/span> size)<\/span> {<\/span>
\n final<\/span> center =<\/span> Offset<\/span>(<\/span>size.<\/span>width \/<\/span> 2<\/span>,<\/span> size.<\/span>height \/<\/span> 2<\/span>)<\/span>;<\/span>
\n final<\/span> maxR =<\/span> min<\/span>(<\/span>size.<\/span>width,<\/span> size.<\/span>height)<\/span> \/<\/span> 2<\/span> –<\/span> 40<\/span>;<\/span><\/p>\n

canvas.<\/span>drawRect<\/span>(<\/span>
\n Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> size.<\/span>width,<\/span> size.<\/span>height)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> const<\/span> Color<\/span>(<\/span>0xFF0a0a15<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

canvas.<\/span>drawCircle<\/span>(<\/span>
\n center,<\/span>
\n maxR,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> Colors<\/span>.<\/span>brown.<\/span>withOpacity<\/span>(<\/span>0.1<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> seedCount;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> theta =<\/span> i *<\/span> goldenAngle +<\/span> time *<\/span> 0.2<\/span>;<\/span>
\n final<\/span> r =<\/span> maxR *<\/span> sqrt<\/span>(<\/span>i \/<\/span> seedCount)<\/span>;<\/span><\/p>\n

final<\/span> x =<\/span> center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta)<\/span>;<\/span>
\n final<\/span> y =<\/span> center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta)<\/span>;<\/span><\/p>\n

final<\/span> t =<\/span> i \/<\/span> seedCount;<\/span>
\n final<\/span> hue =<\/span> 30<\/span> +<\/span> t *<\/span> 30<\/span>;<\/span>
\n final<\/span> saturation =<\/span> 0.8<\/span> –<\/span> t *<\/span> 0.3<\/span>;<\/span>
\n final<\/span> value =<\/span> 0.6<\/span> +<\/span> t *<\/span> 0.4<\/span>;<\/span><\/p>\n

final<\/span> seedSize =<\/span> 4<\/span> +<\/span> 4<\/span> *<\/span> (<\/span>1<\/span> –<\/span> t)<\/span> +<\/span> sin<\/span>(<\/span>time *<\/span> 3<\/span> +<\/span> i *<\/span> 0.1<\/span>)<\/span> *<\/span> 1<\/span>;<\/span><\/p>\n

canvas.<\/span>drawCircle<\/span>(<\/span>
\n Offset<\/span>(<\/span>x,<\/span> y)<\/span>,<\/span>
\n seedSize,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> HSVColor<\/span>.<\/span>fromAHSV<\/span>(<\/span>1<\/span>,<\/span> hue,<\/span> saturation,<\/span> value)<\/span>.<\/span>toColor<\/span>(<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span><\/p>\n

_drawFibonacciSpirals<\/span>(<\/span>canvas,<\/span> center,<\/span> maxR)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> _drawFibonacciSpirals<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Offset<\/span> center,<\/span> double maxR)<\/span> {<\/span>
\n final<\/span> fibNumbers =<\/span> [<\/span>8<\/span>,<\/span> 13<\/span>,<\/span> 21<\/span>,<\/span> 34<\/span>]<\/span>;<\/span>
\n final<\/span> colors =<\/span> [<\/span>Colors<\/span>.<\/span>red,<\/span> Colors<\/span>.<\/span>green,<\/span> Colors<\/span>.<\/span>blue,<\/span> Colors<\/span>.<\/span>purple]<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int f =<\/span> 0<\/span>;<\/span> f <<\/span> fibNumbers.<\/span>length;<\/span> f++<\/span>)<\/span> {<\/span>
\n final<\/span> n =<\/span> fibNumbers[<\/span>f]<\/span>;<\/span>
\n final<\/span> paint =<\/span> Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> colors[<\/span>f]<\/span>.<\/span>withOpacity<\/span>(<\/span>0.3<\/span>)<\/span>
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>stroke
\n .<\/span>.<\/span>strokeWidth =<\/span> 1<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int start =<\/span> 0<\/span>;<\/span> start <<\/span> n;<\/span> start++<\/span>)<\/span> {<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int i =<\/span> start;<\/span> i <<\/span> seedCount;<\/span> i +=<\/span> n)<\/span> {<\/span>
\n final<\/span> theta =<\/span> i *<\/span> goldenAngle;<\/span>
\n final<\/span> r =<\/span> maxR *<\/span> sqrt<\/span>(<\/span>i \/<\/span> seedCount)<\/span>;<\/span>
\n final<\/span> x =<\/span> center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta)<\/span>;<\/span>
\n final<\/span> y =<\/span> center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>i ==<\/span> start)<\/span> {<\/span>
\n path.<\/span>moveTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n path.<\/span>lineTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n canvas.<\/span>drawPath<\/span>(<\/span>path,<\/span> paint)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n bool shouldRepaint<\/span>(<\/span>covariant<\/span> SunflowerPainter<\/span> old)<\/span> =<\/span>><\/span> true<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> GoldenRectangleDemo<\/span> extends<\/span> StatefulWidget<\/span> {<\/span>
\n const<\/span> GoldenRectangleDemo<\/span>(<\/span>{<\/span>super<\/span>.<\/span>key}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n State<\/span><<\/span>GoldenRectangleDemo<\/span>><\/span><\/span> createState<\/span>(<\/span>)<\/span> =<\/span>><\/span> _GoldenRectangleDemoState<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> _GoldenRectangleDemoState extends<\/span> State<\/span><<\/span>GoldenRectangleDemo<\/span>><\/span><\/span>
\n with<\/span> SingleTickerProviderStateMixin<\/span> {<\/span>
\n late AnimationController<\/span> _controller;<\/span>
\n double _time =<\/span> 0<\/span>;<\/span>
\n int _depth =<\/span> 8<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> initState<\/span>(<\/span>)<\/span> {<\/span>
\n super<\/span>.<\/span>initState<\/span>(<\/span>)<\/span>;<\/span>
\n _controller =<\/span> AnimationController<\/span>(<\/span>
\n vsync:<\/span> this<\/span>,<\/span>
\n duration:<\/span> const<\/span> Duration<\/span>(<\/span>milliseconds:<\/span> 16<\/span>)<\/span>,<\/span>
\n )<\/span>.<\/span>.<\/span>repeat<\/span>(<\/span>)<\/span>;<\/span>
\n _controller.<\/span>addListener<\/span>(<\/span>(<\/span>)<\/span> {<\/span>
\n _time +=<\/span> 0.016<\/span>;<\/span>
\n setState<\/span>(<\/span>(<\/span>)<\/span> {<\/span>}<\/span>)<\/span>;<\/span>
\n }<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n void<\/span> dispose<\/span>(<\/span>)<\/span> {<\/span>
\n _controller.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n super<\/span>.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n Widget<\/span> build<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n return<\/span> Scaffold<\/span>(<\/span>
\n appBar:<\/span> AppBar<\/span>(<\/span>title:<\/span> const<\/span> Text<\/span>(<\/span>'\u9ec4\u91d1\u77e9\u5f62'<\/span><\/span>)<\/span>)<\/span>,<\/span>
\n body:<\/span> Column<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> CustomPaint<\/span>(<\/span>
\n painter:<\/span> GoldenRectanglePainter<\/span>(<\/span>_time,<\/span> _depth)<\/span>,<\/span>
\n size:<\/span> Size<\/span>.<\/span>infinite,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Container<\/span>(<\/span>
\n padding:<\/span> const<\/span> EdgeInsets<\/span>.<\/span>all<\/span>(<\/span>16<\/span>)<\/span>,<\/span>
\n child:<\/span> Row<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n const<\/span> Text<\/span>(<\/span>'\u9012\u5f52\u6df1\u5ea6: '<\/span><\/span>)<\/span>,<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> Slider<\/span>(<\/span>
\n value:<\/span> _depth.<\/span>toDouble<\/span>(<\/span>)<\/span>,<\/span>
\n min:<\/span> 2<\/span>,<\/span>
\n max:<\/span> 12<\/span>,<\/span>
\n divisions:<\/span> 10<\/span>,<\/span>
\n onChanged:<\/span> (<\/span>v)<\/span> =<\/span>><\/span> setState<\/span>(<\/span>(<\/span>)<\/span> =<\/span>><\/span> _depth =<\/span> v.<\/span>toInt<\/span>(<\/span>)<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Text<\/span>(<\/span>'<\/span>$<\/span>_depth<\/span><\/span>'<\/span><\/span>)<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

class<\/span> GoldenRectanglePainter<\/span> extends<\/span> CustomPainter<\/span> {<\/span>
\n final<\/span> double time;<\/span>
\n final<\/span> int depth;<\/span><\/p>\n

GoldenRectanglePainter<\/span>(<\/span>this<\/span>.<\/span>time,<\/span> this<\/span>.<\/span>depth)<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> paint<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Size<\/span> size)<\/span> {<\/span>
\n canvas.<\/span>drawRect<\/span>(<\/span>
\n Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> size.<\/span>width,<\/span> size.<\/span>height)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> const<\/span> Color<\/span>(<\/span>0xFF0a0a15<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

final<\/span> center =<\/span> Offset<\/span>(<\/span>size.<\/span>width \/<\/span> 2<\/span>,<\/span> size.<\/span>height \/<\/span> 2<\/span>)<\/span>;<\/span>
\n final<\/span> rectWidth =<\/span> min<\/span>(<\/span>size.<\/span>width,<\/span> size.<\/span>height)<\/span> *<\/span> 0.8<\/span>;<\/span>
\n final<\/span> rectHeight =<\/span> rectWidth \/<\/span> phi;<\/span><\/p>\n

_drawGoldenRectangles<\/span>(<\/span>
\n canvas,<\/span>
\n center.<\/span>dx –<\/span> rectWidth \/<\/span> 2<\/span>,<\/span>
\n center.<\/span>dy –<\/span> rectHeight \/<\/span> 2<\/span>,<\/span>
\n rectWidth,<\/span>
\n rectHeight,<\/span>
\n 0<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

_drawGoldenSpiralInRectangles<\/span>(<\/span>canvas,<\/span> center,<\/span> rectWidth,<\/span> rectHeight)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> _drawGoldenRectangles<\/span>(<\/span>
\n Canvas<\/span> canvas,<\/span>
\n double x,<\/span>
\n double y,<\/span>
\n double width,<\/span>
\n double height,<\/span>
\n int currentDepth,<\/span>
\n )<\/span> {<\/span>
\n if<\/span> (<\/span>currentDepth >=<\/span> depth ||<\/span> width <<\/span> 2<\/span> ||<\/span> height <<\/span> 2<\/span>)<\/span> return<\/span>;<\/span><\/p>\n

final<\/span> hue =<\/span> (<\/span>currentDepth *<\/span> 30<\/span> +<\/span> time *<\/span> 20<\/span>)<\/span> %<\/span> 360<\/span>;<\/span>
\n final<\/span> paint =<\/span> Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> HSVColor<\/span>.<\/span>fromAHSV<\/span>(<\/span>0.3<\/span>,<\/span> hue,<\/span> 0.7<\/span>,<\/span> 0.9<\/span>)<\/span>.<\/span>toColor<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>fill;<\/span><\/p>\n

canvas.<\/span>drawRect<\/span>(<\/span>Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>x,<\/span> y,<\/span> width,<\/span> height)<\/span>,<\/span> paint)<\/span>;<\/span><\/p>\n

final<\/span> strokePaint =<\/span> Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> HSVColor<\/span>.<\/span>fromAHSV<\/span>(<\/span>1<\/span>,<\/span> hue,<\/span> 0.8<\/span>,<\/span> 1<\/span>)<\/span>.<\/span>toColor<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>stroke
\n .<\/span>.<\/span>strokeWidth =<\/span> 2<\/span>;<\/span><\/p>\n

canvas.<\/span>drawRect<\/span>(<\/span>Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>x,<\/span> y,<\/span> width,<\/span> height)<\/span>,<\/span> strokePaint)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>width ><\/span> height)<\/span> {<\/span>
\n _drawGoldenRectangles<\/span>(<\/span>
\n canvas,<\/span>
\n x +<\/span> height,<\/span>
\n y,<\/span>
\n width –<\/span> height,<\/span>
\n height,<\/span>
\n currentDepth +<\/span> 1<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n _drawGoldenRectangles<\/span>(<\/span>
\n canvas,<\/span>
\n x,<\/span>
\n y +<\/span> width,<\/span>
\n width,<\/span>
\n height –<\/span> width,<\/span>
\n currentDepth +<\/span> 1<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

void<\/span> _drawGoldenSpiralInRectangles<\/span>(<\/span>
\n Canvas<\/span> canvas,<\/span>
\n Offset<\/span> center,<\/span>
\n double width,<\/span>
\n double height,<\/span>
\n )<\/span> {<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span>
\n var<\/span> x =<\/span> center.<\/span>dx –<\/span> width \/<\/span> 2<\/span>;<\/span>
\n var<\/span> y =<\/span> center.<\/span>dy –<\/span> height \/<\/span> 2<\/span>;<\/span>
\n var<\/span> w =<\/span> width;<\/span>
\n var<\/span> h =<\/span> height;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> depth;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> rect =<\/span> Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>x,<\/span> y,<\/span> w ><\/span> h ?<\/span> h :<\/span> w,<\/span> w ><\/span> h ?<\/span> h :<\/span> w)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>i ==<\/span> 0<\/span>)<\/span> {<\/span>
\n path.<\/span>arcTo<\/span>(<\/span>rect,<\/span> –<\/span>pi \/<\/span> 2<\/span>,<\/span> pi \/<\/span> 2<\/span>,<\/span> false<\/span>)<\/span>;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n path.<\/span>arcTo<\/span>(<\/span>rect,<\/span> path.<\/span>getBounds<\/span>(<\/span>)<\/span>.<\/span>center.<\/span>dx <<\/span> rect.<\/span>center.<\/span>dx ?<\/span> 0<\/span> :<\/span> –<\/span>pi,<\/span>
\n w ><\/span> h ?<\/span> –<\/span>pi \/<\/span> 2<\/span> :<\/span> pi \/<\/span> 2<\/span>,<\/span> false<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

if<\/span> (<\/span>w ><\/span> h)<\/span> {<\/span>
\n x +=<\/span> h;<\/span>
\n w -=<\/span> h;<\/span>
\n }<\/span> else<\/span> {<\/span>
\n y +=<\/span> w;<\/span>
\n h -=<\/span> w;<\/span>
\n }<\/span><\/p>\n

if<\/span> (<\/span>w <<\/span> 1<\/span> ||<\/span> h <<\/span> 1<\/span>)<\/span> break<\/span>;<\/span>
\n }<\/span><\/p>\n

canvas.<\/span>drawPath<\/span>(<\/span>
\n path,<\/span>
\n Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> Colors<\/span>.<\/span>amber
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>stroke
\n .<\/span>.<\/span>strokeWidth =<\/span> 3<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n bool shouldRepaint<\/span>(<\/span>covariant<\/span> GoldenRectanglePainter<\/span> old)<\/span> =<\/span>><\/span> true<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> FibonacciDemo<\/span> extends<\/span> StatefulWidget<\/span> {<\/span>
\n const<\/span> FibonacciDemo<\/span>(<\/span>{<\/span>super<\/span>.<\/span>key}<\/span>)<\/span>;<\/span><\/p>\n

@override<\/span>
\n State<\/span><<\/span>FibonacciDemo<\/span>><\/span><\/span> createState<\/span>(<\/span>)<\/span> =<\/span>><\/span> _FibonacciDemoState<\/span>(<\/span>)<\/span>;<\/span>
\n}<\/span><\/p>\n

class<\/span> _FibonacciDemoState extends<\/span> State<\/span><<\/span>FibonacciDemo<\/span>><\/span><\/span>
\n with<\/span> SingleTickerProviderStateMixin<\/span> {<\/span>
\n late AnimationController<\/span> _controller;<\/span>
\n double _time =<\/span> 0<\/span>;<\/span>
\n int _visibleCount =<\/span> 1<\/span>;<\/span><\/p>\n

final<\/span> List<\/span><<\/span>int><\/span><\/span> _fib =<\/span> [<\/span>1<\/span>,<\/span> 1<\/span>,<\/span> 2<\/span>,<\/span> 3<\/span>,<\/span> 5<\/span>,<\/span> 8<\/span>,<\/span> 13<\/span>,<\/span> 21<\/span>,<\/span> 34<\/span>,<\/span> 55<\/span>,<\/span> 89<\/span>,<\/span> 144<\/span>]<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> initState<\/span>(<\/span>)<\/span> {<\/span>
\n super<\/span>.<\/span>initState<\/span>(<\/span>)<\/span>;<\/span>
\n _controller =<\/span> AnimationController<\/span>(<\/span>
\n vsync:<\/span> this<\/span>,<\/span>
\n duration:<\/span> const<\/span> Duration<\/span>(<\/span>milliseconds:<\/span> 16<\/span>)<\/span>,<\/span>
\n )<\/span>.<\/span>.<\/span>repeat<\/span>(<\/span>)<\/span>;<\/span>
\n _controller.<\/span>addListener<\/span>(<\/span>(<\/span>)<\/span> {<\/span>
\n _time +=<\/span> 0.016<\/span>;<\/span>
\n if<\/span> (<\/span>_time.<\/span>toInt<\/span>(<\/span>)<\/span> %<\/span> 60<\/span> ==<\/span> 0<\/span> &&<\/span> _visibleCount <<\/span> _fib.<\/span>length)<\/span> {<\/span>
\n setState<\/span>(<\/span>(<\/span>)<\/span> =<\/span>><\/span> _visibleCount++<\/span>)<\/span>;<\/span>
\n }<\/span>
\n setState<\/span>(<\/span>(<\/span>)<\/span> {<\/span>}<\/span>)<\/span>;<\/span>
\n }<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n void<\/span> dispose<\/span>(<\/span>)<\/span> {<\/span>
\n _controller.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n super<\/span>.<\/span>dispose<\/span>(<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n Widget<\/span> build<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n return<\/span> Scaffold<\/span>(<\/span>
\n appBar:<\/span> AppBar<\/span>(<\/span>title:<\/span> const<\/span> Text<\/span>(<\/span>'\u6590\u6ce2\u90a3\u5951\u52a8\u753b'<\/span><\/span>)<\/span>)<\/span>,<\/span>
\n body:<\/span> Column<\/span>(<\/span>
\n children:<\/span> [<\/span>
\n Expanded<\/span>(<\/span>
\n child:<\/span> CustomPaint<\/span>(<\/span>
\n painter:<\/span> FibonacciPainter<\/span>(<\/span>_time,<\/span> _visibleCount,<\/span> _fib)<\/span>,<\/span>
\n size:<\/span> Size<\/span>.<\/span>infinite,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n Container<\/span>(<\/span>
\n padding:<\/span> const<\/span> EdgeInsets<\/span>.<\/span>all<\/span>(<\/span>16<\/span>)<\/span>,<\/span>
\n child:<\/span> Wrap<\/span>(<\/span>
\n spacing:<\/span> 8<\/span>,<\/span>
\n children:<\/span> List<\/span>.<\/span>generate<\/span>(<\/span>
\n _visibleCount,<\/span>
\n (<\/span>i)<\/span> =<\/span>><\/span> Chip<\/span>(<\/span>
\n label:<\/span> Text<\/span>(<\/span>'<\/span>${<\/span>_fib[<\/span>i]<\/span><\/span>}<\/span><\/span>'<\/span><\/span>)<\/span>,<\/span>
\n backgroundColor:<\/span> HSVColor<\/span>.<\/span>fromAHSV<\/span>(<\/span>1<\/span>,<\/span> i *<\/span> 30.0<\/span>,<\/span> 0.7<\/span>,<\/span> 0.9<\/span>)<\/span>.<\/span>toColor<\/span>(<\/span>)<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>,<\/span>
\n ]<\/span>,<\/span>
\n )<\/span>,<\/span>
\n )<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

class<\/span> FibonacciPainter<\/span> extends<\/span> CustomPainter<\/span> {<\/span>
\n final<\/span> double time;<\/span>
\n final<\/span> int visibleCount;<\/span>
\n final<\/span> List<\/span><<\/span>int><\/span><\/span> fib;<\/span><\/p>\n

FibonacciPainter<\/span>(<\/span>this<\/span>.<\/span>time,<\/span> this<\/span>.<\/span>visibleCount,<\/span> this<\/span>.<\/span>fib)<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> paint<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Size<\/span> size)<\/span> {<\/span>
\n final<\/span> center =<\/span> Offset<\/span>(<\/span>size.<\/span>width \/<\/span> 2<\/span>,<\/span> size.<\/span>height \/<\/span> 2<\/span>)<\/span>;<\/span><\/p>\n

canvas.<\/span>drawRect<\/span>(<\/span>
\n Rect<\/span>.<\/span>fromLTWH<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> size.<\/span>width,<\/span> size.<\/span>height)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>.<\/span>.<\/span>color =<\/span> const<\/span> Color<\/span>(<\/span>0xFF0a0a15<\/span>)<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

var<\/span> x =<\/span> center.<\/span>dx;<\/span>
\n var<\/span> y =<\/span> center.<\/span>dy;<\/span>
\n var<\/span> direction =<\/span> 0<\/span>;<\/span>
\n final<\/span> scale =<\/span> min<\/span>(<\/span>size.<\/span>width,<\/span> size.<\/span>height)<\/span> \/<\/span> 300<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> visibleCount &&<\/span> i <<\/span> fib.<\/span>length;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> size =<\/span> fib[<\/span>i]<\/span> *<\/span> scale;<\/span>
\n final<\/span> hue =<\/span> (<\/span>i *<\/span> 30<\/span> +<\/span> time *<\/span> 20<\/span>)<\/span> %<\/span> 360<\/span>;<\/span><\/p>\n

Offset<\/span> rectCenter;<\/span>
\n switch<\/span> (<\/span>direction)<\/span> {<\/span>
\n case<\/span> 0<\/span>:<\/span>
\n rectCenter =<\/span> Offset<\/span>(<\/span>x +<\/span> size \/<\/span> 2<\/span>,<\/span> y +<\/span> size \/<\/span> 2<\/span>)<\/span>;<\/span>
\n x +=<\/span> size;<\/span>
\n break<\/span>;<\/span>
\n case<\/span> 1<\/span>:<\/span>
\n rectCenter =<\/span> Offset<\/span>(<\/span>x –<\/span> size \/<\/span> 2<\/span>,<\/span> y +<\/span> size \/<\/span> 2<\/span>)<\/span>;<\/span>
\n y +=<\/span> size;<\/span>
\n break<\/span>;<\/span>
\n case<\/span> 2<\/span>:<\/span>
\n rectCenter =<\/span> Offset<\/span>(<\/span>x –<\/span> size \/<\/span> 2<\/span>,<\/span> y –<\/span> size \/<\/span> 2<\/span>)<\/span>;<\/span>
\n x -=<\/span> size;<\/span>
\n break<\/span>;<\/span>
\n default<\/span>:<\/span>
\n rectCenter =<\/span> Offset<\/span>(<\/span>x +<\/span> size \/<\/span> 2<\/span>,<\/span> y –<\/span> size \/<\/span> 2<\/span>)<\/span>;<\/span>
\n y -=<\/span> size;<\/span>
\n }<\/span><\/p>\n

canvas.<\/span>drawRect<\/span>(<\/span>
\n Rect<\/span>.<\/span>fromCenter<\/span>(<\/span>center:<\/span> rectCenter,<\/span> width:<\/span> size,<\/span> height:<\/span> size)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> HSVColor<\/span>.<\/span>fromAHSV<\/span>(<\/span>0.3<\/span>,<\/span> hue,<\/span> 0.7<\/span>,<\/span> 0.9<\/span>)<\/span>.<\/span>toColor<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>fill,<\/span>
\n )<\/span>;<\/span><\/p>\n

canvas.<\/span>drawRect<\/span>(<\/span>
\n Rect<\/span>.<\/span>fromCenter<\/span>(<\/span>center:<\/span> rectCenter,<\/span> width:<\/span> size,<\/span> height:<\/span> size)<\/span>,<\/span>
\n Paint<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>color =<\/span> HSVColor<\/span>.<\/span>fromAHSV<\/span>(<\/span>1<\/span>,<\/span> hue,<\/span> 0.8<\/span>,<\/span> 1<\/span>)<\/span>.<\/span>toColor<\/span>(<\/span>)<\/span>
\n .<\/span>.<\/span>style =<\/span> PaintingStyle<\/span>.<\/span>stroke
\n .<\/span>.<\/span>strokeWidth =<\/span> 2<\/span>,<\/span>
\n )<\/span>;<\/span><\/p>\n

direction =<\/span> (<\/span>direction +<\/span> 1<\/span>)<\/span> %<\/span> 4<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

@override<\/span>
\n bool shouldRepaint<\/span>(<\/span>covariant<\/span> FibonacciPainter<\/span> old)<\/span> =<\/span>><\/span> true<\/span>;<\/span>
\n}<\/span><\/p>\n

\n

📝 \u56db\u3001\u6570\u5b66\u539f\u7406\u6df1\u5165\u89e3\u6790<\/h3>\n

📐 4.1 \u6781\u5750\u6807\u66f2\u7ebf\u65b9\u7a0b<\/h4>\n

\u6781\u5750\u6807\u7cfb\u7edf\u4e2d\u6709\u8bb8\u591a\u7ecf\u5178\u7684\u6570\u5b66\u66f2\u7ebf：<\/p>\n

\u73ab\u7470\u66f2\u7ebf（Rose Curves）：<\/p>\n

r = a \u00d7 cos(n \u00d7 \u03b8)<\/p>\n

\u5f53 n \u4e3a\u5947\u6570：n \u4e2a\u82b1\u74e3
\n\u5f53 n \u4e3a\u5076\u6570：2n \u4e2a\u82b1\u74e3<\/p>\n

\u793a\u4f8b：
\nn = 3: \u4e09\u53f6\u73ab\u7470 n = 4: \u516b\u53f6\u73ab\u7470
\n \u2571\u2572 \u2572\u2571\u2572\u2571
\n \u2571 \u2572 \u2571 \u2572
\n \u2571 \u2572 \u2571 \u2572
\n \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500
\n \u2572 \u2571 \u2572 \u2571
\n \u2572 \u2571 \u2572 \u2571
\n \u2572\u2571 \u2572\u2571<\/p>\n

\u5bf9\u6570\u87ba\u65cb\u7684\u6570\u5b66\u6027\u8d28：<\/p>\n

r = a \u00d7 e^(b \u00d7 \u03b8)<\/p>\n

\u7b49\u89d2\u6027\u8d28：\u87ba\u65cb\u7ebf\u4e0a\u4efb\u610f\u70b9\u7684\u5207\u7ebf\u4e0e\u5f84\u5411\u7684\u5939\u89d2\u6052\u5b9a
\n\u5939\u89d2 \u03b1 \u6ee1\u8db3：tan(\u03b1) = 1\/b<\/p>\n

\u81ea\u7136\u754c\u5e94\u7528：
\n– \u9e66\u9e49\u87ba\u58f3：\u751f\u957f\u8fc7\u7a0b\u4e2d\u4fdd\u6301\u5f62\u72b6\u76f8\u4f3c
\n– \u94f6\u6cb3\u7cfb\u65cb\u81c2：\u6052\u661f\u5206\u5e03\u8fd1\u4f3c\u5bf9\u6570\u87ba\u65cb
\n– \u65cb\u98ce\u7ed3\u6784：\u6c14\u6d41\u65cb\u8f6c\u8f68\u8ff9<\/p>\n

\u8d39\u9a6c\u87ba\u65cb\u7684\u7b49\u9762\u79ef\u6027\u8d28：<\/p>\n

r\u00b2 = a\u00b2 \u00d7 \u03b8<\/p>\n

\u9762\u79ef\u516c\u5f0f：A = (1\/2) \u00d7 r\u00b2 \u00d7 \u03b8
\n\u5bf9\u4e8e\u8d39\u9a6c\u87ba\u65cb：A = (1\/2) \u00d7 a\u00b2 \u00d7 \u03b8\u00b2<\/p>\n

\u7b49\u9762\u79ef\u6027\u8d28：\u89d2\u5ea6\u7b49\u91cf\u589e\u52a0，\u626b\u8fc7\u7684\u9762\u79ef\u4e5f\u7b49\u91cf\u589e\u52a0
\n\u5e94\u7528：\u5411\u65e5\u8475\u79cd\u5b50\u6392\u5217，\u6bcf\u4e2a\u79cd\u5b50\u83b7\u5f97\u76f8\u7b49\u7a7a\u95f4<\/p>\n

\n

🔄 4.2 \u9ec4\u91d1\u6bd4\u4f8b\u7684\u6570\u5b66\u6027\u8d28<\/h4>\n

\u4ee3\u6570\u6027\u8d28：<\/p>\n

\u03c6 = (1 + \u221a5) \/ 2 \u2248 1.618033988749…<\/p>\n

\u57fa\u672c\u6052\u7b49\u5f0f：
\n\u03c6\u00b2 = \u03c6 + 1
\n\u03c6\u00b3 = 2\u03c6 + 1
\n\u03c6\u2074 = 3\u03c6 + 2
\n\u03c6\u2075 = 5\u03c6 + 3
\n\u03c6\u207f = F(n)\u03c6 + F(n-1)<\/p>\n

\u5176\u4e2d F(n) \u662f\u7b2c n \u4e2a\u6590\u6ce2\u90a3\u5951\u6570<\/p>\n

\u5171\u8f6d：
\n\u03c6' = (1 – \u221a5) \/ 2 \u2248 -0.618
\n\u03c6 \u00d7 \u03c6' = -1
\n\u03c6 + \u03c6' = 1<\/p>\n

\u8fde\u5206\u6570\u8868\u793a：<\/p>\n

\u03c6 = 1 + 1\/(1 + 1\/(1 + 1\/(1 + …)))<\/p>\n

\u8fd9\u662f\u6240\u6709\u6570\u4e2d\u6536\u655b\u6700\u6162\u7684\u8fde\u5206\u6570
\n\u56e0\u6b64 \u03c6 \u88ab\u79f0\u4e3a"\u6700\u65e0\u7406\u7684\u6570"<\/p>\n

\u51e0\u4f55\u4f5c\u56fe：<\/p>\n

\u7528\u5c3a\u89c4\u4f5c\u56fe\u6784\u9020\u9ec4\u91d1\u5206\u5272\u70b9：<\/p>\n

1. \u4f5c\u7ebf\u6bb5 AB
\n2. \u5728 B \u70b9\u4f5c\u5782\u7ebf BC = AB\/2
\n3. \u8fde\u63a5 AC
\n4. \u4ee5 C \u4e3a\u5706\u5fc3，CB \u4e3a\u534a\u5f84\u753b\u5f27\u4ea4 AC \u4e8e D
\n5. \u4ee5 A \u4e3a\u5706\u5fc3，AD \u4e3a\u534a\u5f84\u753b\u5f27\u4ea4 AB \u4e8e P<\/p>\n

\u5219 P \u4e3a AB \u7684\u9ec4\u91d1\u5206\u5272\u70b9
\nAP\/AB = \u03c6 – 1 \u2248 0.618<\/p>\n

\n

🌸 4.3 \u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u901a\u9879\u516c\u5f0f<\/h4>\n

\u6bd4\u5185\u516c\u5f0f（Binet\u2019s Formula）：<\/p>\n

F(n) = (\u03c6\u207f – (-\u03c6)\u207b\u207f) \/ \u221a5<\/p>\n

\u8fd9\u662f\u6590\u6ce2\u90a3\u5951\u6570\u5217\u7684\u5c01\u95ed\u5f62\u5f0f\u89e3
\n\u76f4\u63a5\u8ba1\u7b97\u7b2c n \u9879，\u65e0\u9700\u9012\u5f52<\/p>\n

\u8bc1\u660e\u601d\u8def：
\n\u8bbe F(n) = F(n-1) + F(n-2)
\n\u7279\u5f81\u65b9\u7a0b：x\u00b2 = x + 1
\n\u89e3\u4e3a \u03c6 \u548c \u03c6' = -1\/\u03c6
\n\u901a\u89e3：F(n) = A\u00b7\u03c6\u207f + B\u00b7\u03c6'\u207f
\n\u7531\u521d\u59cb\u6761\u4ef6\u786e\u5b9a A = 1\/\u221a5, B = -1\/\u221a5<\/p>\n

\u6590\u6ce2\u90a3\u5951\u6052\u7b49\u5f0f：<\/p>\n

F(n+m) = F(n)\u00b7F(m+1) + F(n-1)\u00b7F(m)<\/p>\n

F(2n) = F(n)\u00b7(F(n+1) + F(n-1))<\/p>\n

F(n)\u00b2 + F(n+1)\u00b2 = F(2n+1)<\/p>\n

F(1) + F(2) + … + F(n) = F(n+2) – 1<\/p>\n

F(1)\u00b2 + F(2)\u00b2 + … + F(n)\u00b2 = F(n)\u00b7F(n+1)<\/p>\n

\n

🎯 4.4 \u9ec4\u91d1\u89d2\u5ea6\u7684\u4f18\u5316\u539f\u7406<\/h4>\n

\u4e3a\u4ec0\u4e48\u662f 137.5\u00b0：<\/p>\n

\u9ec4\u91d1\u89d2\u5ea6 = 360\u00b0 \u00d7 (1 – 1\/\u03c6) \u2248 137.507764\u00b0<\/p>\n

\u6709\u7406\u903c\u8fd1：
\n360\u00b0 \u00d7 1\/2 = 180\u00b0 \u2192 2 \u6761\u5c04\u7ebf
\n360\u00b0 \u00d7 1\/3 = 120\u00b0 \u2192 3 \u6761\u5c04\u7ebf
\n360\u00b0 \u00d7 2\/5 = 144\u00b0 \u2192 5 \u6761\u5c04\u7ebf
\n360\u00b0 \u00d7 3\/8 = 135\u00b0 \u2192 8 \u6761\u5c04\u7ebf<\/p>\n

\u9ec4\u91d1\u89d2\u5ea6\u662f\u65e0\u7406\u6570\u89d2\u5ea6
\n\u6c38\u8fdc\u4e0d\u4f1a\u56de\u5230\u8d77\u70b9
\n\u5b9e\u73b0\u6700\u4f18\u7a7a\u95f4\u586b\u5145<\/p>\n

\u7a7a\u95f4\u586b\u5145\u6548\u7387：<\/p>\n

\u5bf9\u4e8e n \u4e2a\u5143\u7d20\u6392\u5217：<\/p>\n

\u6709\u7406\u89d2\u5ea6 \u03b8 = p\/q \u00d7 360\u00b0：
\n– \u53ea\u4ea7\u751f q \u6761\u5c04\u7ebf
\n– \u5143\u7d20\u6cbf\u5c04\u7ebf\u805a\u96c6
\n– \u7a7a\u95f4\u5229\u7528\u7387\u4f4e<\/p>\n

\u9ec4\u91d1\u89d2\u5ea6 \u03b8 = 137.5\u00b0：
\n– \u6c38\u4e0d\u91cd\u590d
\n– \u5747\u5300\u5206\u5e03
\n– \u6700\u5927\u7a7a\u95f4\u5229\u7528\u7387<\/p>\n

\u6570\u5b66\u8bc1\u660e：
\n\u9ec4\u91d1\u89d2\u5ea6\u7684\u8fde\u5206\u6570\u5c55\u5f00\u5168\u4e3a 1
\n\u4f7f\u5f97\u4efb\u610f\u6709\u9650\u903c\u8fd1\u90fd\u662f\u6700\u4f18\u7684<\/p>\n

\n

🔬 \u4e94\u3001\u9ad8\u7ea7\u5e94\u7528\u573a\u666f<\/h3>\n

🎨 5.1 \u6570\u636e\u53ef\u89c6\u5316<\/h4>\n

\u87ba\u65cb\u5e03\u5c40\u5728\u6570\u636e\u53ef\u89c6\u5316\u4e2d\u7684\u72ec\u7279\u4f18\u52bf：<\/p>\n

\u65f6\u95f4\u5e8f\u5217\u87ba\u65cb\u56fe：<\/p>\n

\u5c06\u65f6\u95f4\u6570\u636e\u6620\u5c04\u5230\u87ba\u65cb：
\n– \u5185\u5708：\u8f83\u65e9\u65f6\u95f4
\n– \u5916\u5708：\u8f83\u665a\u65f6\u95f4
\n– \u76f8\u540c\u5b63\u8282\/\u5468\u671f\u5bf9\u9f50<\/p>\n

\u4f18\u52bf：
\n– \u5468\u671f\u6027\u6a21\u5f0f\u4e00\u76ee\u4e86\u7136
\n– \u957f\u671f\u8d8b\u52bf\u6e05\u6670\u53ef\u89c1
\n– \u8282\u7701\u663e\u793a\u7a7a\u95f4<\/p>\n

\u5c42\u6b21\u6570\u636e\u87ba\u65cb：<\/p>\n

\u6811\u72b6\u7ed3\u6784\u7684\u87ba\u65cb\u8868\u793a：
\n– \u6839\u8282\u70b9\u5728\u4e2d\u5fc3
\n– \u5b50\u8282\u70b9\u5411\u5916\u6269\u5c55
\n– \u5144\u5f1f\u8282\u70b9\u6309\u89d2\u5ea6\u5206\u5e03<\/p>\n

\u5e94\u7528\u573a\u666f：
\n– \u6587\u4ef6\u7cfb\u7edf\u6d4f\u89c8
\n– \u7ec4\u7ec7\u67b6\u6784\u5c55\u793a
\n– \u77e5\u8bc6\u56fe\u8c31\u53ef\u89c6\u5316<\/p>\n

\n

🌐 5.2 \u751f\u6210\u827a\u672f<\/h4>\n

\u87ba\u65cb\u5728\u751f\u6210\u827a\u672f\u4e2d\u7684\u521b\u610f\u5e94\u7528：<\/p>\n

\u53c2\u6570\u5316\u87ba\u65cb\u827a\u672f：<\/p>\n

\/\/ \u87ba\u65cb\u827a\u672f\u751f\u6210\u5668<\/span>
\nclass<\/span> SpiralArtGenerator<\/span> {<\/span>
\n final<\/span> int layers;<\/span>
\n final<\/span> double twistFactor;<\/span>
\n final<\/span> ColorScheme<\/span> colors;<\/span><\/p>\n

List<\/span><<\/span>Path<\/span>><\/span><\/span> generate<\/span>(<\/span>)<\/span> {<\/span>
\n final<\/span> paths =<\/span> <<\/span>Path<\/span>><\/span><\/span>[<\/span>]<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int layer =<\/span> 0<\/span>;<\/span> layer <<\/span> layers;<\/span> layer++<\/span>)<\/span> {<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span>
\n final<\/span> phase =<\/span> layer *<\/span> 2<\/span> *<\/span> pi \/<\/span> layers;<\/span><\/p>\n

for<\/span> (<\/span>double theta =<\/span> 0<\/span>;<\/span> theta <<\/span> 10<\/span> *<\/span> pi;<\/span> theta +=<\/span> 0.01<\/span>)<\/span> {<\/span>
\n final<\/span> r =<\/span> _calculateRadius<\/span>(<\/span>theta,<\/span> layer)<\/span>;<\/span>
\n final<\/span> x =<\/span> r *<\/span> cos<\/span>(<\/span>theta +<\/span> phase)<\/span>;<\/span>
\n final<\/span> y =<\/span> r *<\/span> sin<\/span>(<\/span>theta +<\/span> phase)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>theta ==<\/span> 0<\/span>)<\/span> path.<\/span>moveTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n else<\/span> path.<\/span>lineTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span><\/p>\n

paths.<\/span>add<\/span>(<\/span>path)<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> paths;<\/span>
\n }<\/span><\/p>\n

double _calculateRadius<\/span>(<\/span>double theta,<\/span> int layer)<\/span> {<\/span>
\n \/\/ \u7ec4\u5408\u591a\u79cd\u87ba\u65cb\u6a21\u5f0f<\/span>
\n return<\/span> 50<\/span> *<\/span> exp<\/span>(<\/span>0.1<\/span> *<\/span> theta)<\/span> +<\/span>
\n 20<\/span> *<\/span> sin<\/span>(<\/span>theta *<\/span> twistFactor +<\/span> layer)<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u9ec4\u91d1\u87ba\u65cb\u6784\u56fe：<\/p>\n

\u5728\u6444\u5f71\u548c\u7ed8\u753b\u4e2d\u5e94\u7528\u9ec4\u91d1\u87ba\u65cb：<\/p>\n

1. \u5c06\u753b\u9762\u6309\u9ec4\u91d1\u77e9\u5f62\u5206\u5272
\n2. \u7ed8\u5236\u9ec4\u91d1\u87ba\u65cb\u66f2\u7ebf
\n3. \u91cd\u8981\u5143\u7d20\u653e\u7f6e\u5728\u87ba\u65cb\u7ebf\u4e0a
\n4. \u89c6\u89c9\u7126\u70b9\u4f4d\u4e8e\u87ba\u65cb\u4e2d\u5fc3<\/p>\n

\u6548\u679c：
\n– \u81ea\u7136\u5f15\u5bfc\u89c6\u7ebf
\n– \u548c\u8c10\u5e73\u8861\u7684\u6784\u56fe
\n– \u7b26\u5408\u5ba1\u7f8e\u76f4\u89c9<\/p>\n

\n

📱 5.3 \u9e3f\u8499\u591a\u7aef\u9002\u914d<\/h4>\n

\u5728\u9e3f\u8499\u7cfb\u7edf\u4e0a\u5b9e\u73b0\u87ba\u65cb\u53ef\u89c6\u5316\u7684\u591a\u7aef\u9002\u914d：<\/p>\n

\u54cd\u5e94\u5f0f\u5c3a\u5bf8\u8ba1\u7b97：<\/p>\n

class<\/span> ResponsiveSpiral<\/span> {<\/span>
\n static<\/span> double calculateRadius<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n final<\/span> size =<\/span> MediaQuery<\/span>.<\/span>of<\/span>(<\/span>context)<\/span>.<\/span>size;<\/span>
\n final<\/span> deviceType =<\/span> _getDeviceType<\/span>(<\/span>size)<\/span>;<\/span><\/p>\n

switch<\/span> (<\/span>deviceType)<\/span> {<\/span>
\n case<\/span> DeviceType<\/span>.<\/span>phone:<\/span>
\n return<\/span> min<\/span>(<\/span>size.<\/span>width,<\/span> size.<\/span>height)<\/span> *<\/span> 0.35<\/span>;<\/span>
\n case<\/span> DeviceType<\/span>.<\/span>tablet:<\/span>
\n return<\/span> min<\/span>(<\/span>size.<\/span>width,<\/span> size.<\/span>height)<\/span> *<\/span> 0.4<\/span>;<\/span>
\n case<\/span> DeviceType<\/span>.<\/span>tv:<\/span>
\n return<\/span> min<\/span>(<\/span>size.<\/span>width,<\/span> size.<\/span>height)<\/span> *<\/span> 0.3<\/span>;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

static<\/span> int calculateDetailLevel<\/span>(<\/span>BuildContext<\/span> context)<\/span> {<\/span>
\n final<\/span> performance =<\/span> DevicePerformance<\/span>.<\/span>getLevel<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

switch<\/span> (<\/span>performance)<\/span> {<\/span>
\n case<\/span> PerformanceLevel<\/span>.<\/span>high:<\/span>
\n return<\/span> 128<\/span>;<\/span>
\n case<\/span> PerformanceLevel<\/span>.<\/span>medium:<\/span>
\n return<\/span> 64<\/span>;<\/span>
\n case<\/span> PerformanceLevel<\/span>.<\/span>low:<\/span>
\n return<\/span> 32<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u6027\u80fd\u5206\u7ea7\u6e32\u67d3：<\/p>\n

class<\/span> AdaptiveSpiralPainter<\/span> extends<\/span> CustomPainter<\/span> {<\/span>
\n final<\/span> int detailLevel;<\/span><\/p>\n

AdaptiveSpiralPainter<\/span>(<\/span>this<\/span>.<\/span>detailLevel)<\/span>;<\/span><\/p>\n

@override<\/span>
\n void<\/span> paint<\/span>(<\/span>Canvas<\/span> canvas,<\/span> Size<\/span> size)<\/span> {<\/span>
\n \/\/ \u6839\u636e\u6027\u80fd\u7b49\u7ea7\u8c03\u6574\u6e32\u67d3\u7ec6\u8282<\/span>
\n final<\/span> stepCount =<\/span> detailLevel *<\/span> 4<\/span>;<\/span>
\n final<\/span> particleCount =<\/span> detailLevel ~\/<\/span> 2<\/span>;<\/span><\/p>\n

\/\/ \u7ed8\u5236\u87ba\u65cb<\/span>
\n _drawSpiral<\/span>(<\/span>canvas,<\/span> size,<\/span> stepCount)<\/span>;<\/span><\/p>\n

\/\/ \u7ed8\u5236\u7c92\u5b50（\u9ad8\u6027\u80fd\u8bbe\u5907）<\/span>
\n if<\/span> (<\/span>detailLevel ><\/span> 64<\/span>)<\/span> {<\/span>
\n _drawParticles<\/span>(<\/span>canvas,<\/span> size,<\/span> particleCount)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\n

📊 \u516d\u3001\u6027\u80fd\u4f18\u5316\u7b56\u7565<\/h3>\n

\u26a1 6.1 \u6e32\u67d3\u4f18\u5316<\/h4>\n

\u87ba\u65cb\u6e32\u67d3\u7684\u6027\u80fd\u4f18\u5316\u6280\u5de7：<\/p>\n

\u9884\u8ba1\u7b97\u8def\u5f84：<\/p>\n

class<\/span> CachedSpiralPath<\/span> {<\/span>
\n Path<\/span>?<\/span> _cachedPath;<\/span>
\n int _lastTurns =<\/span> 0<\/span>;<\/span>
\n double _lastGrowthRate =<\/span> 0<\/span>;<\/span><\/p>\n

Path<\/span> getPath<\/span>(<\/span>int turns,<\/span> double growthRate,<\/span> Offset<\/span> center,<\/span> double maxR)<\/span> {<\/span>
\n if<\/span> (<\/span>_cachedPath !=<\/span> null<\/span> &&<\/span>
\n _lastTurns ==<\/span> turns &&<\/span>
\n _lastGrowthRate ==<\/span> growthRate)<\/span> {<\/span>
\n return<\/span> _cachedPath!<\/span>;<\/span>
\n }<\/span><\/p>\n

_cachedPath =<\/span> _computePath<\/span>(<\/span>turns,<\/span> growthRate,<\/span> center,<\/span> maxR)<\/span>;<\/span>
\n _lastTurns =<\/span> turns;<\/span>
\n _lastGrowthRate =<\/span> growthRate;<\/span><\/p>\n

return<\/span> _cachedPath!<\/span>;<\/span>
\n }<\/span><\/p>\n

Path<\/span> _computePath<\/span>(<\/span>int turns,<\/span> double growthRate,<\/span> Offset<\/span> center,<\/span> double maxR)<\/span> {<\/span>
\n final<\/span> path =<\/span> Path<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>double theta =<\/span> 0<\/span>;<\/span> theta <=<\/span> turns *<\/span> 2<\/span> *<\/span> pi;<\/span> theta +=<\/span> 0.02<\/span>)<\/span> {<\/span>
\n final<\/span> r =<\/span> maxR *<\/span> 0.1<\/span> *<\/span> exp<\/span>(<\/span>growthRate *<\/span> theta)<\/span>;<\/span>
\n if<\/span> (<\/span>r ><\/span> maxR)<\/span> break<\/span>;<\/span><\/p>\n

final<\/span> x =<\/span> center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta)<\/span>;<\/span>
\n final<\/span> y =<\/span> center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>theta ==<\/span> 0<\/span>)<\/span> path.<\/span>moveTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n else<\/span> path.<\/span>lineTo<\/span>(<\/span>x,<\/span> y)<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> path;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u4f7f\u7528 Isolate \u8ba1\u7b97：<\/p>\n

Future<\/span><<\/span>List<\/span><<\/span>Offset<\/span>><\/span>><\/span><\/span> computeSunflowerSeeds<\/span>(<\/span>SunflowerParams<\/span> params)<\/span> async<\/span> {<\/span>
\n return<\/span> await<\/span> compute<\/span>(<\/span>_generateSeeds,<\/span> params)<\/span>;<\/span>
\n}<\/span><\/p>\n

List<\/span><<\/span>Offset<\/span>><\/span><\/span> _generateSeeds<\/span>(<\/span>SunflowerParams<\/span> params)<\/span> {<\/span>
\n final<\/span> seeds =<\/span> <<\/span>Offset<\/span>><\/span><\/span>[<\/span>]<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int i =<\/span> 0<\/span>;<\/span> i <<\/span> params.<\/span>count;<\/span> i++<\/span>)<\/span> {<\/span>
\n final<\/span> theta =<\/span> i *<\/span> goldenAngle;<\/span>
\n final<\/span> r =<\/span> params.<\/span>maxRadius *<\/span> sqrt<\/span>(<\/span>i \/<\/span> params.<\/span>count)<\/span>;<\/span><\/p>\n

seeds.<\/span>add<\/span>(<\/span>Offset<\/span>(<\/span>
\n params.<\/span>center.<\/span>dx +<\/span> r *<\/span> cos<\/span>(<\/span>theta)<\/span>,<\/span>
\n params.<\/span>center.<\/span>dy +<\/span> r *<\/span> sin<\/span>(<\/span>theta)<\/span>,<\/span>
\n )<\/span>)<\/span>;<\/span>
\n }<\/span><\/p>\n

return<\/span> seeds;<\/span>
\n}<\/span><\/p>\n

\n

💾 6.2 \u5185\u5b58\u4f18\u5316<\/h4>\n

\u5bf9\u8c61\u6c60\u6a21\u5f0f：<\/p>\n

class<\/span> SpiralPointPool<\/span> {<\/span>
\n static<\/span> final<\/span> SpiralPointPool<\/span> _instance =<\/span> SpiralPointPool<\/span>.<\/span>_<\/span>(<\/span>)<\/span>;<\/span>
\n final<\/span> List<\/span><<\/span>List<\/span><<\/span>Offset<\/span>><\/span>><\/span><\/span> _pools =<\/span> [<\/span>]<\/span>;<\/span><\/p>\n

factory<\/span> SpiralPointPool<\/span>(<\/span>)<\/span> =<\/span>><\/span> _instance;<\/span>
\n SpiralPointPool<\/span>.<\/span>_<\/span>(<\/span>)<\/span>;<\/span><\/p>\n

List<\/span><<\/span>Offset<\/span>><\/span><\/span> acquire<\/span>(<\/span>int size)<\/span> {<\/span>
\n for<\/span> (<\/span>var<\/span> pool in<\/span> _pools)<\/span> {<\/span>
\n if<\/span> (<\/span>pool.<\/span>length >=<\/span> size)<\/span> {<\/span>
\n _pools.<\/span>remove<\/span>(<\/span>pool)<\/span>;<\/span>
\n return<\/span> pool;<\/span>
\n }<\/span>
\n }<\/span>
\n return<\/span> List<\/span>.<\/span>generate<\/span>(<\/span>size,<\/span> (<\/span>i)<\/span> =<\/span>><\/span> Offset<\/span>.<\/span>zero)<\/span>;<\/span>
\n }<\/span><\/p>\n

void<\/span> release<\/span>(<\/span>List<\/span><<\/span>Offset<\/span>><\/span><\/span> pool)<\/span> {<\/span>
\n if<\/span> (<\/span>_pools.<\/span>length <<\/span> 10<\/span>)<\/span> {<\/span>
\n _pools.<\/span>add<\/span>(<\/span>pool)<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

\u61d2\u52a0\u8f7d\u7b56\u7565：<\/p>\n

class<\/span> LazySpiralData<\/span> {<\/span>
\n List<\/span><<\/span>Offset<\/span>><\/span><\/span>?<\/span> _points;<\/span>
\n final<\/span> int Function<\/span>(<\/span>)<\/span> _pointCount;<\/span>
\n final<\/span> Offset<\/span> Function<\/span>(<\/span>int)<\/span> _pointGenerator;<\/span><\/p>\n

LazySpiralData<\/span>(<\/span>this<\/span>.<\/span>_pointCount,<\/span> this<\/span>.<\/span>_pointGenerator)<\/span>;<\/span><\/p>\n

List<\/span><<\/span>Offset<\/span>><\/span><\/span> get<\/span> points {<\/span>
\n _points ?<\/span>?<\/span>=<\/span> List<\/span>.<\/span>generate<\/span>(<\/span>
\n _pointCount<\/span>(<\/span>)<\/span>,<\/span>
\n (<\/span>i)<\/span> =<\/span>><\/span> _pointGenerator<\/span>(<\/span>i)<\/span>,<\/span>
\n )<\/span>;<\/span>
\n return<\/span> _points!<\/span>;<\/span>
\n }<\/span><\/p>\n

Offset<\/span> operator<\/span> [<\/span>]<\/span>(<\/span>int index)<\/span> =<\/span>><\/span> points[<\/span>index]<\/span>;<\/span>
\n}<\/span><\/p>\n

\n

🎓 \u4e03\u3001\u5b66\u4e60\u8d44\u6e90\u4e0e\u62d3\u5c55<\/h3>\n

📚 \u63a8\u8350\u9605\u8bfb<\/h4>\n\n\u4e3b\u9898\u8d44\u6e90\u96be\u5ea6<\/tr>\n\n\n\n\n\n\n
\u9ec4\u91d1\u6bd4\u4f8b<\/td>\n\u300a\u795e\u5723\u6bd4\u4f8b\u300b- \u5362\u5361\u00b7\u5e15\u4e54\u5229<\/td>\n\u2b50\u2b50<\/td>\n<\/tr>\n
\u6590\u6ce2\u90a3\u5951\u6570\u5217<\/td>\n\u300a\u6590\u6ce2\u90a3\u5951\u6570\u5217\u300b- \u6258\u9a6c\u65af\u00b7\u79d1\u65af\u9f50<\/td>\n\u2b50\u2b50<\/td>\n<\/tr>\n
\u87ba\u65cb\u51e0\u4f55<\/td>\n\u300a\u87ba\u65cb：\u4ece\u81ea\u7136\u5230\u827a\u672f\u300b<\/td>\n\u2b50\u2b50<\/td>\n<\/tr>\n
\u5206\u5f62\u51e0\u4f55<\/td>\n\u300a\u5927\u81ea\u7136\u7684\u5206\u5f62\u51e0\u4f55\u5b66\u300b<\/td>\n\u2b50\u2b50\u2b50<\/td>\n<\/tr>\n
\u6781\u5750\u6807\u53d8\u6362<\/td>\n\u300a\u9ad8\u7b49\u6570\u5b66\u300b- \u6781\u5750\u6807\u7ae0\u8282<\/td>\n\u2b50\u2b50<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

🔗 \u76f8\u5173\u9879\u76ee<\/h4>\n
    \n
  • D3.js \u87ba\u65cb\u56fe：\u6570\u636e\u53ef\u89c6\u5316\u7684\u87ba\u65cb\u5e03\u5c40<\/li>\n
  • Processing \u87ba\u65cb\u827a\u672f：\u521b\u610f\u7f16\u7a0b\u793a\u4f8b<\/li>\n
  • Wolfram MathWorld：\u6570\u5b66\u516c\u5f0f\u53c2\u8003<\/li>\n
  • Desmos \u56fe\u5f62\u8ba1\u7b97\u5668：\u4ea4\u4e92\u5f0f\u63a2\u7d22<\/li>\n<\/ul>\n

    🎯 \u7ec3\u4e60\u5efa\u8bae<\/h4>\n
  • \u57fa\u7840\u7ec3\u4e60：\u7ed8\u5236\u4e0d\u540c\u53c2\u6570\u7684\u5bf9\u6570\u87ba\u65cb<\/li>\n
  • \u8fdb\u9636\u7ec3\u4e60：\u5b9e\u73b0\u5411\u65e5\u8475\u79cd\u5b50\u52a8\u753b<\/li>\n
  • \u6311\u6218\u7ec3\u4e60：\u521b\u5efa\u4ea4\u4e92\u5f0f\u87ba\u65cb\u827a\u672f\u751f\u6210\u5668<\/li>\n
    \n

    📝 \u516b\u3001\u603b\u7ed3<\/h3>\n

    \u672c\u7bc7\u6587\u7ae0\u6df1\u5165\u63a2\u8ba8\u4e86\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272\u7684\u6570\u5b66\u539f\u7406\u53ca\u5176\u5728 Flutter \u4e2d\u7684\u53ef\u89c6\u5316\u5b9e\u73b0\u3002<\/p>\n

    \u2705 \u6838\u5fc3\u77e5\u8bc6\u70b9\u56de\u987e<\/h4>\n\n\u77e5\u8bc6\u70b9\u8bf4\u660e<\/tr>\n\n\n\n\n\n\n\n
    📐 \u9ec4\u91d1\u6bd4\u4f8b<\/td>\n\u03c6 \u2248 1.618，\u81ea\u7136\u754c\u6700\u4f18\u7f8e\u7684\u6bd4\u4f8b<\/td>\n<\/tr>\n
    🔢 \u6590\u6ce2\u90a3\u5951\u6570\u5217<\/td>\n\u76f8\u90bb\u9879\u6bd4\u503c\u8d8b\u8fd1\u9ec4\u91d1\u6bd4\u4f8b<\/td>\n<\/tr>\n
    🌀 \u87ba\u65cb\u66f2\u7ebf<\/td>\n\u963f\u57fa\u7c73\u5fb7\u3001\u5bf9\u6570\u3001\u8d39\u9a6c\u7b49\u7c7b\u578b<\/td>\n<\/tr>\n
    🌻 \u9ec4\u91d1\u89d2\u5ea6<\/td>\n137.5\u00b0，\u6700\u4f18\u7a7a\u95f4\u6392\u5217\u89d2\u5ea6<\/td>\n<\/tr>\n
    📦 \u9ec4\u91d1\u77e9\u5f62<\/td>\n\u9012\u5f52\u5206\u5272\u6784\u9020\u9ec4\u91d1\u87ba\u65cb<\/td>\n<\/tr>\n
    \u26a1 \u6027\u80fd\u4f18\u5316<\/td>\n\u9884\u8ba1\u7b97\u3001\u5bf9\u8c61\u6c60\u3001\u61d2\u52a0\u8f7d<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u2b50 \u6700\u4f73\u5b9e\u8df5\u8981\u70b9<\/h4>\n
      \n
    • \u2705 \u4f7f\u7528\u6781\u5750\u6807\u7b80\u5316\u87ba\u65cb\u8ba1\u7b97<\/li>\n
    • \u2705 \u9ec4\u91d1\u89d2\u5ea6\u5b9e\u73b0\u5747\u5300\u5206\u5e03<\/li>\n
    • \u2705 \u9884\u8ba1\u7b97\u8def\u5f84\u63d0\u5347\u6027\u80fd<\/li>\n
    • \u2705 \u54cd\u5e94\u5f0f\u9002\u914d\u591a\u7aef\u8bbe\u5907<\/li>\n<\/ul>\n

      🚀 \u8fdb\u9636\u65b9\u5411<\/h4>\n
        \n
      • 🔮 3D \u87ba\u65cb\u7a7a\u95f4\u53ef\u89c6\u5316<\/li>\n
      • \u2728 \u97f3\u9891\u9a71\u52a8\u7684\u87ba\u65cb\u52a8\u753b<\/li>\n
      • 🎨 \u53c2\u6570\u5316\u87ba\u65cb\u827a\u672f\u751f\u6210<\/li>\n
      • 📊 \u87ba\u65cb\u5e03\u5c40\u6570\u636e\u53ef\u89c6\u5316<\/li>\n<\/ul>\n
        \n

        💡 \u63d0\u793a：\u672c\u6587\u4ee3\u7801\u57fa\u4e8e Flutter for Harmony \u5f00\u53d1，\u53ef\u5728\u9e3f\u8499\u8bbe\u5907\u4e0a\u6d41\u7545\u8fd0\u884c\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

        \u6b22\u8fce\u52a0\u5165\u5f00\u6e90\u9e3f\u8499\u8de8\u5e73\u53f0\u793e\u533a：https:\/\/openharmonycrossplatform.csdn.net 🌀 \u4e00\u3001\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272：\u6570\u5b66\u4e4b\u7f8e
        \n📚 1.1 \u9ec4\u91d1\u6bd4\u4f8b\u7684\u53d1\u73b0
        \n\u9ec4\u91d1\u6bd4\u4f8b（Golden Ratio），\u53c8\u79f0\u9ec4\u91d1\u5206\u5272，\u662f\u4e00\u4e2a\u65e0\u7406\u6570，\u901a\u5e38\u7528\u5e0c\u814a\u5b57\u6bcd \u03c6（phi）\u8868\u793a，\u5176\u503c\u7ea6\u4e3a 1.61803398<\/p>\n","protected":false},"author":2,"featured_media":77342,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2878],"topic":[],"class_list":["post-77343","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-flutter"],"yoast_head":"\nFlutter for Harmony \u8de8\u5e73\u53f0\u5f00\u53d1\u5b9e\u6218\uff1a\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272\u2014\u2014\u81ea\u7136\u754c\u7684\u97f5\u5f8b\u5bc6\u7801 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/77343.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Flutter for Harmony \u8de8\u5e73\u53f0\u5f00\u53d1\u5b9e\u6218\uff1a\u87ba\u65cb\u4e0e\u9ec4\u91d1\u5206\u5272\u2014\u2014\u81ea\u7136\u754c\u7684\u97f5\u5f8b\u5bc6\u7801 - 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