{"id":667,"date":"2014-01-21T12:50:11","date_gmt":"2014-01-21T11:50:11","guid":{"rendered":"http:\/\/darksun190.cn\/?p=667"},"modified":"2022-12-17T15:37:10","modified_gmt":"2022-12-17T07:37:10","slug":"%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95%e6%8b%9f%e5%90%88%e4%b8%80%e4%ba%9b%e5%9f%ba%e6%9c%ac%e7%a9%ba%e9%97%b4%e5%85%83%e7%b4%a0%e7%9a%84c%e5%ae%9e%e7%8e%b0-%ef%bc%88","status":"publish","type":"post","link":"http:\/\/darksun190.cn\/blog\/?p=667","title":{"rendered":"\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u4e00\u4e9b\u57fa\u672c\u7a7a\u95f4\u5143\u7d20\u7684C#\u5b9e\u73b0 \u2014\u2014  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href=\"http:\/\/scholar.google.com\/\">google \u5b66\u672f\u641c\u7d22<\/a>\uff0c\u53ef\u4ee5\u770b\u5230\u4e00\u4e2a\u8bba\u6587\u88ab\u5f15\u7528\u7684\u6b21\u6570\uff0c\u540e\u9762\u9644\u7684\u4e00\u7bc7\u8bba\u6587\u88ab\u5f15\u7528\u4e86150\u591a\u6b21\uff0c\u57fa\u672c\u4e0a\u662f\u8fd9\u4e2a\u8bdd\u9898\u91cc\u6700\u65e9\u7684\u51e0\u7bc7\u8bba\u6587\uff0c\u4e5f\u662f\u8bb2\u7684\u6700\u57fa\u7840\u7684\u8bba\u6587\u3002<\/p>\n<p>\u53e6\u5916\u8fd8\u8981\u611f\u8c22<a href=\"http:\/\/en.wikipedia.org\/\">\u7ef4\u57fa\u767e\u79d1<\/a>\uff0c\u4e00\u4e9b\u57fa\u672c\u5df2\u7ecf\u5fd8\u8bb0\u7684\u6570\u5b66\u6982\u5ff5\u90fd\u662f\u901a\u8fc7\u8fd9\u4e2a\u60f3\u8d77\u6765\u7684\uff0c\u8fd8\u53ef\u4ee5\u5f53\u4e13\u4e1a\u8bcd\u5178\u7528\uff0c\u4e00\u7bc7\u6587\u7ae0\u5207\u6362\u4e2d\u82f1\u6587\uff0c\u53ef\u4ee5\u6781\u5927\u7684\u5e2e\u52a9\u7406\u89e3\u3002<\/p>\n<p>\u4ee5\u4e0b\u662f\u53c2\u8003\u8d44\u6599\uff0c\u4f1a\u4e0d\u65ad\u66f4\u65b0\u3002<\/p>\n<p>C#\u7c7b\uff1a<\/p>\n<p><a href=\"http:\/\/numerics.mathdotnet.com\/\">math.net<\/a>\u5e93\u662f\u4e00\u4e2aC#\u5b9e\u73b0\u7684\u6570\u503c\u8ba1\u7b97\u5e93\uff0c\u5728\u7b97\u6cd5\u5b9e\u73b0\u4e2d\u5927\u91cf\u5b9e\u7528\u4e86\u8fd9\u4e2a\u5e93\u63d0\u4f9b\u7684\u7ebf\u4ee3\u77e9\u9635\u64cd\u4f5c\u3002\u5982\u679c\u4f7f\u7528C++\uff0c\u4e00\u4e2a\u66f4\u6709\u540d\u7684\u5e93\u662f<a href=\"http:\/\/www.boost.org\/\">boost<\/a><\/p>\n<p><a href=\"http:\/\/msdn.microsoft.com\/\">msdn<\/a>\u6709\u4efb\u4f55\u95ee\u9898\u548c\u9519\u8bef\u6765msdn\u80af\u5b9a\u80fd\u67e5\u5230\uff0c\u6bd4csdn\u8981\u9760\u8c31\u592a\u591a\u4e86\u3002<\/p>\n<p><a href=\"http:\/\/stackoverflow.com\/\">stackoverflow<\/a>\u65e0\u6570\u6b21\u628a\u6211\u4ece\u7edd\u671b\u6df1\u6e0a\u62ef\u6551\u4e0a\u6765\u7684\u4eba\uff0c\u4ec0\u4e48\u95ee\u9898\u90fd\u53ef\u4ee5\u95ee\uff0c\u4ec0\u4e48\u95ee\u9898\u90fd\u6709\u4eba\u95ee\uff0c\u51e0\u4e4e\u90fd\u4f1a\u5f97\u5230\u6b63\u786e\u7684\u89e3\u91ca\u548c\u53c2\u8003\u4fe1\u606f\u3002<\/p>\n<p>\u7b97\u6cd5\u53ca\u539f\u7406\u7c7b\uff1a<\/p>\n<p><a href=\"http:\/\/www.imagingshop.com\/articles\/least-squares\">\u4f7f\u7528Math.NET\u8fdb\u884c\u7ebf\u6027\u4e0e\u975e\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u62df\u5408<\/a>\uff0c\u6211\u6700\u65e9\u627e\u5230\u7684\u6587\u7ae0\u4e4b\u4e00\uff0c\u6211\u51e0\u4e4e\u4ee5\u4e3a\u5355\u51ed\u8fd9\u7bc7\u6587\u7ae0\u5c31\u53ef\u4ee5\u5e2e\u52a9\u6211\u641e\u5b9a\u95ee\u9898\u3002<br \/>\n\u8fd9\u7bc7\u6587\u7ae0\u7684\u4f18\u70b9\u662f\u7f57\u5217\u4e86\u4ece\u57fa\u672c\u5230\u5e38\u7528\u7684\u51e0\u79cd\u7ebf\u6027\u4e0e\u975e\u7ebf\u6027\u7b97\u6cd5\uff0c\u63d0\u4f9b\u4e86\u6bd4\u8f83\u8be6\u7ec6\u7684\u63a8\u5bfc\u8fc7\u7a0b\uff08\u4e0d\u5305\u62ec\u7ebf\u4ee3\u7684\u5b9a\u7406\uff09\uff0c\u548c<span style=\"color: #ff0000;\"><strong>\u6240\u6709\u7684C#\u4ee3\u7801\u5b9e\u73b0<\/strong><\/span>\u3002\uff08\u4e0b\u8f7d<a href=\"http:\/\/www.imagingshop.com\/download\/article-least-squares-binary.zip\">\u4e8c\u8fdb\u5236<\/a>\uff0c<a href=\"http:\/\/www.imagingshop.com\/download\/article-least-squares-source.zip\">\u6e90\u4ee3\u7801<\/a>\uff09<br \/>\n\u4e0d\u8fc7\u8fd9\u7bc7\u6587\u7ae0\u91cc\u53ea\u6709\u5355\u53d8\u91cf\u4e8c\u7ef4\u7a7a\u95f4\u4e0a\u7684\u62df\u5408\u3002<br \/>\n\u4f7f\u7528\u8fd9\u7bc7\u6587\u7ae0\u53ca\u4ee3\u7801\u53ef\u4ee5\u4e86\u89e3\u5982\u4f55\u4f7f\u7528Math.NET\u8fdb\u884c\u77e9\u9635\u64cd\u4f5c\uff0c\u5e2e\u52a9\u6781\u5927\uff0c\u56e0\u4e3a\u5176\u4ed6\u7684\u6587\u7ae0\u504f\u5411\u4e8e\u8bba\u6587\uff0c\u5f80\u5f80\u63a8\u5bfc\u51fa\u89e3\u6cd5\u540e\u8fde\u8ba1\u7b97\u6b65\u9aa4\u90fd\u4e0d\u7ed9\uff0c\u4f7f\u7528\u8fd9\u91cc\u63d0\u4f9b\u7684\u7b97\u6cd5\u53ef\u4ee5\u5f97\u5230\u6700\u540e\u4e00\u6b65\u7684\u7ed3\u679c\u3002<br \/>\n\u6211\u5728\u4ee3\u7801\u4e2d\u627e\u5230\u4e86\u4e00\u4e2a\u5c0fBUG\uff0c\u4e8e\u662f\u7ed9\u4f5c\u8005\u5199\u4e86\u4fe1\uff0c\u4f5c\u8005\u5f88\u70ed\u5fc3\u7684\u56de\u590d\u5e76\u4e14\u544a\u8bc9\u6211\u6709\u4e2a\u4e2d\u56fd\u670b\u53cb\u8fdb\u884c\u4e86\u7ffb\u8bd1\uff0c\u8fd9\u662f\u8d75\u6bc5\u529b\u540c\u5b66\u7684<a href=\"http:\/\/cs2.swfc.edu.cn\/~zyl\/?p=875\">\u7ffb\u8bd1<\/a>\u3002\u66f4\u63a8\u8350\u5148\u9605\u8bfb\u8fd9\u4e2a\u7248\u672c\uff0c\u56e0\u4e3a\u6240\u6709\u7684\u57fa\u672c\u6982\u5ff5\u90fd\u505a\u4e86\u4ecb\u7ecd\uff0c\u4e0d\u7528\u81ea\u5df1\u53bb\u67e5\u6559\u6750\u6216\u8005\u7ef4\u57fa\u767e\u79d1\u4e86\u3002<\/p>\n<p><a href=\"http:\/\/www.caves.org\/section\/commelect\/DUSI\/openmag\/pdf\/SphereFitting.pdf\">\u65e0\u540d\u6587\u7ae0<\/a>\uff0c\u8fd9\u662f\u6211\u6b63\u5728\u4f7f\u7528\u800c\u4e14\u5e2e\u52a9\u6392\u540d\u7b2c\u4e8c\u7684\u6587\u7ae0\uff0c\u770b\u683c\u5f0f\u50cf\u8bba\u6587\u6216\u8005\u4f1a\u8bae\u4e0a\u7684\u6280\u672f\u62a5\u544a\uff0c\u4f46\u662f\u6ca1\u627e\u5230\u6807\u9898\uff0c\u8fd9\u7bc7\u6587\u7ae0\u63d0\u4f9b\u4e86\u7b1b\u5361\u5c14\u7a7a\u95f4\u4e0a\u7684\u7ebf\uff0c\u5706\u67f1\uff0c\u5706\u9525\uff0c\u7403\u7b49\u7684\u62df\u5408\u7b97\u6cd5\uff0c\u7531\u4e8e\u6ca1\u627e\u5230\u5f15\u7528\u4fe1\u606f\uff0c\u65e0\u6cd5\u5224\u65ad\u8fd9\u7bc7\u6587\u7ae0\u7684\u6b63\u786e\u6216\u8005\u6743\u5a01\u6027\uff0c\u6211\u76ee\u524d\u770b\u5230\u7a7a\u95f4\u76f4\u7ebf\u90e8\u5206\uff0c\u548c\u6211\u4eec\u516c\u53f8\u7684\u8f6f\u4ef6\u7684\u8ba1\u7b97\u7ed3\u679c\u53d6\u5f97\u4e00\u81f4\uff0c\u672a\u6765\u4e24\u5929\u4f1a\u7ee7\u7eed\u9a8c\u8bc1\u3002(1\u670823\u65e5\u6dfb\u52a0\uff0c\u5df2\u9a8c\u8bc1\u76f4\u7ebf\u5e73\u9762\u548c\u5706\u67f1\uff0c\u7b97\u6cd5\u6b63\u786e\uff09<br \/>\n\u7f3a\u70b9\u662f\u8fd9\u7bc7\u6587\u7ae0\u91cc\u53ea\u6709\u57fa\u672c\u6570\u636e\u7684\u8ba1\u7b97\u65b9\u6cd5\uff0c\u548c\u7b97\u6cd5\u601d\u8def\uff0c\u7a0d\u5fae\u5177\u4f53\u70b9\u7684\u63a8\u5bfc\u90fd\u6ca1\u6709\u3002\u4f8b\u5982\u2014\u2014\u77e9\u9635A\u662f\u6bcf\u4e2a\u70b9\u51cf\u5e73\u5747\u7b97\u51fa\u6765\u7684\uff0c\u7136\u540e\u4f7f\u7528SVD\u5bf9A\u8fdb\u884c\u8ba1\u7b97\u5c31\u53ef\u4ee5\u5f97\u5230\u7a7a\u95f4\u5411\u91cf\u7684\u89e3\u3002<br \/>\n\u5982\u679c\u6ca1\u6709\u7ebf\u4ee3\u57fa\u7840\u6216\u8005\u76f8\u5173\u7684\u7b97\u6cd5\u6982\u5ff5\u4f1a\u89c9\u5f97\u83ab\u540d\u5176\u5999\uff0c\u7ed3\u5408\u7b2c\u4e00\u7bc7\u6587\u7ae0\u770b\u5c31\u597d\u5f88\u591a\u4e86\u3002<\/p>\n<p><a href=\"http:\/\/ralph.cs.cf.ac.uk\/papers\/Geometry\/fit.pdf\">\u66f4\u539f\u7406\u6027\u7684\u4e00\u7bc7<\/a>\uff0c\u8fd9\u7bc7\u6587\u7ae0\u6709\u4e24\u4e2a\u7248\u672c\uff0c\u8fd9\u7bc7\u7a0d\u8001\uff0c\u65b0\u7684\u6ca1\u4ed4\u7ec6\u770b\uff0c\u548c\u8fd9\u4e2a\u51e0\u4e4e\u4e00\u6837<a href=\"http:\/\/ralph.cs.cf.ac.uk\/papers\/Geometry\/faithful.pdf\">Faithful\u7248\u672c<\/a>\uff0c\u8981\u8d5e\u4e00\u4e0b\u8fd9\u4e2aProf.\u8bba\u6587\u90fd\u653e\u5230\u4e86\u4e2a\u4eba\u7f51\u7ad9\u4e0a\uff0c\u7701\u5f97\u53bb\u5404\u4e2a\u9ed1\u5fc3\u7f51\u7ad9\u4e0a\u4ed8\u8d39\uff0c\u6211\u89c9\u5f97\u8bba\u6587\u8fd9\u79cd\u4e1c\u897f\u5199\u51fa\u6765\u5c31\u662f\u4e3a\u4e86\u8ba9\u5927\u5bb6\u770b\u7684\uff0c\u5356\u51e0\u5341\u5200\u5b9e\u5728\u662f\u592a\u9ed1\u4e86\u554a\u3002<br \/>\n\u4e0d\u8fc7\u5bf9\u5e94\u7528\u5c42\u9762\u5e2e\u52a9\u4e0d\u5927\uff0c\u4e0d\u8fc7\u5982\u679c\u60f3\u5bf9\u7b97\u6cd5\u5b9e\u73b0\u6539\u8fdb\uff08\u4f8b\u5982\u4ece\u6700\u5c0f\u4e8c\u4e58\u81f3\u6700\u5c0f\u5143\u7d20\u6cd5\uff09\uff0c\u5e94\u8be5\u4f1a\u6709\u5e2e\u52a9\u7684\uff0c\u7b49\u6211\u6709\u9700\u6c42\u65f6\u518d\u770b\u5427\u3002<\/p>\n<p>\u53e6\u5916\u8fd8\u6709\u51e0\u7bc7\u662f\u9488\u5bf9\u5706\u67f1\u7684\uff0c\u56e0\u4e3a\u6211\u4e2a\u4eba\u5de5\u4f5c\u7684\u9700\u6c42\u4e3b\u8981\u9488\u5bf9\u5706\u67f1\u7684\u62df\u5408\uff0c\u6240\u4ee5\u4e5f\u5217\u5728\u8fd9\u91cc\u4e86\u3002<\/p>\n<p><a href=\"http:\/\/library.wolfram.com\/infocenter\/Conferences\/7521\/cylinder_5_points_computation.pdf\">5\u70b9\u8ba1\u7b97\u5706\u67f1\u7684\u7b97\u6cd5<\/a>\uff0c\u7ed9\u51fa\u4e86\u8be6\u7ec6\u7684\u63a8\u5bfc\u548c\u5206\u6790\uff0c\u4ea7\u751f\u591a\u79cd\u7ed3\u679c\u7684\u539f\u56e0\uff0c\u4ee5\u53caMathematica\u4e0b\u7684\u4ee3\u7801\u5b9e\u73b0\u3002<\/p>\n<p><a href=\"http:\/\/arxiv.org\/pdf\/1008.5259.pdf\">\u5706\u67f1\u62df\u5408\u7684\u4ee3\u6570\u7b97\u6cd5\u5b9e\u73b0<\/a><\/p>\n<p><a href=\"http:\/\/www.geometrictools.com\/Documentation\/CylinderFitting.pdf\">\u6700\u5c0f\u8bef\u5dee\uff08\u6761\u4ef6\uff09\u53ca\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\u5706\u67f1\u7684\u5b9e\u73b0<\/a>\u5e94\u8be5\u662f\u4e00\u4e2a\u56fe\u5f62\u5e93\u7684\u6587\u6863\uff0c\u5e94\u8be5\u662f\u57fa\u4e8eC++\u548cOpenGL\u7684\u5e93\uff0c\u4e5f\u63d0\u4f9b\u4e86\u4ee3\u7801\u5b9e\u73b0\u3002\u800c\u4e14\u5e93\u4e2d\u76f4\u63a5\u5b9e\u73b0\u4e86\u57fa\u672c\u5143\u7d20\u7684\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\u5b9e\u73b0\uff0c<a href=\"http:\/\/www.geometrictools.com\/LibMathematics\/Approximation\/Wm5ApprCylinderFit3.cpp\">\u5706\u67f1C++\u5b9e\u73b0<\/a>\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5199\u8fd9\u4e9b\uff08\u4e3a\u4e86\u907f\u514d\u5355\u4e2a\u8fc7\u957f\uff09\u6587\u7ae0\u7684\u76ee\u7684\u6709\u4e24\u4e2a\uff0c\u4e00\u662f\u8bb0\u5f55\u4e0b\u6700\u8fd1\u5de5\u4f5c\u7684\u8fc7\u7a0b\u548c\u53c2\u8003\u7684\u6863\u6848\uff0c\u907f\u514d\u4ee5\u540e\u5fd8\u8bb0\u3002\u4e8c\u662f\u4e07\u4e00\u6709\u4eba\u548c &hellip; <a href=\"http:\/\/darksun190.cn\/blog\/?p=667\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u4e00\u4e9b\u57fa\u672c\u7a7a\u95f4\u5143\u7d20\u7684C#\u5b9e\u73b0 \u2014\u2014  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