{"id":512,"date":"2021-08-27T16:21:00","date_gmt":"2021-08-27T08:21:00","guid":{"rendered":"https:\/\/aif.amtbbs.org\/?p=512"},"modified":"2021-08-27T16:21:00","modified_gmt":"2021-08-27T08:21:00","slug":"%e7%a8%8b%e5%ba%8f%e8%a7%82%e7%82%b9%e4%b8%8b%e7%9a%84%e7%ba%bf%e6%80%a7%e4%bb%a3%e6%95%b0","status":"publish","type":"post","link":"https:\/\/aif.amtbbs.org\/index.php\/2021\/08\/27\/512\/","title":{"rendered":"\u7a0b\u5e8f\u89c2\u70b9\u4e0b\u7684\u7ebf\u6027\u4ee3\u6570"},"content":{"rendered":"

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          \u6240\u4ee5\uff0c\u4ece\u5e94\u7528\u7684\u89d2\u5ea6\u770b\uff0c\u7ebf\u6027\u4ee3\u6570\u662f\u4e00\u79cd\u4eba\u4e3a\u8bbe\u8ba1\u7684\u9886\u57df\u7279\u5b9a\u8bed\u8a00(DSL)<\/strong>\uff0c\u5b83\u5efa\u7acb\u4e86\u4e00\u5957\u6a21\u578b\u5e76\u901a\u8fc7\u7b26\u53f7\u7cfb\u7edf\u5b8c\u6210\u8bed\u6cd5\u548c\u8bed\u4e49\u7684\u6620\u5c04\u3002\u5b9e\u9645\u4e0a\uff0c\u5411\u91cf\u3001\u77e9\u9635\u3001\u8fd0\u7b97\u89c4\u5219\u7684\u8bed\u6cd5\u548c\u8bed\u4e49\u90fd\u662f\u4eba\u4e3a\u7684\u8bbe\u8ba1\uff0c\u8fd9\u548c\u4e00\u95e8\u8bed\u8a00\u4e2d\u7684\u5404\u79cd\u6982\u5ff5\u6027\u8d28\u76f8\u540c\uff0c\u5b83\u662f\u4e00\u79cd\u521b\u9020\uff0c\u4f46\u662f\u524d\u63d0\u662f\u5fc5\u987b\u6ee1\u8db3\u8bed\u8a00\u5951\u7ea6\u3002<\/p>\n

          \u4e3a\u4ec0\u4e48\u8981\u6709\u7ebf\u6027\u4ee3\u6570\uff1f<\/h2>\n

          \u53ef\u80fd\u6709\u4eba\u5bf9\u628a\u7ebf\u6027\u4ee3\u6570\u5f53\u6210\u4e00\u95e8DSL\u4e0d\u653e\u5fc3\uff0c\u6211\u7ed9\u4f60\u4e00\u4e2a\u77e9\u9635\uff0c\u4f60\u5c31\u628a\u6211\u7684\u56fe\u5f62\u65cb\u8f6c\u4e8660\u5ea6\u6cbfx\u8f74\u62c9\u4f38\u4e862\u500d\uff0c\u6211\u603b\u611f\u89c9\u4e0d\u8e0f\u5b9e\u554a\uff0c\u6211\u90fd\u4e0d\u77e5\u9053\u4f60\u201c\u5e95\u5c42\u201d\u662f\u600e\u4e48\u505a\uff01\u5176\u5b9e\uff0c\u8fd9\u5c31\u50cf\u6709\u7684\u7a0b\u5e8f\u5458\u7528\u9ad8\u7ea7\u8bed\u8a00\u4e0d\u8e0f\u5b9e\uff0c\u89c9\u5f97\u5e95\u5c42\u624d\u662f\u7a0b\u5e8f\u7684\u672c\u8d28\uff0c\u8001\u662f\u60f3\u77e5\u9053\u8fd9\u53e5\u8bdd\u7f16\u8bd1\u6210\u6c47\u7f16\u662f\u4ec0\u4e48\u6837\uff1f\u90a3\u4e2a\u64cd\u4f5c\u53c8\u5206\u914d\u4e86\u591a\u5c11\u5185\u5b58\uff1f\u522b\u4eba\u5728Shell\u91cc\u76f4\u63a5\u6572\u4e00\u4e2awget\u547d\u4ee4\u5c31\u80fd\u53d6\u4e0b\u4e00\u4e2a\u7f51\u9875\uff0c\u4ed6\u975e\u8981\u7528C\u8bed\u8a00\u82b1\u51e0\u5341\u5206\u949f\u6765\u5199\u4e00\u5806\u4ee3\u7801\u624d\u8e0f\u5b9e\u3002\u5176\u5b9e\uff0c\u6240\u8c13\u5e95\u5c42\u548c\u4e0a\u5c42\u53ea\u662f\u4e00\u79cd\u4e60\u60ef\u6027\u7684\u8bf4\u6cd5\uff0c\u5e76\u4e0d\u662f\u8c01\u6bd4\u8c01\u66f4\u672c\u8d28\u3002\u7a0b\u5e8f\u7684\u7f16\u8bd1\u548c\u89e3\u91ca\u672c\u8d28\u4e0a\u662f\u4e0d\u540c\u6a21\u578b\u95f4\u7684\u8bed\u4e49\u6620\u5c04<\/strong>\uff0c\u901a\u5e38\u60c5\u51b5\u4e0b\u662f\u9ad8\u7ea7\u8bed\u8a00\u6620\u5c04\u4e3a\u4f4e\u7ea7\u8bed\u8a00\uff0c\u4f46\u662f\u5b8c\u5168\u4e5f\u53ef\u4ee5\u628a\u65b9\u5411\u53cd\u8fc7\u6765\u3002Fabrice Bellard\u7528JavaScript\u5199\u4e86\u4e00\u4e2a\u865a\u62df\u673a\uff0c\u628aLinux\u8dd1\u5728JavaScript\u865a\u62df\u673a\u4e0a\uff0c\u8fd9\u5c31\u662f\u628a\u673a\u5668\u6a21\u578b\u5f80JavaScript\u6a21\u578b\u4e0a\u6620\u5c04\u3002<\/p>\n

          \u5efa\u7acb\u65b0\u6a21\u578b\u80af\u5b9a\u4f9d\u8d56\u4e8e\u73b0\u6709\u7684\u6a21\u578b\uff0c\u4f46\u8fd9\u662f\u5efa\u6a21\u7684\u624b\u6bb5\u800c\u4e0d\u662f\u76ee\u7684\uff0c\u4efb\u4f55\u4e00\u79cd\u65b0\u6a21\u578b\u7684\u76ee\u7684\u90fd\u4e3a\u4e86\u66f4\u7b80\u5355\u5730\u5206\u6790\u548c\u89e3\u51b3\u67d0\u4e00\u7c7b\u95ee\u9898\u3002\u7ebf\u6027\u4ee3\u6570\u5728\u5efa\u7acb\u7684\u65f6\u5019\uff0c\u5b83\u7684\u5404\u79cd\u6982\u5ff5\u548c\u8fd0\u7b97\u89c4\u5219\u4f9d\u8d56\u4e8e\u521d\u7b49\u6570\u5b66\u7684\u77e5\u8bc6\uff0c\u4f46\u662f\u4e00\u65e6\u5efa\u7acb\u8d77\u6765\u8fd9\u5c42\u62bd\u8c61\u6a21\u578b\u4e4b\u540e\uff0c\u6211\u4eec\u5c31\u5e94\u8be5\u4e60\u60ef\u4e8e\u76f4\u63a5\u5229\u7528\u9ad8\u5c42\u6b21\u7684\u62bd\u8c61\u6a21\u578b\u53bb\u5206\u6790\u548c\u89e3\u51b3\u95ee\u9898<\/strong>\u3002\u8bf4\u5230\u7ebf\u6027\u4ee3\u6570\u662f\u4e3a\u4e86\u6bd4\u521d\u7b49\u6570\u5b66\u66f4\u5bb9\u6613\u5730\u5206\u6790\u548c\u89e3\u51b3\u95ee\u9898\uff0c\u4e0b\u9762\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u5b9e\u9645\u611f\u53d7\u4e00\u4e0b\u5b83\u7684\u597d\u5904\uff1a<\/p>\n

          \u7ed9\u5b9a\u4e09\u89d2\u5f62\u7684\u9876\u70b9(x1, y1)<\/code>,\u00a0(x2, y2)<\/code>,\u00a0(x3, y3)<\/code>\uff0c\u6c42\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u3002<\/p><\/blockquote>\n

          \u521d\u7b49\u6570\u5b66\u4e2d\u4e09\u89d2\u5f62\u9762\u79ef\u6700\u8457\u540d\u7684\u8ba1\u7b97\u516c\u5f0f\u662farea = 1\/2 * base * height\u00a0<\/code>\uff0c\u5f53\u4e09\u89d2\u5f62\u6709\u4e00\u6761\u8fb9\u6070\u597d\u5728\u5750\u6807\u8f74\u4e0a\u65f6\u6211\u4eec\u5c31\u5f88\u5bb9\u6613\u7b97\u51fa\u5b83\u7684\u9762\u79ef\u3002\u4f46\u662f\uff0c\u5047\u5982\u540c\u6837\u4e00\u4e2a\u4e09\u89d2\u5f62\u6211\u4eec\u628a\u5750\u6807\u8f74\u65cb\u8f6c\u4e00\u4e0b\uff0c\u8ba9\u5b83\u7684\u8fb9\u4e0d\u5728\u5750\u6807\u8f74\u4e0a\uff0c\u600e\u4e48\u529e\uff1f\u6211\u4eec\u8fd8\u80fd\u5f97\u5230\u5b83\u7684\u5e95\u548c\u9ad8\u5417\uff1f\u7b54\u6848\u80af\u5b9a\u662f\u53ef\u4ee5\u7684\uff0c\u4f46\u662f\u5c31\u660e\u663e\u590d\u6742\u4e86\uff0c\u800c\u4e14\u8fd8\u8981\u5206\u5f88\u591a\u79cd\u60c5\u51b5\u53bb\u5206\u522b\u8ba8\u8bba\u3002<\/p>\n

          \u76f8\u53cd\uff0c\u5982\u679c\u6211\u4eec\u7528\u7ebf\u6027\u4ee3\u6570\u77e5\u8bc6\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u5c31\u975e\u5e38\u8f7b\u677e\u3002\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\u4e24\u4e2a\u5411\u91cfa\uff0cb\u7684\u53c9\u79ef(Cross Product)\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u5176\u65b9\u5411\u4e0ea\uff0cb\u5782\u76f4\uff0c\u5176\u5927\u5c0f\u7b49\u4e8ea\uff0cb\u6784\u6210\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef:<\/p>\n

          \"\u56fe\u7247\"<\/section>\n

          \u6211\u4eec\u53ef\u4ee5\u628a\u4e09\u89d2\u5f62\u7684\u8fb9\u89c6\u4e3a\u5411\u91cf\uff0c\u6240\u4ee5\u4e09\u89d2\u5f62\u7684\u9762\u79ef\u7b49\u4e8e\u4e24\u4e2a\u8fb9\u5411\u91cf\u7684\u53c9\u79ef\u5411\u91cf\u7684\u957f\u5ea6\u9664\u4ee5\u4e8c\uff1a<\/p>\n

          area = 1\/2 * length(cross_product((x2 - x1, y2 - y1), (x3 - x1, y3 - y1)))<\/code><\/pre>\n
          \u6ce8\uff1alength\u8868\u793a\u53d6\u5411\u91cf\u957f\u5ea6\uff0ccross_product\u8868\u793a\u4e24\u4e2a\u5411\u91cf\u7684\u53c9\u79ef\u3002<\/p>\n
          \u8fd9\u6837\u4e00\u4e2a\u5728\u521d\u7b49\u6570\u5b66\u91cc\u9762\u6709\u70b9\u513f\u5c0f\u96be\u7684\u95ee\u9898\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\u77ac\u95f4\u641e\u5b9a\uff01\u53ef\u80fd\u6709\u4eba\u4f1a\u8bf4\uff0c\u4f60\u76f4\u63a5\u57fa\u4e8e\u53c9\u79ef\u6765\u505a\uff0c\u5f53\u7136\u7b80\u5355\u4e86\uff0c\u4f46\u662f\u53c9\u79ef\u672c\u8eab\u4e0d\u662f\u4e5f\u633a\u590d\u6742\u7684\u5417\uff1f\u4f60\u628a\u5b83\u5c55\u5f00\u8bd5\u8bd5\u770b\u5462\uff1f\u662f\u7684\uff0c\u6a21\u578b\u7684\u4f5c\u7528\u5c31\u662f\u628a\u4e00\u90e8\u5206\u590d\u6742\u6027\u9690\u85cf\u5230\u6a21\u578b\u4e2d<\/strong>\uff0c\u4f7f\u5f97\u6a21\u578b\u7684\u4f7f\u7528\u8005\u53ef\u4ee5\u66f4\u52a0\u7b80\u5355\u5730\u89e3\u51b3\u95ee\u9898\u3002\u66fe\u7ecf\u6709\u4eba\u8d28\u7591C++\u592a\u590d\u6742\uff0cC++\u4e4b\u7236Bjarne Stroustrup\u8fd9\u6837\u56de\u7b54\uff1a<\/p>\n
          Complexity will go somewhere: if not the language then the application code.<\/p><\/blockquote>\n
          \u5728\u7279\u5b9a\u73af\u5883\u4e0b\uff0c\u95ee\u9898\u7684\u590d\u6742\u6027\u662f\u7531\u5176\u672c\u8d28\u51b3\u5b9a\u7684\uff0cC++\u628a\u4e00\u90e8\u5206\u7684\u590d\u6742\u6027\u7eb3\u5165\u4e86\u8bed\u8a00\u548c\u6807\u51c6\u5e93\uff0c\u76ee\u7684\u662f\u4f7f\u5f97\u5e94\u7528\u7a0b\u5e8f\u66f4\u4e3a\u7b80\u5355\u3002\u5f53\u7136\uff0c\u5e76\u975e\u6240\u6709\u573a\u5408C++\u90fd\u4f7f\u5f97\u95ee\u9898\u66f4\u52a0\u7b80\u5355\uff0c\u4f46\u662f\u4ece\u539f\u7406\u4e0a\u8bb2\uff0cC++\u7684\u590d\u6742\u6027\u662f\u6709\u9053\u7406\u7684\u3002\u9664\u4e86C++\uff0cJava\u3001SQL\u3001CSS\u7b49\u5404\u79cd\u8bed\u8a00\u548c\u6846\u67b6\u83ab\u4e0d\u5982\u662f\uff0c\u60f3\u8c61\u4e00\u4e0b\uff0c\u5982\u679c\u4e0d\u4f7f\u7528\u6570\u636e\u5e93\uff0c\u52a8\u4e0d\u52a8\u5c31\u81ea\u5df1\u53bb\u505a\u6570\u636e\u5b58\u50a8\u548c\u7ba1\u7406\u662f\u591a\u4e48\u590d\u6742\u554a\uff01\u8fd9\u6837\u6211\u4eec\u5c31\u4e0d\u96be\u7406\u89e3\u4e3a\u4ec0\u4e48\u7ebf\u6027\u4ee3\u6570\u8981\u5b9a\u4e49\u53c9\u79ef\u8fd9\u6837\u5947\u602a\u7684\u8fd0\u7b97\u4e86\uff0c\u5b83\u548cC++\u628a\u5f88\u591a\u5e38\u7528\u7684\u7b97\u6cd5\u548c\u5bb9\u5668\u7eb3\u5165STL\u662f\u540c\u4e00\u9053\u7406\u3002\u540c\u6837\u7684\uff0c\u751a\u81f3\u4f60\u8fd8\u53ef\u4ee5\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\u5b9a\u4e49\u81ea\u5df1\u60f3\u8981\u7684\u8fd0\u7b97\u62ff\u6765\u590d\u7528\u3002\u6240\u4ee5\uff0c\u6570\u5b66\u4e00\u70b9\u513f\u4e0d\u6b7b\u677f\uff0c\u5b83\u548c\u7a0b\u5e8f\u4e00\u6837\u662f\u6d3b\u6d3b\u6cfc\u6cfc\u7684\uff0c\u4f60\u7406\u89e3\u4e86\u5b83\u7684\u6765\u9f99\u53bb\u8109\u5c31\u80fd\u9a7e\u9a6d\u81ea\u5982\u3002\u8bf4\u5230\u8fd9\u91cc\uff0c\u6211\u4eec\u5c31\u987a\u4fbf\u56de\u7b54\u4e00\u4e2a\u5f88\u5e38\u89c1\u7684\u7591\u60d1\uff1a<\/p>\n
          \u7ebf\u6027\u4ee3\u6570\u7684\u70b9\u79ef\u3001\u53c9\u79ef\u8fd8\u6709\u77e9\u9635\u8fd0\u7b97\u90fd\u5f88\u5947\u602a\uff0c\u4e3a\u4ec0\u4e48\u8981\u5b9a\u4e49\u8fd9\u4e9b\u8fd0\u7b97\u5462\uff1f\u5b83\u4eec\u7684\u5b9a\u4e49\u53c8\u4e3a\u4ec0\u4e48\u662f\u8fd9\u4e2a\u6837\u5b50\u5462\uff1f<\/p><\/blockquote>\n
          \u5176\u5b9e\uff0c\u548c\u7a0b\u5e8f\u590d\u7528\u4e00\u6837\uff0c\u7ebf\u6027\u4ee3\u6570\u5b9a\u4e49\u70b9\u79ef\u3001\u53c9\u79ef\u548c\u77e9\u9635\u8fd0\u7b97\u662f\u56e0\u4e3a\u5b83\u4eec\u7684\u5e94\u7528\u975e\u5e38\u5e7f\uff0c\u6709\u5f88\u5927\u7684\u590d\u7528\u4ef7\u503c\uff0c\u53ef\u4ee5\u4f5c\u4e3a\u6211\u4eec\u5206\u6790\u548c\u89e3\u51b3\u95ee\u9898\u7684\u57fa\u7840\u3002\u6bd4\u5982\uff0c\u5f88\u591a\u95ee\u9898\u90fd\u6d89\u53ca\u5230\u4e00\u4e2a\u5411\u91cf\u5230\u53e6\u4e00\u4e2a\u5411\u91cf\u7684\u6295\u5f71\u6216\u662f\u6c42\u4e24\u4e2a\u5411\u91cf\u7684\u5939\u89d2\uff0c\u90a3\u4e48\u5c31\u4f1a\u8003\u8651\u4e13\u95e8\u5b9a\u4e49\u70b9\u79ef(Dot Product)\u8fd9\u4e2a\u8fd0\u7b97\uff1a<\/p>\n
          \"\u56fe\u7247\"<\/section>\n
          \u70b9\u79ef\u6982\u5ff5\u7684\u63d0\u51fa\u5c5e\u4e8e\u8bbe\u8ba1\uff0c\u6709\u53d1\u6325\u521b\u9020\u7684\u4f59\u5730\uff1b\u4e00\u65e6\u8bbe\u8ba1\u5b9a\u4e86\uff0c\u5177\u4f53\u516c\u5f0f\u5c31\u4e0d\u80fd\u968f\u610f\u53d1\u6325\u4e86\uff0c\u5fc5\u987b\u7b26\u5408\u903b\u8f91\uff0c\u4fdd\u8bc1\u5b83\u6620\u5c04\u5230\u521d\u7b49\u6570\u5b66\u6a21\u578b\u7684\u6b63\u786e\u6027\u3002\u8fd9\u5c31\u50cf\u4e00\u95e8\u9ad8\u7ea7\u8bed\u8a00\u53ef\u4ee5\u5b9a\u4e49\u5f88\u591a\u6982\u5ff5\uff0c\u4ec0\u4e48\u9ad8\u9636\u51fd\u6570\u3001\u95ed\u5305\u7b49\u7b49\uff0c\u4f46\u662f\u5b83\u5fc5\u987b\u4fdd\u8bc1\u6620\u5c04\u5230\u5e95\u5c42\u5b9e\u73b0\u65f6\u5728\u6267\u884c\u4ea7\u751f\u7684\u6548\u679c\u7b26\u5408\u5176\u5b9a\u4e49\u7684\u89c4\u8303\u3002<\/p>\n
          \u7ebf\u6027\u4ee3\u6570\u597d\u5728\u54ea\u91cc\uff1f<\/h2>\n
          \u4e0a\u9762\u8bf4\u4e86\uff0c\u7ebf\u6027\u4ee3\u6570\u662f\u4e00\u79cd\u9ad8\u5c42\u6b21\u62bd\u8c61\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528\u5b66\u4e60\u4e00\u95e8\u7a0b\u5e8f\u8bed\u8a00\u7684\u65b9\u6cd5\u53bb\u5b66\u4e60\u5b83\u7684\u8bed\u6cd5\u548c\u8bed\u4e49\uff0c\u4f46\u662f\u8fd9\u4e00\u8ba4\u8bc6\u4e0d\u53ea\u9488\u5bf9\u7ebf\u6027\u4ee3\u6570\uff0c\u5b83\u662f\u5bf9\u6bcf\u4e00\u95e8\u6570\u5b66\u5b66\u79d1\u901a\u7528\u7684\uff0c\u53ef\u80fd\u6709\u4eba\u4f1a\u6709\u7591\u95ee<\/p>\n
          \u5fae\u79ef\u5206\u3001\u6982\u7387\u8bba\u4e5f\u662f\u9ad8\u5c42\u6b21\u62bd\u8c61\uff0c\u90a3\u4e48\u7ebf\u6027\u4ee3\u6570\u8fd9\u79cd\u9ad8\u5c42\u6b21\u62bd\u8c61\u7684\u7279\u70b9\u5728\u54ea\u91cc\u5462\uff1f<\/p><\/blockquote>\n
          \u8fd9\u5c31\u95ee\u5230\u4e86\u6839\u672c\u4e0a\uff0c\u7ebf\u6027\u4ee3\u6570\u7684\u6838\u5fc3\uff1a\u5411\u91cf\u6a21\u578b<\/strong>\u3002\u6211\u4eec\u5728\u521d\u7b49\u6570\u5b66\u4e2d\u5b66\u4e60\u7684\u5750\u6807\u7cfb\u5c5e\u4e8e\u7b1b\u5361\u5c14\u6240\u63d0\u51fa\u7684\u89e3\u6790\u6a21\u578b\uff0c\u8fd9\u4e2a\u6a21\u578b\u5f88\u6709\u7528\uff0c\u4f46\u540c\u65f6\u4e5f\u6709\u5f88\u5927\u7684\u7f3a\u70b9\u3002\u5750\u6807\u7cfb\u662f\u4eba\u4e3a\u52a0\u4e0a\u7684\u865a\u62df\u53c2\u8003\u7cfb\uff0c\u4f46\u662f\u6211\u4eec\u8981\u89e3\u51b3\u7684\u95ee\u9898\uff0c\u6bd4\u5982\u6c42\u9762\u79ef\uff0c\u56fe\u5f62\u65cb\u8f6c\u3001\u62c9\u4f38\u7b49\u5e94\u7528\u90fd\u662f\u548c\u5750\u6807\u7cfb\u65e0\u5173\u7684\uff0c\u5efa\u7acb\u4e00\u4e2a\u865a\u62df\u7684\u5750\u6807\u7cfb\u5f80\u5f80\u65e0\u52a9\u4e8e\u89e3\u51b3\u95ee\u9898\uff0c\u521a\u624d\u4e09\u89d2\u5f62\u9762\u79ef\u7684\u4f8b\u5b50\u5c31\u662f\u8fd9\u6837\u3002<\/p>\n
          \u5411\u91cf\u6a21\u578b\u5f88\u597d\u5730\u514b\u670d\u4e86\u89e3\u6790\u6a21\u578b\u7684\u7f3a\u70b9\uff0c\u5982\u679c\u8bf4\u89e3\u6790\u6a21\u578b\u4ee3\u8868\u4e86\u67d0\u79cd\u201c\u7edd\u5bf9\u6027\u201d\u7684\u4e16\u754c\u89c2\uff0c\u90a3\u4e48\u5411\u91cf\u6a21\u578b\u5c31\u4ee3\u8868\u4e86\u67d0\u79cd\u201c\u76f8\u5bf9\u6027\u201d\u7684\u4e16\u754c\u89c2\uff0c\u6211\u63a8\u8350\u628a\u5411\u91cf\u6a21\u578b\u548c\u89e3\u6790\u6a21\u578b\u770b\u4f5c\u5bf9\u7acb\u7684\u4e24\u79cd\u6a21\u578b\u3002<\/p>\n
          \u5411\u91cf\u6a21\u578b\u4e2d\u5b9a\u4e49\u4e86\u5411\u91cf\u548c\u6807\u91cf\u7684\u6982\u5ff5\u3002\u5411\u91cf\u5177\u6709\u5927\u5c0f\u548c\u65b9\u5411\uff0c\u6ee1\u8db3\u7ebf\u6027\u7ec4\u5408\u6cd5\u5219\uff1b\u6807\u91cf\u662f\u53ea\u6709\u5927\u5c0f\u6ca1\u6709\u65b9\u5411\u7684\u91cf\uff08\u6ce8\uff1a\u6807\u91cf\u7684\u53e6\u4e00\u79cd\u66f4\u6df1\u523b\u7684\u5b9a\u4e49\u662f\u5728\u5750\u6807\u53d8\u6362\u4e2d\u4fdd\u6301\u4e0d\u53d8\u7684\u91cf\uff09\u3002\u5411\u91cf\u6a21\u578b\u7684\u4f18\u70b9\u4e4b\u4e00\u662f\u5176\u5750\u6807\u7cfb\u65e0\u5173\u6027<\/strong>\uff0c\u4e5f\u5c31\u662f\u76f8\u5bf9\u6027\uff0c\u5b83\u5728\u5b9a\u4e49\u5411\u91cf\u548c\u8fd0\u7b97\u89c4\u5219\u7684\u65f6\u5019\u4ece\u4e00\u5f00\u59cb\u5c31\u629b\u5f00\u4e86\u5750\u6807\u7cfb\u7684\u675f\u7f1a\uff0c\u4e0d\u7ba1\u4f60\u5750\u6807\u8f74\u600e\u4e48\u65cb\u8f6c\uff0c\u6211\u90fd\u80fd\u9002\u5e94\uff0c\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u3001\u5185\u79ef\u3001\u53c9\u79ef\u3001\u7ebf\u6027\u53d8\u6362\u7b49\u7b49\u8fd0\u7b97\u5168\u90e8\u90fd\u662f\u5750\u6807\u7cfb\u65e0\u5173\u7684\u3002\u6ce8\u610f\uff0c\u6240\u8c13\u5750\u6807\u7cfb\u65e0\u5173\u6027\u4e0d\u662f\u8bf4\u5c31\u6ca1\u6709\u5750\u6807\u7cfb\u4e86\uff0c\u8fd8\u662f\u6709\u7684\uff0c\u521a\u624d\u4e09\u89d2\u5f62\u4f8b\u5b50\u7684\u9876\u70b9\u5c31\u662f\u7528\u5750\u6807\u8868\u793a\u7684\uff0c\u53ea\u662f\u5728\u89e3\u51b3\u95ee\u9898\u7684\u65f6\u5019\u4e0d\u540c\u7684\u5750\u6807\u7cfb\u4e0d\u4f1a\u6784\u6210\u5f71\u54cd\u3002\u7528\u4e00\u4e2a\u6bd4\u55bb\uff0cJava\u53f7\u79f0\u5e73\u53f0\u65e0\u5173\uff0c\u4e0d\u662f\u8bf4Java\u5c31\u662f\u7a7a\u4e2d\u697c\u9601\uff0c\u800c\u662f\u8bf4\u4f60\u7528Java\u7f16\u7a0b\u65f6\u5e95\u5c42\u662fLinux\u8fd8\u662fWindows\u5f80\u5f80\u5bf9\u4f60\u6ca1\u6709\u5f71\u54cd\u3002<\/p>\n
          \u5411\u91cf\u6a21\u578b\u6709\u4ec0\u4e48\u597d\u5904\u5462\uff1f\u9664\u4e86\u521a\u624d\u4e09\u89d2\u5f62\u9762\u79ef\u95ee\u9898\u662f\u4e00\u4e2a\u4f8b\u5b50\uff0c\u4e0b\u9762\u6211\u518d\u4e3e\u4e00\u4e2a\u51e0\u4f55\u7684\u4f8b\u5b50\uff1a<\/p>\n
          \u7ed9\u5b9a\u4e09\u7ef4\u5750\u6807\u7cfb\u4e2d\u7684\u4e00\u70b9(x0, y0, z0)<\/code>\u548c\u4e00\u4e2a\u5e73\u9762a*x + b*y + c*z + d = 0<\/code>\uff0c\u6c42\u70b9\u5230\u5e73\u9762\u7684\u5782\u76f4\u8ddd\u79bb\uff1f<\/p><\/blockquote>\n
          \"\u56fe\u7247\"<\/p>\n
          \u8fd9\u4e2a\u95ee\u9898\u5982\u679c\u662f\u8981\u4ece\u89e3\u6790\u51e0\u4f55\u7684\u89d2\u5ea6\u53bb\u89e3\u51b3\u51e0\u4e4e\u590d\u6742\u5230\u6ca1\u6cd5\u4e0b\u624b\uff0c\u9664\u975e\u662f\u5e73\u9762\u6070\u597d\u662f\u8fc7\u5750\u6807\u8f74\u7684\u7279\u6b8a\u60c5\u51b5\uff0c\u4f46\u662f\u5982\u679c\u4ece\u5411\u91cf\u6a21\u578b\u8003\u8651\u5c31\u5f88\u7b80\u5355\uff1a\u6839\u636e\u5e73\u9762\u65b9\u7a0b\uff0c\u5e73\u9762\u7684\u6cd5\u5411\u91cf(Normal Vector)\u662fv=(a, b, c)<\/code>\uff0c\u8bbe\u4ece\u5e73\u9762\u4e0a\u4efb\u610f\u4e00\u70b9(x, y, z)<\/code>\u5230(x0, y0, z0)<\/code>\u7684\u5411\u91cf\u4e3aw<\/code>\uff0c\u90a3\u4e48\u901a\u8fc7\u70b9\u79efdot_product(w, v)<\/code>\u7b97\u51faw<\/code>\u5230v<\/code>\u7684\u6295\u5f71\u5411\u91cfp<\/code>\uff0c\u5176\u5927\u5c0f\u5c31\u662f(x0, y0, z0)<\/code>\u5230\u5e73\u9762a*x + b*y + c*z + d = 0<\/code>\u7684\u5782\u76f4\u8ddd\u79bb\u3002\u8fd9\u91cc\u7528\u5230\u4e86\u5411\u91cf\u6a21\u578b\u7684\u57fa\u672c\u6982\u5ff5\uff1a\u6cd5\u5411\u91cf\uff0c\u6295\u5f71\u5411\u91cf\uff0c\u70b9\u79ef\uff0c\u6574\u4e2a\u95ee\u9898\u89e3\u51b3\u8fc7\u7a0b\u7b80\u6d01\u660e\u5feb\u3002<\/p>\n
          \u4e0b\u9762\u518d\u7ed9\u5927\u5bb6\u7559\u4e00\u9053\u76f8\u4f3c\u7684\u7ec3\u4e60\u9898\uff08\u719f\u6089\u673a\u5668\u5b66\u4e60\u7684\u670b\u53cb\u53ef\u80fd\u4f1a\u53d1\u73b0\u8fd9\u662f\u7ebf\u6027\u4ee3\u6570\u5728\u7ebf\u6027\u5206\u7c7b\u4e2d\u7684\u5e94\u7528\uff09\uff1a<\/p>\n
          \u7ed9\u5b9an\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e24\u70b9(a1, a2, ... an)<\/code>\uff0c(b1, b2, ... bn)<\/code>\u548c\u4e00\u4e2a\u8d85\u5e73\u9762c1*x1 + c2*x2 ... + cn*xn + d = 0<\/code>\uff0c\u8bf7\u5224\u65ad\u4e24\u70b9\u5728\u8d85\u5e73\u9762\u7684\u540c\u4fa7\u6216\u5f02\u4fa7\uff1f<\/p><\/blockquote>\n
          \u79bb\u5f00\u5411\u91cf\uff0c\u4e0b\u9762\u6211\u4eec\u8981\u8bf7\u51fa\u7ebf\u6027\u4ee3\u6570\u7684\u53e6\u4e00\u4e2a\u4e3b\u89d2\uff1a\u77e9\u9635(Matrix)\u3002<\/p>\n
          \u7ebf\u6027\u4ee3\u6570\u5b9a\u4e49\u4e86\u77e9\u9635\u548c\u5411\u91cf\u3001\u77e9\u9635\u548c\u77e9\u9635\u7684\u4e58\u6cd5\uff0c\u8fd0\u7b97\u89c4\u5219\u5f88\u590d\u6742\uff0c\u7528\u6765\u505a\u4ec0\u4e48\u4e5f\u4e0d\u6e05\u695a\uff0c\u5f88\u591a\u521d\u5b66\u8005\u90fd\u4e0d\u80fd\u5f88\u597d\u5730\u7406\u89e3\uff0c\u53ef\u4ee5\u8bf4\u77e9\u9635\u662f\u5b66\u597d\u7ebf\u6027\u4ee3\u6570\u7684\u62e6\u8def\u864e\u3002\u9047\u5230\u590d\u6742\u7684\u4e1c\u897f\uff0c\u5f80\u5f80\u9700\u8981\u5148\u907f\u514d\u4e00\u5934\u9677\u5165\u7ec6\u8282\uff0c\u5148\u4ece\u6574\u4f53\u4e0a\u628a\u63e1\u5b83\u3002\u5176\u5b9e\uff0c\u4ece\u7a0b\u5e8f\u7684\u89d2\u5ea6\u770b\uff0c\u65e0\u8bba\u5f62\u5f0f\u591a\u4e48\u5947\u602a\uff0c\u5b83\u65e0\u975e\u662f\u4e00\u79cd\u8bed\u6cd5\uff0c\u8bed\u6cd5\u5fc5\u7136\u5bf9\u5e94\u4e86\u8bed\u4e49\uff0c\u6240\u4ee5\u7406\u89e3\u77e9\u9635\u7684\u91cd\u70b9\u5728\u4e8e\u7406\u89e3\u5176\u8bed\u4e49\u3002\u77e9\u9635\u7684\u8bed\u4e49\u4e0d\u6b62\u4e00\u79cd\uff0c\u5728\u4e0d\u540c\u7684\u73af\u5883\u4e2d\u6709\u4e0d\u540c\u7684\u8bed\u4e49\uff0c\u5728\u540c\u4e00\u73af\u5883\u4e2d\u4e5f\u53ef\u4ee5\u6709\u4e0d\u540c\u7684\u89e3\u8bfb\uff0c\u6700\u5e38\u89c1\u7684\u5305\u62ec\uff1a1)\u8868\u793a\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\uff1b2)\u8868\u793a\u5217\u5411\u91cf\u6216\u884c\u5411\u91cf\u7684\u96c6\u5408\uff1b3)\u8868\u793a\u5b50\u77e9\u9635\u7684\u96c6\u5408\u3002<\/p>\n
          \u77e9\u9635\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\u5bf9\u5e94\u7684\u662f\u7ebf\u6027\u53d8\u6362\u8bed\u4e49\uff1a\u7528\u77e9\u9635A<\/code>\u4e58\u4ee5\u4e00\u4e2a\u5411\u91cfv<\/code>\u5f97\u5230w<\/code>\uff0c\u77e9\u9635A<\/code>\u5c31\u4ee3\u8868\u4e86v<\/code>\u5230w<\/code>\u7684\u7ebf\u6027\u53d8\u6362\u3002\u6bd4\u5982\uff0c\u5982\u679c\u60f3\u8981\u628a\u5411\u91cfv0<\/code>\u6309\u9006\u65f6\u9488\u65b9\u5411\u65cb\u8f6c60\u5ea6\u5f97\u5230v'<\/code>\uff0c\u53ea\u9700\u8981\u7528\u65cb\u8f6c\u53d8\u6362\u77e9\u9635\uff08Rotation Matrix)\u53bb\u4e58v0<\/code>\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n
          \"\u56fe\u7247\"<\/p>\n
          \"\u56fe\u7247\"<\/p>\n
          \u9664\u4e86\u65cb\u8f6c\u53d8\u6362\uff0c\u62c9\u4f38\u53d8\u6362\u4e5f\u662f\u4e00\u79cd\u5e38\u89c1\u7684\u53d8\u6362\uff0c\u6bd4\u5982\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u62c9\u4f38\u77e9\u9635\u628a\u5411\u91cf\u6cbfx\u8f74\u62c9\u4f382\u500d\uff08\u8bf7\u8bd5\u7740\u81ea\u5df1\u7ed9\u51fa\u62c9\u4f38\u77e9\u9635\u7684\u5f62\u5f0f\uff09\u3002\u66f4\u91cd\u8981\u7684\u662f\uff0c\u77e9\u9635\u4e58\u6cd5\u6709\u4e00\u4e2a\u5f88\u597d\u7684\u6027\u8d28\uff1a\u6ee1\u8db3\u7ed3\u5408\u7387\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u53ef\u4ee5\u5bf9\u7ebf\u6027\u53d8\u6362\u8fdb\u884c\u53e0\u52a0<\/strong>\u3002\u4e3e\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u201c\u6cbf\u9006\u65f6\u9488\u65cb\u8f6c60\u5ea6\u201d\u7684\u77e9\u9635M\u548c\u201c\u6cbfx\u8f74\u62c9\u4f382\u500d\u201d\u7684\u77e9\u9635N\u76f8\u4e58\uff0c\u5f97\u5230\u4e00\u4e2a\u65b0\u77e9\u9635T\u6765\u4ee3\u8868\u201c\u6cbf\u9006\u65f6\u9488\u65cb\u8f6c60\u5ea6\u5e76\u6cbfx\u8f74\u62c9\u4f382\u500d\u201d\u3002\u8fd9\u662f\u4e0d\u662f\u5f88\u50cf\u6211\u4eecShell\u4e2d\u628a\u591a\u4e2a\u547d\u4ee4\u901a\u8fc7\u7ba1\u9053\u8fdb\u884c\u53e0\u52a0\u5462\uff1f<\/p>\n
          \u4e0a\u9762\u91cd\u70b9\u4ecb\u7ecd\u4e86\u5411\u91cf\u6a21\u578b\u7684\u5750\u6807\u7cfb\u65e0\u5173\u6027\uff0c\u9664\u6b64\u4e4b\u5916\uff0c\u5411\u91cf\u6a21\u578b\u7684\u53e6\u4e00\u4f18\u70b9\u662f\u5b83\u80fd\u63cf\u8ff0\u7ebf\u6027\u5173\u7cfb<\/strong>\uff0c\u4e0b\u9762\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u719f\u6089\u7684Fibonacci\u6570\u5217\u7684\u4f8b\u5b50\uff1a<\/p>\n
          Fibonacci\u6570\u5217\u5b9a\u4e49\u4e3a\uff1af(n) = f(n-1) + f(n-2), f(0) = 0, f(1) = 1<\/code>\uff1b\u95ee\u9898\uff1a\u8f93\u5165n\uff0c\u8bf7\u7ed9\u51fa\u6c42f(n)<\/code>\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e0d\u8d85\u8fc7O(logn)\u7684\u7b97\u6cd5\u3002<\/p><\/blockquote>\n
          \u9996\u5148\uff0c\u6211\u4eec\u6784\u9020\u4e24\u4e2a\u5411\u91cfv1=(f(n+1), f(n))<\/code>\u548cv2=(f(n+2), f(n+1))<\/code>\uff0c\u6839\u636eFibonacci\u6570\u5217\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4ecev1<\/code>\u5230v2<\/code>\u7684\u9012\u63a8\u53d8\u6362\u77e9\u9635\uff1a<\/p>\n
          \"\u56fe\u7247\"<\/p>\n
          \u5e76\u8fdb\u4e00\u6b65\u5f97\u5230\uff1a<\/p>\n
          \"\u56fe\u7247\"<\/p>\n
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