{"id":305558,"date":"2024-05-20T19:49:24","date_gmt":"2024-05-20T11:49:24","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/305558.html"},"modified":"2024-05-20T19:49:30","modified_gmt":"2024-05-20T11:49:30","slug":"%e5%a6%82%e4%bd%95%e8%be%93%e5%87%ba%e4%b8%a4%e4%b8%aa%e7%bb%8f%e7%ba%ac%e5%ba%a6%e4%b9%8b%e9%97%b4%e6%af%8f%e6%ae%b5%e8%b7%9d%e7%a6%bb%e7%9a%84%e7%bb%8f%e7%ba%ac%e5%ba%a6%e5%9d%90%e6%a0%87","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/305558.html","title":{"rendered":"\u5982\u4f55\u8f93\u51fa\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u4e4b\u95f4\u6bcf\u6bb5\u8ddd\u79bb\u7684\u7ecf\u7eac\u5ea6\u5750\u6807"},"content":{"rendered":"<p style=\"text-align:center\"><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/26221905\/c6e68b98-0c84-41be-a1d3-814711ac96e2.webp\" alt=\"\u5982\u4f55\u8f93\u51fa\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u4e4b\u95f4\u6bcf\u6bb5\u8ddd\u79bb\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\" \/><\/p>\n<p><p>\u7ecf\u7eac\u5ea6\u5750\u6807\u662f\u786e\u5b9a\u5730\u7403\u8868\u9762\u4efb\u610f\u70b9\u4f4d\u7f6e\u7684\u7cfb\u7edf\u3002\u8ba1\u7b97\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u5e76\u8f93\u51fa\u5404\u6bb5\u7ecf\u7eac\u5ea6\uff0c\u4e3b\u8981\u6d89\u53ca\u7403\u9762\u4e09\u89d2\u5b66\u548c\u5730\u7406\u4fe1\u606f\u7cfb\u7edf\uff08GIS\uff09\u7684\u77e5\u8bc6\u3002<strong>\u7403\u9762\u4e0a\u7684\u4e24\u70b9\u95f4\u6700\u77ed\u8def\u5f84\u79f0\u4e3a\u5927\u5706\u822a\u7ebf\u3001\u8def\u5f84\u53ef\u4ee5\u901a\u8fc7\u5206\u5272\u70b9\u7ec6\u5316<\/strong>\u3002\u4ee5\u5730\u7403\u4e3a\u53c2\u8003\uff0c\u5f53\u5df2\u77e5\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u70b9\u65f6\uff0c\u6700\u77ed\u8def\u5f84\u5373\u8fd9\u4e24\u70b9\u95f4\u7684\u5927\u5706\u8def\u5f84\u3002\u901a\u5e38\uff0c\u8fd9\u6761\u8def\u5f84\u4e0d\u4f1a\u9075\u5faa\u6052\u5b9a\u7684\u7ecf\u5ea6\u6216\u7eac\u5ea6\u7ebf\uff0c\u800c\u662f\u4f1a\u5448\u5f27\u7ebf\u5f62\u3002\u901a\u5e38\uff0c\u53ef\u4ee5\u4f7f\u7528Haversine\u516c\u5f0f\u6765<a href=\"https:\/\/docs.pingcode.com\/agile\/project-management\/estimation\" target=\"_blank\">\u4f30\u7b97<\/a>\u4e24\u70b9\u95f4\u7684\u8ddd\u79bb\uff0c\u5e76\u5229\u7528\u7ebf\u6027\u63d2\u503c\u7b49\u65b9\u6cd5\uff0c\u6765\u8ba1\u7b97\u8def\u5f84\u4e0a\u7684\u5206\u6bb5\u70b9\u5750\u6807\u3002<\/p>\n<\/p>\n<p><h3>\u4e00\u3001\u786e\u5b9a\u8ddd\u79bb\u548c\u8def\u5f84<\/h3>\n<\/p>\n<p><p>\u8981\u6c42\u51fa\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u70b9\u4e4b\u95f4\u8ddd\u79bb\u7684\u4e0d\u540c\u6bb5\uff0c\u5e76\u8f93\u51fa\u5404\u6bb5\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\uff0c\u4e3b\u8981\u5305\u62ec\u4e24\u4e2a\u6b65\u9aa4\uff1a\u9996\u5148\uff0c\u8ba1\u7b97\u4e24\u70b9\u4e4b\u95f4\u7684\u603b\u8ddd\u79bb\uff1b\u5176\u6b21\uff0c\u786e\u5b9a\u8fd9\u4e24\u70b9\u95f4\u7684\u8def\u5f84\u3002\u4f7f\u7528Haversine\u516c\u5f0f\u53ef\u4ee5\u6c42\u51fa\u7403\u9762\u4e24\u70b9\u95f4\u7684\u8fd1\u4f3c\u8ddd\u79bb\u3002\u5927\u5706\u822a\u7ebf\u53ef\u4ee5\u901a\u8fc7\u89e3\u6790\u5730\u7403\u8868\u9762\u4e0a\u4e24\u70b9\u95f4\u7684\u521d\u59cb\u822a\u5411\u548c\u7ec8\u70b9\u822a\u5411\u6765\u786e\u5b9a\u3002<\/p>\n<\/p>\n<p><h3>\u4e8c\u3001\u4f7f\u7528Haversine\u516c\u5f0f<\/h3>\n<\/p>\n<p><p><strong>Haversine\u516c\u5f0f\u662f\u8ba1\u7b97\u7403\u9762\u4e0a\u4e24\u70b9\u95f4\u8ddd\u79bb\u7684\u7ecf\u5178\u516c\u5f0f<\/strong>\uff0c\u662f\u8ba1\u7b97\u5927\u5706\u8ddd\u79bb\u7684\u4e00\u4e2a\u975e\u5e38\u597d\u7684\u8fd1\u4f3c\u65b9\u6cd5\u3002\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p><p>( a = \\sin\u00b2(\\frac{\u0394\u03c6}{2}) + \\cos \u03c6_1 * \\cos \u03c6_2 * \\sin\u00b2(\\frac{\u0394\u03bb}{2}) )<\/p>\n<\/p>\n<p><p>( c = 2 * \\text{atan2}( \\sqrt{a}, \\sqrt{1-a} ) )<\/p>\n<\/p>\n<p><p>( d = R * c )<\/p>\n<\/p>\n<p><p>\u5176\u4e2d\uff0c( \u03c6_1, \u03c6_2 )\u662f\u4e24\u70b9\u7684\u7eac\u5ea6\uff0c( \u03bb_1, \u03bb_2 )\u662f\u4e24\u70b9\u7684\u7ecf\u5ea6\uff0c( R )\u662f\u5730\u7403\u534a\u5f84\uff08\u5927\u7ea66371\u516c\u91cc\uff09\uff0c( d )\u662f\u4e24\u70b9\u95f4\u7684\u8ddd\u79bb\u3002\u901a\u8fc7\u8ba1\u7b97\u8d77\u59cb\u70b9\u548c\u7ec8\u70b9\u4e4b\u95f4\u7684\u7ecf\u7eac\u5ea6\u5dee\u503c\uff0c\u53ef\u4ee5\u5728\u8fd9\u4e2a\u516c\u5f0f\u7684\u57fa\u7840\u4e0a\uff0c\u6c42\u51fa\u4e24\u5730\u4e4b\u95f4\u7684\u5927\u5706\u8ddd\u79bb\u3002<\/p>\n<\/p>\n<p><h3>\u4e09\u3001\u7ec6\u5316\u8def\u5f84\u5750\u6807<\/h3>\n<\/p>\n<p><p>\u5f53\u6211\u4eec\u6709\u4e86\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u540e\uff0c\u4e0b\u4e00\u6b65\u5219\u662f\u5c06\u8fd9\u4e2a\u8def\u5f84\u5206\u5272\u6210\u591a\u4e2a\u5c0f\u6bb5\u3002\u6bcf\u4e00\u5c0f\u6bb5\u7684\u5750\u6807\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u63d2\u503c\u7684\u65b9\u6cd5\u6765\u8ba1\u7b97\u3002<strong>\u7ebf\u6027\u63d2\u503c\u662f\u4e00\u79cd\u6570\u5b66\u65b9\u6cd5\uff0c\u7528\u4e8e\u901a\u8fc7\u4e24\u4e2a\u5df2\u77e5\u7684\u5750\u6807\u70b9\uff0c\u4f30\u7b97\u51fa\u5728\u8fd9\u4e24\u70b9\u95f4\u7684\u5176\u4ed6\u70b9\u7684\u5750\u6807<\/strong>\u3002\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p><p>( lat = lat_1 + (lat_2 &#8211; lat_1) * \\frac{i}{n} )<\/p>\n<\/p>\n<p><p>( lon = lon_1 + (lon_2 &#8211; lon_1) * \\frac{i}{n} )<\/p>\n<\/p>\n<p><p>\u5176\u4e2d\uff0c( lat_1, lon_1 ) \u662f\u8d77\u59cb\u70b9\u7684\u7eac\u5ea6\u548c\u7ecf\u5ea6\uff0c( lat_2, lon_2 ) \u662f\u7ec8\u70b9\u7684\u7eac\u5ea6\u548c\u7ecf\u5ea6\u3002( i ) \u8868\u793a\u5f53\u524d\u6bb5\u6570\uff0c\u800c ( n ) \u8868\u793a\u603b\u6bb5\u6570\u3002\u901a\u8fc7\u53d8\u6362 ( i ) \u7684\u503c\uff0c\u5373\u53ef\u83b7\u53d6\u5927\u5706\u8def\u5f84\u4e0a\u5404\u4e2a\u7b49\u8ddd\u79bb\u7684\u70b9\u7684\u5750\u6807\u3002<\/p>\n<\/p>\n<p><h3>\u56db\u3001\u5b9e\u73b0\u7b97\u6cd5\u548c\u4ee3\u7801<\/h3>\n<\/p>\n<p><p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u901a\u5e38\u4f7f\u7528\u7f16\u7a0b\u8bed\u8a00\u6765\u5b9e\u73b0\u4ee5\u4e0a\u7684\u8ba1\u7b97\u8fc7\u7a0b\u3002Python\u662f\u5b8c\u6210\u8fd9\u4e00\u4efb\u52a1\u7684\u5e38\u7528\u8bed\u8a00\uff0c\u56e0\u4e3a\u5b83\u6709\u5982NumPy\u3001Pandas\u548cGeoPandas\u8fd9\u6837\u5f3a\u5927\u7684\u6570\u636e\u5206\u6790\u5e93\uff0c\u4ee5\u53ca\u50cfHaversine\u548cGeopy\u8fd9\u6837\u7528\u4e8e\u5730\u7406\u8ba1\u7b97\u7684\u4e13\u7528\u5e93\u3002\u8fd9\u4e9b\u5e93\u80fd\u591f\u7b80\u5316\u8ba1\u7b97\u5e76\u63d0\u9ad8\u7cbe\u5ea6\u3002<\/p>\n<\/p>\n<p><h3>\u4e94\u3001\u6ce8\u610f\u4e8b\u9879\u4e0e\u8bef\u5dee<\/h3>\n<\/p>\n<p><p>\u5728\u8ba1\u7b97\u8f93\u51fa\u8fc7\u7a0b\u4e2d\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\u5730\u7403\u5e76\u4e0d\u662f\u4e00\u4e2a\u5b8c\u7f8e\u7684\u7403\u4f53\uff0c\u800c\u662f\u4e00\u4e2a\u6241\u7387\u7565\u5927\u7684\u692d\u7403\u4f53\uff0c\u8fd9\u4f1a\u5bf9\u8ba1\u7b97\u7ed3\u679c\u4ea7\u751f\u4e00\u5b9a\u7684\u5f71\u54cd\u3002\u56e0\u6b64\uff0cHaversine\u516c\u5f0f\u8ba1\u7b97\u5f97\u5230\u7684\u662f\u8fd1\u4f3c\u503c\u3002\u5728\u8981\u6c42\u66f4\u9ad8\u7cbe\u5ea6\u7684\u5e94\u7528\u4e2d\uff0c\u53ef\u80fd\u9700\u8981\u4f7f\u7528\u66f4\u4e3a\u7cbe\u786e\u7684\u5730\u7406\u8ba1\u7b97\u5e93\u6216\u65b9\u6cd5\uff0c\u4f8b\u5982Vincenty\u516c\u5f0f\u6216\u8005\u57fa\u4e8eWGS-84\u692d\u7403\u4f53\u6a21\u578b\u7684\u7b97\u6cd5\u3002<\/p>\n<\/p>\n<p><p>\u6b64\u5916\uff0c\u5b9e\u9645\u5e94\u7528\u4e2d\u8fd8\u9700\u8981\u8003\u8651\u8bf8\u5982\u5730\u5f62\u8d77\u4f0f\u3001\u5efa\u7b51\u7269\u906e\u6321\u7b49\u56e0\u7d20\u7684\u5f71\u54cd\u3002\u5bf9\u4e8e\u5bfc\u822a\u3001\u65e0\u4eba\u9a7e\u9a76\u6216\u5730\u7406\u6570\u636e\u5206\u6790\u7b49\u9886\u57df\uff0c\u4e86\u89e3\u548c\u5904\u7406\u8fd9\u4e9b\u56e0\u7d20\u662f\u975e\u5e38\u5173\u952e\u7684\u3002<\/p>\n<\/p>\n<p><p>\u603b\u4e4b\uff0c\u901a\u8fc7\u4ee5\u4e0a\u6b65\u9aa4\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u8ba1\u7b97\u51fa\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u5750\u6807\u4e4b\u95f4\u6bcf\u6bb5\u8ddd\u79bb\u7684\u7ecf\u7eac\u5ea6\u70b9\u3002\u7136\u800c\uff0c\u7cbe\u786e\u7684\u8ba1\u7b97\u548c\u8f93\u51fa\u8fd9\u4e9b\u70b9\u9700\u8981\u5bf9\u5730\u7406\u6570\u636e\u548c\u76f8\u5173\u7b97\u6cd5\u6709\u6df1\u5165\u7684\u7406\u89e3\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p><strong>Q: \u6709\u6ca1\u6709\u73b0\u6210\u7684\u5de5\u5177\u6216\u65b9\u6cd5\u53ef\u4ee5\u8f93\u51fa\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u4e4b\u95f4\u6bcf\u6bb5\u8ddd\u79bb\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\uff1f<\/strong><\/p>\n<p>A: \u662f\u7684\uff0c\u6709\u4e00\u4e9b\u5de5\u5177\u6216\u65b9\u6cd5\u53ef\u4ee5\u5e2e\u52a9\u60a8\u8f93\u51fa\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u4e4b\u95f4\u6bcf\u6bb5\u8ddd\u79bb\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u3002\u5176\u4e2d\u4e00\u79cd\u5e38\u7528\u7684\u65b9\u6cd5\u662f\u4f7f\u7528\u5730\u56fe\u5e94\u7528\u7a0b\u5e8f\u3001\u5728\u7ebf\u5730\u56fe\u5de5\u5177\u6216\u4ee3\u7801\u7f16\u7a0b\u6765\u8ba1\u7b97\u548c\u8f93\u51fa\u8fd9\u4e9b\u5750\u6807\u3002\u60a8\u53ef\u4ee5\u6309\u7167\u4ee5\u4e0b\u6b65\u9aa4\u8fdb\u884c\u64cd\u4f5c\uff1a<\/p>\n<ol>\n<li>\u4f7f\u7528\u5730\u56fe\u5e94\u7528\u7a0b\u5e8f\u6216\u5728\u7ebf\u5730\u56fe\u5de5\u5177\uff0c\u627e\u5230\u60a8\u6240\u9700\u8981\u7684\u8d77\u59cb\u70b9\u548c\u7ec8\u6b62\u70b9\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u3002<\/li>\n<li>\u4f7f\u7528\u6570\u5b66\u8ba1\u7b97\u6216\u7f16\u7a0b\u4ee3\u7801\uff0c\u6839\u636e\u8d77\u59cb\u70b9\u548c\u7ec8\u6b62\u70b9\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u8ba1\u7b97\u51fa\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002<\/li>\n<li>\u5c06\u8d77\u59cb\u70b9\u548c\u7ec8\u6b62\u70b9\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u8fdb\u884c\u63d2\u503c\uff0c\u6309\u7167\u4e00\u5b9a\u7684\u8ddd\u79bb\u95f4\u9694\u8ba1\u7b97\u51fa\u6bcf\u4e2a\u70b9\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u7ebf\u6027\u63d2\u503c\u6216\u5176\u4ed6\u63d2\u503c\u7b97\u6cd5\u5b9e\u73b0\u3002<\/li>\n<li>\u5c06\u8ba1\u7b97\u5f97\u5230\u7684\u6bcf\u4e2a\u70b9\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u8f93\u51fa\uff0c\u5e76\u6309\u7167\u60a8\u7684\u9700\u8981\u8fdb\u884c\u683c\u5f0f\u5316\u6216\u4fdd\u5b58\u3002<\/li>\n<\/ol>\n<p>\u6ce8\u610f\uff1a\u6839\u636e\u60a8\u9700\u8981\u7684\u7cbe\u5ea6\u548c\u8ddd\u79bb\uff0c\u8ba1\u7b97\u5f97\u5230\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u53ef\u80fd\u4f1a\u6709\u4e00\u5b9a\u7684\u8bef\u5dee\u3002\u4f7f\u7528\u66f4\u51c6\u786e\u7684\u516c\u5f0f\u6216\u7b97\u6cd5\uff0c\u4ee5\u53ca\u9ad8\u7cbe\u5ea6\u7684\u5730\u7406\u6570\u636e\u6e90\uff0c\u53ef\u4ee5\u63d0\u9ad8\u8ba1\u7b97\u7ed3\u679c\u7684\u7cbe\u5ea6\u3002<\/p>\n<p><strong>Q: \u9664\u4e86\u5728\u7ebf\u5730\u56fe\u5de5\u5177\u548c\u7f16\u7a0b\u4ee3\u7801\uff0c\u8fd8\u6709\u5176\u4ed6\u65b9\u6cd5\u53ef\u4ee5\u8f93\u51fa\u4e24\u4e2a\u7ecf\u7eac\u5ea6\u4e4b\u95f4\u6bcf\u6bb5\u8ddd\u79bb\u7684\u7ecf\u7eac\u5ea6\u5750\u6807\u5417\uff1f<\/strong><\/p>\n<p>A: 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