{"id":970,"date":"2018-05-16T18:14:10","date_gmt":"2018-05-16T10:14:10","guid":{"rendered":"http:\/\/www.whudj.cn\/?p=970"},"modified":"2018-05-16T18:14:10","modified_gmt":"2018-05-16T10:14:10","slug":"%e5%8f%a0%e7%bd%ae%e7%ae%97%e6%b3%955%e6%8b%93%e6%89%91%e6%9e%84%e5%bb%ba%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"http:\/\/www.whudj.cn\/?p=970","title":{"rendered":"\u53e0\u7f6e\u7b97\u6cd5(5):\u62d3\u6251\u6784\u5efa\u7b97\u6cd5"},"content":{"rendered":"<p>\u62d3\u6251(topology)\u662f\u7531DCEL\u6784\u6210\u7684\u4e00\u79cd\u5e73\u9762\u9576\u5d4c\u6570\u636e\u7ed3\u6784\u3002\u62d3\u6251\u6570\u636e\u7ed3\u6784\u5c06\u5e73\u9762\u5212\u5206\u4e3a\u82e5\u5e72\u76f8\u4e92\u90bb\u63a5\u4e14\u4e0d\u538b\u76d6\u7684\u62d3\u6251\u9762\u3002\u5728\u62d3\u6251\u7ed3\u6784\u4e0a\u5b9e\u65bd\u7684\u6807\u8bb0\u7b97\u6cd5\u662f\u53e0\u7f6e\u7b97\u6cd5\u7684\u6838\u5fc3(<a href=\"http:\/\/www.whudj.cn\/?p=861\">\u7b2c\u56db\u8282<\/a>)\u3002\u8fd9\u4e00\u8282\uff0c\u6211\u5c06\u4ecb\u7ecd\u62d3\u6251\u6784\u5efa\u7b97\u6cd5\u3002<!--more--><\/p>\n<p><span style=\"text-decoration: underline;\"><strong>1.\u62d3\u6251\u6784\u5efa\u7684\u603b\u4f53\u6d41\u7a0b<\/strong><\/span><\/p>\n<p><span style=\"text-decoration: underline;\"><strong>1.1 \u9884\u5904\u7406<\/strong><\/span><\/p>\n<p>\u5728\u9762\u53e0\u7f6e\u5206\u6790\u7b97\u6cd5\u4e2d\uff0c\u8f93\u5165\u6570\u636e\u4e3a\u82e5\u5e72\u591a\u8fb9\u5f62(polygon)\u5bf9\u8c61\uff0c\u8fd9\u4e9b\u591a\u8fb9\u5f62\u95f4\u7684\u7a7a\u95f4\u5173\u7cfb\u4e0d\u5b9a\u3002\u9884\u5904\u7406\u7684\u4efb\u52a1\u662f\u5b8c\u6210\u591a\u8fb9\u5f62\u5230 Arc-Node \u7ed3\u6784\u7684\u8f6c\u6362\u3002\u5176\u4e2d\u5305\u542b\u4e86\u7ebf\u96c6\u6c42\u4ea4\u3001\u53bb\u91cd\u7b49\u7b97\u6cd5\u73af\u8282\uff0c\u8fd9\u4e24\u4e2a\u73af\u8282\u5b8c\u5168\u5de5\u4f5c\u5728\u51e0\u4f55\u7b97\u6cd5\u5c42\u9762\u4e0a\uff08\u62d3\u6251\u7684\u6784\u5efa\u5927\u90e8\u5206\u5c5e\u4e8e\u56fe\u7684\u6784\u5efa\uff0c\u76f8\u5bf9\u51e0\u4f55\u7b97\u6cd5\u590d\u6742\u5ea6\u4f4e\uff09\uff0c\u7b97\u6cd5\u590d\u6742\u5ea6\u8f83\u9ad8\uff0c\u6548\u7387\u662f\u5b9e\u73b0\u7684\u65f6\u5019\u9700\u8981\u8003\u8651\u7684\u91cd\u4e2d\u4e4b\u91cd\uff0c\u56e0\u6b64\u9700\u8981\u5408\u7406\u5b89\u6392\u5904\u7406\u6d41\u7a0b\uff0c\u5e76\u4e14\u4f9d\u636e\u4e0d\u540c\u7a7a\u95f4\u7d22\u5f15\u7684\u4f18\u52a3\u52bf\u914d\u5408\u4f7f\u7528\u3002<\/p>\n<p>\u53e0\u7f6e\u5206\u6790\u4e13\u9898\u6211\u8ba1\u5212\u4ece\u4e0a\u81f3\u4e0b\uff0c\u4ece\u5e94\u7528\u81f3\u5b9e\u73b0\u5ef6\u4f38\uff0c\u56e0\u6b64\u9884\u5904\u7406\u7684\u76f8\u5173\u5b9e\u73b0\uff0c\u6211\u4f1a\u5728\u540e\u671f\u53e6\u884c\u4ecb\u7ecd\uff0c\u8fd9\u91cc\uff0c\u6211\u4eec\u9700\u8981\u4e86\u89e3\u7684\u662f\u9884\u5904\u7406\u7684\u8f93\u5165\u53ca\u8f93\u51fa\u3002<\/p>\n<p>\u8f93\u5165\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-972\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/polygon_input.png\" alt=\"\" width=\"276\" height=\"200\" \/><\/p>\n<p>\u8f93\u51fa\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-973 size-full\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/arc_node_output.png\" alt=\"\" width=\"500\" height=\"221\" \/><\/p>\n<p>\u9884\u5904\u7406\u7684\u8f93\u51fa\u5373\u62d3\u6251\u6784\u5efa\u7684\u8f93\u5165\u3002<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>1.2 \u62d3\u6251\u6784\u5efa<\/strong><\/span><\/p>\n<p>\u62d3\u6251\u6784\u5efa\u7684\u4efb\u52a1\u662f\u5728arc-node\u7ed3\u6784\u57fa\u7840\u4e0a\uff0c\u6784\u5efaface\u3002\u8fd9\u4e9bface\u53ef\u4ee5\u4fdd\u5b58\u90bb\u63a5\u5173\u7cfb\u3002\u5728\u4e0a\u4e00\u8282\u4e2d\uff0c\u6211\u4eec\u770b\u5230\uff0cgeos\u4e2d\u662f\u6ca1\u6709face\u7ed3\u6784\u7684\uff0c\u56e0\u6b64\u4e0d\u80fd\u591f\u51ed\u501fgraph\u7ed3\u6784\u67e5\u8be2\u8fb9\u4e0d\u5b58\u5728\u4ea4\u70b9\u7684\u76f8\u4ea4\u5173\u7cfb(\u5982\u4e0b\u56fe)\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-981\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/why_we_need_topo_face.png\" alt=\"\" width=\"293\" height=\"150\" \/><\/p>\n<p>\u3002geos\u91c7\u7528\u51e0\u4f55\u8ba1\u7b97\u7684\u65b9\u5f0f\u83b7\u5f97\u8fd9\u6837\u7684\u5173\u7cfb\uff0c\u8003\u8651\u5230geos\u9762\u5411\u4e8c\u5143\u8ba1\u7b97\u6548\u7387\u5c1a\u53ef\u4ee5\u63a5\u53d7\uff0c\u800c\u9762\u5411\u6570\u636e\u96c6\u7684\u7a7a\u95f4\u5206\u6790\u8fd0\u7b97\u65f6\uff0c\u6784\u5efatopo face\u5c31\u5fc5\u4e0d\u53ef\u5c11\u4e86\u3002<\/p>\n<p>\u62d3\u6251\u6784\u5efa\u7684\u8f93\u51fa\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-974 size-full\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/topology_output.png\" alt=\"\" width=\"583\" height=\"200\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td>\u5728geos\u4e2d\uff0c\u5b58\u5728\u4e24\u5957\u529f\u80fd\u7c7b\u4f3c\u7684\u7ed3\u6784\uff0c\u4e00\u5957\u6309\u7167\u4e1a\u52a1\u540d\u79f0\u79f0\u4e3a<span class=\"lang:c++ decode:true crayon-inline \">geos::geomgraph<\/span>\u00a0\uff0c\u4e00\u5957\u6309\u7167\u5b9a\u4e49\u79f0\u4e3a<span class=\"lang:c++ decode:true crayon-inline\">geos::planargraph<\/span>\u3002geos\u4e2dgeometry\u7684intersection,union,difference,spatial predict \u7b49\u7b97\u6cd5\u90fd\u662f\u5efa\u7acb\u5728geomgraph\u57fa\u7840\u4e0a\u7684\uff0c\u800c\u4e00\u4e9b\u5c0f\u7684\u7b97\u6cd5\u5982\u00a0<span class=\"lang:c++ decode:true crayon-inline\">operation::polygonizer<\/span>\u00a0\u7b49\u662f\u6784\u5efa\u5728planargraph\u4e0a\u7684\u3002\u6211\u8ba4\u4e3a\u8fd9\u4e24\u5957\u7ed3\u6784\u53ef\u4ee5\u5747\u5408\u5e76\u5230geomgraph\u4e2d\u3002\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u505a\u4e24\u5957\u7ed3\u6784\uff0c\u6211\u76ee\u524d\u8fd8\u6ca1\u6709\u7406\u89e3\u6e05\u695a\u3002<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"text-decoration: underline;\"><strong>2.\u62d3\u6251\u6784\u5efa\u7b97\u6cd5<\/strong><\/span><\/p>\n<p>\u62d3\u6251\u6784\u5efa\u7b97\u6cd5\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e09\u4e2a\u5b50\u6b65\u9aa4\u3002<\/p>\n<p><strong><span style=\"text-decoration: underline;\">2.1 \u6807\u8bb0\u60ac\u6302(dangle)\uff1a<\/span><\/strong><\/p>\n<p>\u5982\u679c\u8f93\u5165\u7684\u6570\u636e\u5747\u4e3a\u591a\u8fb9\u5f62\u5bf9\u8c61\uff0c\u90a3\u4e48\u6807\u8bb0\u60ac\u6302\u8fd9\u4e00\u6b65\u662f\u6ca1\u6709\u5fc5\u8981\u6267\u884c\u7684\uff0c\u56e0\u4e3a\u4e0d\u53ef\u80fd\u4ea7\u751f\u60ac\u6302\u3002\u4f46\u662f\u8003\u8651\u5230\u591a\u79cd\u4e0d\u7528\u4e0d\u540c\u7684\u5e94\u7528\u573a\u666f(\u6bd4\u5982geos\u4e2d\u7684\u5229\u7528\u4e00\u7ec4\u6298\u7ebf\u6784\u5efa\u591a\u8fb9\u5f62\uff0c\u6216\u8005\u5229\u7528\u8f93\u5165\u7684\u6298\u7ebf\u5207\u5272\u591a\u8fb9\u5f62)\uff0c\u9700\u8981\u5f15\u5165\u8fd9\u4e00\u6b65\u3002<\/p>\n<p>\u6240\u8c13\u7684\u60ac\u6302\u8fb9\u5c31\u662f\u6307\u4efb\u4e00\u7aef\u70b9\u5ea6\u6570\u7b49\u4e8e1\u7684\u5f27\u6bb5\u3002\u6807\u8bb0\u60ac\u6302\uff0c\u4e0d\u80fd\u53ea\u5c06\u7aef\u70b9\u5ea6\u6570\u4e3a1\u7684\u7ebf\u6bb5\u6807\u8bb0\u51fa\u6765\uff0c\u800c\u662f\u8981\u201c\u987a\u85e4\u6478\u74dc\u201d\uff0c\u5c06\u56e0\u4e3a\u6807\u8bb0\u60ac\u6302\u5bfc\u81f4\u7684\u66f4\u591a\u7684\u60ac\u6302\u5f27\u6bb5\u6807\u8bb0\u51fa\u6765\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-984\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/dangle_line.png\" alt=\"\" width=\"255\" height=\"96\" \/><\/p>\n<p>\u6bd4\u5982\u4e0a\u56fe\u7684\u60c5\u51b5\uff0c\u5f53\u4ece\u4e00\u4e2a\u60ac\u6302\u7aef\u5f00\u59cb\u6807\u8bb0\uff0c\u672c\u6765\u5ea6\u6570\u4e3a2,3,4\u7684\u8282\u70b9\u5173\u8054\u7684\u5f27\u6bb5\u4e5f\u4f1a\u88ab\u6807\u8bb0\u4e3a\u60ac\u6302\u3002<\/p>\n<table>\n<tbody>\n<tr>\n<td>\u8282\u70b9\u7684\u5ea6\u6570(degree)\u6307\u8282\u70b9\u5173\u8054\u7684\u5f27\u6bb5\u7684\u4e2a\u6570\uff0c\u5f53arc\u88ab\u6807\u8bb0\u4e3adangle\u65f6\uff0c\u4e0d\u53c2\u4e0e\u5ea6\u6570\u8ba1\u7b97<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-987\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/how_to_mark_dangle.png\" alt=\"\" width=\"839\" height=\"300\" \/><\/p>\n<p>\u88ab\u6807\u8bb0\u4e3a\u60ac\u6302\u7684\u5f27\u6bb5\u4e0d\u53c2\u4e0e\u62d3\u6251\u6784\u9762\u3002<\/p>\n<p><strong><span style=\"text-decoration: underline;\">2.2\u00a0 \u62d3\u6251\u6784\u9762<\/span><\/strong><\/p>\n<p>\u62d3\u6251\u9762\u751f\u6210\u7684\u6cd5\u5219\u662f\uff1a\u4e0b\u4e00\u5f27\u6bb5\u662f\u5f53\u524d\u5f27\u6bb5\u987a\u65f6\u9488\u65cb\u8f6c\u540e\u7684\u7b2c\u4e00\u6761\u5f27\u6bb5\u3002\u56e0\u6b64\uff0c\u62d3\u6251\u6784\u9762\u9700\u8981\u5bf9\u6bcf\u4e2a\u8282\u70b9\u7684\u51fa\u5c04\u6709\u5411\u5f27\u6bb5\u6309\u7167\u65f6\u9488\u987a\u5e8f\u8fdb\u884c\u6392\u5217\u3002\u6392\u5e8f\u987a\u5e8f\u53ef\u4ee5\u4e3a\u987a\u65f6\u9488\u6216\u8005\u9006\u65f6\u9488\u5e8f\u3002\u9700\u8981\u8bf4\u660e\u7684\u662f\uff0c\u6392\u5e8f\u4f9d\u636e\u7684\u662f\u6bcf\u4e2a\u6709\u5411\u5f27\u6bb5\u7684\u524d\u4e24\u4e2avertex\u6784\u6210\u7684\u65b9\u5411\u8fdb\u884c\u6392\u5e8f\u7684\uff0c\u800c\u4e0d\u662f\u6574\u4e2a\u5f27\u6bb5\u3002<\/p>\n<p><strong><span style=\"text-decoration: underline;\">2.2.1 \u6392\u5e8f\u65b9\u6cd5<\/span><\/strong><\/p>\n<p>\u6bd4\u8f83\u7b80\u5355\u7684\u4e00\u79cd\u60f3\u6cd5\u662f\u6839\u636e\u65b9\u4f4d\u89d2(\u822a\u5411)\u8fdb\u884c\u6392\u5e8f\u3002\u56e0\u4e3a\u53cd\u4e09\u89d2\u51fd\u6570\u4ee3\u4ef7\u8f83\u5927\uff0c\u6709\u6ca1\u6709\u66f4\u9ad8\u6548\u7684\u65b9\u5f0f\u5462\uff1f\u4e00\u4e2a\u60f3\u6cd5\u662f\u4f7f\u7528\u4e09\u89d2\u51fd\u6570\u503c\uff0c\u4f46\u662f\u6b63\u5f26\u3001\u4f59\u5f26\u5728\\([0,2\\pi)\\)\u8303\u56f4\u4e0a\u90fd\u4e0d\u662f\u5355\u8c03\u7684\uff0c\u6b63\u5207\u66f4\u662f\u8fd8\u6709\u503c\u57df\u7684\u95ee\u9898(\u65e0\u6cd5\u8868\u793a\\(\\frac{1}{2}\\pi\\))\u3002\u65e2\u7136\u4e0d\u80fd\u591f\u5728\\([0,2\\pi)\\)\u4e0a\u5355\u8c03\uff0c\u53ef\u4ee5\u5c06\u89d2\u5ea6\u5b9a\u4e49\u57df\u5212\u5206\u4e3a\\([0,\\pi),[\\pi,2\\pi)\\)\u4e24\u90e8\u5206\u5440\u3002\u6240\u4ee5\u8bf4 \u5b9a\u4e49\u57df\u5212\u5206+\u4f59\u5f26\/\u6b63\u5f26\u662f\u4e00\u79cd\u53ef\u884c\u7684\u65b9\u6cd5\u3002<\/p>\n<p>\u8fd8\u6ca1\u6709\u5176\u4ed6\u65b9\u5f0f\uff1f\u8fd8\u6709\u4e00\u79cd\u601d\u8def\u662f\u6392\u5e8f\u7684\u65f6\u5019\u53ea\u8981\u7ed9\u51fa\u4e24\u4e2a\u5143\u7d20\u7684\u76f8\u5bf9\u5173\u7cfb\u7684\u5b9a\u4e49\uff0c\u5e76\u4e14\u8fd9\u6837\u7684\u5173\u7cfb\u6ee1\u8db3\u4f20\u9012\u7387\u5c31\u53ef\u4ee5\u4e86\uff0c\u5728\u7f16\u7a0b\u7684\u65f6\u5019\u5bf9\u5e94\u6240\u8c13\u7684\u4eff\u51fd\u6570\u3002geos\u662f\u600e\u4e48\u5904\u7406\u7684\uff1f\u4e00\u662f\u4f7f\u7528\u5411\u91cf\u7684\u76f8\u5bf9\u4f4d\u7f6e\u5173\u7cfb\uff1a$$\\vec v\\times \\vec v_1&gt;0; \\vec v_1\u5728\\vec v\u5de6\u4fa7 \\\\ \\vec v\\times\\vec v_0&lt;0 ;\\vec v_0\u5728\\vec v\u53f3\u4fa7$$<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-994\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/cross_product.png\" alt=\"\" width=\"88\" height=\"60\" \/><\/p>\n<p>\u4e8c\u662f\u5229\u7528\u8c61\u9650(Quadrant) \u89e3\u51b3\u5355\u8c03\u6027\u7684\u95ee\u9898\u3002\u8c61\u9650\u5728geos\u4e2d\u591a\u6b21\u88ab\u4f7f\u7528\uff0c\u5728 <span class=\"lang:c++ decode:true crayon-inline \">geos::algorithm<\/span>\u00a0\u547d\u540d\u7a7a\u95f4\u4e2d\u3002\u540e\u9762\u63d0\u5230\u5355\u8c03\u94fe\uff0c\u4ecd\u7136\u8981\u5229\u7528\u8c61\u9650\u3002geos\u7684\u8c61\u9650\u987a\u5e8f\u4e0e\u4e2d\u5b66\u6570\u5b66\u4e2d\u7684\u8c61\u9650\u5b9a\u4e49\u4e00\u81f4\u3002<\/p>\n<p>\u7efc\u5408\u4e00\u4e0b\uff0c\u4ee5\u9006\u65f6\u9488\u6392\u5e8f\u4e3a\u4f8b\uff1a<\/p>\n<ol>\n<li>\u5982\u679c\\(Quadrant(\\vec v_0)&lt;Quadrant(\\vec v_1) \\) ,\u5219\\( \\vec v_0&lt;\\vec v_1 \\)\uff1b<\/li>\n<li>\u5982\u679c\\(Quadrant(\\vec v_0)&gt;Quadrant(\\vec v_1) \\) ,\u5219\\( \\vec v_0&gt;\\vec v_1 \\)\uff1b<\/li>\n<li>\u5426\u5219\u82e5\\( \\vec v_0\\times \\vec v_1&gt;0\\);\u5219\\( \\vec v_0&lt;\\vec v_1 \\)\uff1b<\/li>\n<\/ol>\n<p><strong><span style=\"text-decoration: underline;\">2.2.2\u00a0 \u6784\u9762\u4ee5\u53ca cut edge\u7684\u5904\u7406<\/span><\/strong><\/p>\n<p>\u62d3\u6251\u6784\u9762\u7684\u7ec8\u6b62\u6761\u4ef6\u5c31\u662f\u6240\u6709\u7684 \u6709\u5411\u8fb9\u5168\u90e8\u904d\u5386\u5b8c\u6bd5\u3002\u6784\u5efa\u4e00\u4e2a\u62d3\u6251\u9762\u7684\u7ec8\u6b62\u6761\u4ef6\u662f\u8fb9\u7684\u95ed\u5408\uff0c\u5373\u4ece\u4e00\u6761\u8fb9\u51fa\u53d1\uff0c\u987a\u65f6\u9488\u65cb\u8f6c\u627e\u4e0b\u4e00\u6761\u8fb9\uff0c\u76f4\u81f3\u8d70\u5b8c\u4e00\u5708\uff0c\u56de\u5230\u8d77\u70b9\u4e3a\u6b62\u3002\u4f2a\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-998\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/build_face_no_cut_edge.png\" alt=\"\" width=\"420\" height=\"300\" \/><\/p>\n<p>\u4f9d\u636e\u4e0a\u8ff0\u4ee3\u7801\u8fd0\u884c\uff0c\u8fd8\u4f1a\u9047\u5230\u4e00\u4e2a\u95ee\u9898\uff0c\u5373\u6709\u7684\u8fb9\u50cf\u201c\u6865\u201d\u4e00\u6837\u5c06\u62d3\u6251\u9762\u5207\u5272\u3002\u5728geos\u4e2d\uff0c\u8fd9\u6837\u7684\u95ee\u9898\u79f0\u4e4b\u4e3acut-edge\u95ee\u9898\u3002\u89c1\u4e0b\u56fe\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-999\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/topo_bridge.png\" alt=\"\" width=\"207\" height=\"207\" \/><\/p>\n<p>\u4e24\u79cd\u53eb\u6cd5\u90fd\u6bd4\u8f83\u5f62\u8c61\uff0c\u6309\u7167\u4e0a\u9762\u7684\u6d41\u7a0b\u6784\u5efa\u62d3\u6251\u9762\uff0c\u5219\u5728\u7ea2\u8272\u7ebf\u4e0a\uff0c\u9762\u7684\u4e24\u6761\u8fb9\u91cd\u5408\uff0c\u8fd9\u6837\u4e0d\u7b26\u5408polygon\u7684\u201csimple\u201d\u5b9a\u4e49\uff0c\u56e0\u6b64\uff0c\u5728\u6784\u9762\u65f6\uff0c\u8fd9\u6837\u7684\u201c\u6865\u201d\u6216\u8005\u8bf4\u201c\u5207\u5272\u8fb9\u201d\u90fd\u9700\u8981\u88ab\u5254\u9664\u3002\u4e0d\u5e78\u7684\u662f\uff0c\u8fd9\u6837\u7684\u8fb9\u5e76\u4e0d\u662f\u60ac\u6302\uff0c\u4e0d\u80fd\u5728\u4e00\u5f00\u59cb\u6807\u8bb0\u60ac\u6302\u65f6\u88ab\u5904\u7406\u3002<\/p>\n<p>\u89e3\u51b3\u65b9\u6848\u662f\uff0c\u53d1\u73b0cut-edge\u65f6\uff08\u5b83\u4eec\u7684left-face\u4e0eright-face\u76f8\u540c\uff09\uff0c\u5c06\u5b83\u4eec\u6807\u8bb0\u4e3a\u60ac\u6302\uff0c\u4ece\u53c2\u4e0e\u6784\u9762\u7684\u5f27\u6bb5\u4e2d\u5254\u9664\u3002\u5254\u9664\u540e\uff0c\u5176\u6240\u6d89\u53ca\u5230\u7684\u8fb9\u7684\u5173\u7cfb\u9700\u8981\u66f4\u65b0\u3002<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>2.2.3 \u5916\u5708\u4e0e\u6d1e\u7684\u5408\u5e76\u5904\u7406<\/strong><\/span><\/p>\n<p>\u5b8c\u62102.2.2\u6b65\u9aa4\u540e\uff0c\u6211\u4eec\u4f1a\u53d1\u73b0\u4e00\u4e2a\u95ee\u9898\uff0c\u7531\u5e73\u9762\u56fe\u6784\u6210\u7684\u62d3\u6251\u9762\u662f\u5b58\u5728\u91cd\u53e0\u7684\uff0c\u6bd4\u5982\u4e0b\u56fe\u4e2d\u5916\u5708\u5de6\u4fa7\u7684\u9762\u4e0e\u5185\u5708\u5de6\u4fa7\u7684\u9762\u5176\u5b9e\u5e94\u8be5\u662f\u540c\u4e00\u4e2a\u9762\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u9700\u8981\u66f4\u65b0\u5185\u5708\u7684\u9762\uff0c\u5f62\u8c61\u7684\u8bf4\uff0c\u5c31\u662f\u7ed9\u5916\u5708&#8221;\u6316\u6d1e&#8221;\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1001\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/shell_holes.png\" alt=\"\" width=\"255\" height=\"194\" \/><\/p>\n<p>\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u9700\u8981\u4f7f\u7528\u5185\u5916\u5708\u7684\u7a7a\u95f4\u5173\u7cfb\uff0c\u56e0\u6b64\u4e5f\u662f\u9700\u8981\u51e0\u4f55\u8fd0\u7b97\u7684\u3002\u4efb\u52a1\u53ef\u4ee5\u63cf\u8ff0\u4e3a\uff1a\u9488\u5bf9\u6bcf\u4e2a\u5185\u5708\uff08\u987a\u65f6\u9488\u5708\uff0c\u6216\u6d1e\uff09\uff0c\u627e\u5230\u5c06\u5176\u5305\u56f4\u7684\u6700\u5185\u4fa7\u5185\u5708\u3002\u4e24\u4e2a\u95ee\u9898\u9700\u8981\u89e3\u51b3\u3002<\/p>\n<p>1.\u5982\u4f55\u5224\u65ad\u62d3\u6251\u9762\u662f\u9006\u65f6\u9488\u987a\u5e8f\u8fd8\u662f\u987a\u65f6\u9488\u987a\u5e8f\u3002<\/p>\n<p>\u5224\u65ad\u591a\u8fb9\u5f62\u987a\u9006\u65f6\u9488\u987a\u5e8f\u7684\u7b97\u6cd5\u89c1\u535a\u6587 <a href=\"http:\/\/www.whudj.cn\/?p=1010\">\u591a\u8fb9\u5f62\u9762\u79ef\u4ee5\u53ca\u987a\u9006\u65f6\u9488\u987a\u5e8f\u5224\u65ad<\/a><\/p>\n<p>2.\u5982\u4f55\u641c\u7d22\u5230\u5305\u542b\u5185\u5708\u6700\u5185\u4fa7\u7684\u5916\u5708\u3002<\/p>\n<ol>\n<li>\u9996\u5148\uff0c\u53d6\u5185\u5708\u6700\u5de6\u4fa7\u70b9\uff08x\u503c\u6700\u5c0f\u7684\u70b9\uff09\\(X\\).<\/li>\n<li>\u7531\\(X\\)\u5411\u5de6\u5f15\u5c04\u7ebf\uff0c\u4e0e\u76f8\u4ea4\u7684\u5916\u5708\u8ba1\u7b97\u51fax\u503c\uff0c\u4fdd\u7559\\(X\\)\u5de6\u4fa7\u7684\u5916\u5708\u3002\u6309\u7167\u4ea4\u70b9x\u503c\u7531\u5927\u5230\u5c0f\u6392\u5e8f\u3002<\/li>\n<li>\u9010\u4e2a\u5bf9\u4fdd\u7559\u4e0b\u7684\u5916\u5708\u5224\u65ad\u70b9\\(X\\)\u662f\u5426\u5728\u5916\u5708\u5185\u3002\u627e\u5230\u7684\u9996\u4e2a\u5916\u5708\u4e3a\u5f85\u6c42\u5916\u5708\u3002<\/li>\n<li>\u5982\u679c\u627e\u4e0d\u5230\u5916\u5708\uff0c\u5219\u8bc1\u660e\u6b64\u5916\u5708\u4e3auniverse face\u7684\u5185\u5708\u3002<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1003\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2018\/05\/search_shell.png\" alt=\"\" width=\"335\" height=\"200\" \/><\/p>\n<p>\u4e0a\u56fe\u770b\u5bf9\u4e8e\u5185\u5708\\(C_6\\)\u5176\u5de6\u4fa7\u7684\u5916\u5708\u5206\u522b\u4e3a \\(C_5,C_4,C_2\\) \u5176\u4e2d\\(X\\)\u4f4d\u4e8e\\(C_2\\)\u4e2d\uff0c\u56e0\u6b64\uff0c\u5185\u5708\\(C_6\\)\u7684\u5916\u5708\u4e3a\\(C_2\\) (\u56fe\u7247\u6765\u6e90\uff1aBerg M D, Cheong O, Kreveld M V, et al. Computational Geometry: Algorithms and Applications[M]. Springer Publishing Company, Incorporated, 2000.)<\/p>\n<p><span style=\"text-decoration: underline;\"><strong>3.\u5907\u6ce8<\/strong><\/span><\/p>\n<ul>\n<li>\u672c\u6587\u7684\u62d3\u6251\u6784\u5efa\u65b9\u6cd5\uff0c\u5728\u90e8\u5206\u6570\u636e\u7ed3\u6784\u3001\u90e8\u5206\u7b97\u6cd5\u65b9\u9762\u5747\u5206\u522b\u53c2\u8003\u91c7\u7eb3\u4e86 geos \u4e0e \u300acomputational geometry\u300b(\u7b2c\u4e09\u7248\uff0cBerg\u7b49\u8457)\u4e2d\u7684\u90e8\u5206\u5185\u5bb9\u3002\u4f46\u662f\u6574\u4f53\u65b9\u6cd5\u3001\u6d41\u7a0b\u5e76\u4e0d\u5b8c\u5168\u4e0e\u4ee5\u4e0a\u4e24\u8005\u76f8\u540c\u3002\u5bf9\u4e0a\u4e24\u8005\u7684\u5904\u7406\u65b9\u6cd5\u611f\u5174\u8da3\u7684\u8bfb\u8005\u8bf7\u6ce8\u610f\u3002<\/li>\n<li>\u5173\u4e8e\u7a0b\u5e8f\u6e90\u4ee3\u7801\u3002\u56e0\u4e3a\u53e0\u7f6e\u5206\u6790\u6d89\u53ca\u7684\u7b97\u6cd5\u6bd4\u8f83\u591a\u800c\u4e14\u590d\u6742\uff0c\u56e0\u6b64\u8003\u8651\u5355\u72ec\u5efa\u7acb\u5de5\u7a0b\u5206\u4eab\u81f3github\u3002\u76ee\u524d\u7a0b\u5e8f\u6b63\u5728\u7f16\u5199\u4e2d\uff0c\u540e\u671f\u4f1a\u7edf\u4e00\u66f4\u65b0\u4ee3\u7801\u5730\u5740\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u62d3\u6251(topology)\u662f\u7531DCEL\u6784\u6210\u7684\u4e00\u79cd\u5e73\u9762\u9576\u5d4c\u6570\u636e\u7ed3\u6784\u3002\u62d3\u6251\u6570\u636e\u7ed3\u6784\u5c06\u5e73 &hellip; <a href=\"http:\/\/www.whudj.cn\/?p=970\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[31],"tags":[],"_links":{"self":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/970"}],"collection":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=970"}],"version-history":[{"count":26,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/970\/revisions"}],"predecessor-version":[{"id":1026,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/970\/revisions\/1026"}],"wp:attachment":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=970"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=970"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=970"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}