{"id":190,"date":"2026-05-10T18:48:22","date_gmt":"2026-05-10T10:48:22","guid":{"rendered":"https:\/\/geocommunity.vip\/?p=190"},"modified":"2026-05-10T19:10:07","modified_gmt":"2026-05-10T11:10:07","slug":"%e6%b3%b0%e6%a3%ae%e5%a4%9a%e8%be%b9%e5%bd%a2","status":"publish","type":"post","link":"https:\/\/geocommunity.vip\/index.php\/2026\/05\/10\/%e6%b3%b0%e6%a3%ae%e5%a4%9a%e8%be%b9%e5%bd%a2\/","title":{"rendered":"\u6cf0\u68ee\u591a\u8fb9\u5f62"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u672c\u8282\u5305\u542b\uff1a\u57fa\u7840\u77e5\u8bc6\u3001\u683c\u6797\u5384\u59c6\u626b\u63cf\u6cd5\u751f\u6210\u51f8\u5305\uff08Python\uff09\u3001Bowyer-Watson\u6cd5\u6784\u9020delaunay\u4e09\u89d2\u7f51\uff08Python\uff09\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/ICON.png\" alt=\"\" class=\"wp-image-208\" style=\"width:65px;height:auto\" srcset=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/ICON.png 1024w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/ICON-300x300.png 300w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/ICON-150x150.png 150w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/ICON-768x768.png 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u58f0\u660e\uff1a\u672c\u6587\u4e2d\u6240\u6709\u673a\u7406\u56fe\u5747\u7531 <strong>F-PolyImage \u56fe\u7247\u751f\u6210\u5de5\u5177<\/strong>\uff08geocommunity.vip\uff09 \u521b\u4f5c\u5b8c\u6210\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-9aae12907115ee0d2e43c67277fc1f01\">\u4e00\u3001\u6cf0\u68ee\u591a\u8fb9\u5f62\u7684\u5b9a\u4e49<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-41-1024x768.png\" alt=\"\" class=\"wp-image-191\" style=\"width:673px;height:auto\" srcset=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-41-1024x768.png 1024w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-41-300x225.png 300w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-41-768x576.png 768w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-41-400x300.png 400w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-41.png 1448w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u56fe\u4e2d\uff0cP1-P5\u4e3a\u751f\u6210\u70b9\uff0c\u6784\u6210\u70b9\u96c6\u3002\u6839\u636e\u6cf0\u68ee\u591a\u8fb9\u5f62\u7684\u6027\u8d28\uff0c\u4e24\u751f\u6210\u70b9\u7684\u5782\u76f4\u5e73\u5206\u7ebf\u6784\u6210Voronoi\u8fb9\u754c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uff08\u5230\u8fd9\u91cc\uff0c\u53ea\u9700\u638c\u63e1\u6cf0\u68ee\u591a\u8fb9\u5f62\u662f\u4ec0\u4e48\u5373\u53ef\uff09<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-7ff8940f6e1517f63ba23379a44299c0\">\u4e8c\u3001\u6cf0\u68ee\u591a\u8fb9\u5f62\u7684\u57fa\u672c\u6027\u8d28<\/h3>\n\n\n\n<h5 class=\"wp-block-heading\">1\u3001\u8fb9\u754c\u662f\u4e24\u70b9\u8fde\u7ebf\u7684\u5782\u76f4\u5e73\u5206\u7ebf<\/h5>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"806\" src=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/f763aace3805ef513c6b75caf571cb6e_720.png\" alt=\"\" class=\"wp-image-197\" style=\"aspect-ratio:0.7816580246142313;width:348px;height:auto\" srcset=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/f763aace3805ef513c6b75caf571cb6e_720.png 630w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/f763aace3805ef513c6b75caf571cb6e_720-234x300.png 234w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">2\u3001\u6bcf\u4e2a\u6cf0\u68ee\u591a\u8fb9\u5f62\u662f\u51f8\u591a\u8fb9\u5f62<\/h5>\n\n\n\n<h5 class=\"wp-block-heading\">3\u3001\u4ec0\u4e48\u662f\u51f8\u5305\uff0c\u5982\u4f55\u6784\u5efa\uff1f<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u6709\u79bb\u6563\u70b9\uff08\u6837\u672c\u70b9\u3001\u7ad9\u70b9\u3001\u79cd\u5b50\u70b9\uff09\u6574\u4f53\u5f62\u6210\u7684\u6700\u5c0f\u51f8\u8fb9\u754c\u3002\u4ee5\u4e0b\u56fe\u76f4\u89c2\u89e3\u91ca\uff08\u6bcf\u4e2a\u9489\u5b50\u770b\u4e3a\u6bcf\u4e2a\u751f\u6210\u70b9\uff0c\u6a61\u76ae\u7b4b\u5373\u6700\u5c0f\u51f8\u8fb9\u754c\uff09\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-44-1024x683.png\" alt=\"\" class=\"wp-image-193\" style=\"aspect-ratio:1.5000127378799073;width:665px;height:auto\" srcset=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-44-1024x683.png 1024w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-44-300x200.png 300w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-44-768x512.png 768w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-44-421x281.png 421w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/F-PolyImage-44.png 1536w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u683c\u6797\u5384\u59c6\u626b\u63cf\u6cd5\u5b9e\u73b0\u51f8\u5305\u6784\u5efa\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9009\u5b9a\u539f\u70b9\uff1ay\u6700\u5c0f\uff0cy\u76f8\u540c\u53d6x\u6700\u5c0f\u3002<\/li>\n\n\n\n<li>\u6309\u7167\u6781\u89d2\u9006\u65f6\u9488\u6392\u5e8f\uff0c\u6781\u89d2\u76f8\u540c\u6309\u8ddd\u79bb\u6392\u5e8f\u3002<\/li>\n\n\n\n<li>\u6808\u8fc7\u6ee4\uff0c\u53c9\u79ef\u5982\u679c&lt;=0\uff0c\u5219\u5220\u9664\u9876\u70b9\u3002\uff08\u53c9\u79ef&lt;=0\uff0c\u8868\u793a\u53f3\u62d0\u5411\u3002\uff09<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>import math\n\n# \u683c\u6797\u5384\u59c6\u626b\u63cf\u6cd5\u751f\u6210\u51f8\u58f3\n\ndef cross_product(o, a, b):\n    '''\n    \u5411\u91cf OA = (a&#91;0] - o&#91;0], a&#91;1] - o&#91;1])\n    \u5411\u91cf OB = (b&#91;0] - o&#91;0], b&#91;1] - o&#91;1])\n    '''\n    return (a&#91;0] - o&#91;0]) * (b&#91;1] - o&#91;1]) - (a&#91;1] - o&#91;1]) * (b&#91;0] - o&#91;0])\n\ndef graham_scan(points):\n    if len(points) &lt;= 2:\n        return\n    \n    # 1\u3001\u9009\u5b9a\u539f\u70b9\uff1ay\u6700\u5c0f\uff0cy\u76f8\u540c\u53d6x\u6700\u5c0f\u3002\n    pivot = min(points, key = lambda p:(p&#91;1], p&#91;0]))\n\n    # 2\u3001\u6309\u7167\u6781\u89d2\u9006\u65f6\u9488\u6392\u5e8f\uff0c\u6781\u89d2\u76f8\u540c\u6309\u8ddd\u79bb\u6392\u5e8f\u3002\n    others = &#91;p for p in points if p != pivot]\n    others.sort(key = lambda p:(math.atan2(p&#91;1] - pivot&#91;1], p&#91;0] - pivot&#91;0]), (p&#91;0] - pivot) ** 2 + (p&#91;1] - pivot&#91;1]) ** 2))\n\n    # 3\u3001\u6808\u8fc7\u6ee4\uff0c\u53c9\u79ef\u5982\u679c&lt;=0\uff0c\u5219\u5220\u9664\u9876\u70b9\u3002\n    stack = &#91;]\n    for p in &#91;pivot] + others:\n        while len(stack &gt;= 2) and cross_product(stack&#91;-2], stack&#91;-1], p) &lt;= 0:\n            stack.pop()\n        stack.append(p)\n    \n    return stack<\/code><\/pre>\n\n\n\n<h5 class=\"wp-block-heading\">4\u3001\u51f8\u5305\u4e0a\u7684\u70b9\u5bf9\u5e94\u65e0\u754c\u6cf0\u68ee\u591a\u8fb9\u5f62<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u67d0\u4e2a\u70b9\u5728\u70b9\u96c6\u7684\u6700\u5916\u5c42\uff0c\u4e5f\u5c31\u662f\u5728\u51f8\u5305\u4e0a\uff0c\u90a3\u4e48\u5b83\u7684\u52bf\u529b\u8303\u56f4\u4f1a\u5411\u5916\u65e0\u9650\u5ef6\u4f38\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u4ee5\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5185\u90e8\u70b9\u7684\u6cf0\u68ee\u591a\u8fb9\u5f62\u901a\u5e38\u662f\u5c01\u95ed\u6709\u9650\u591a\u8fb9\u5f62\uff1b<\/li>\n\n\n\n<li>\u51f8\u5305\u70b9\u7684\u6cf0\u68ee\u591a\u8fb9\u5f62\u662f\u65e0\u754c\u7684\uff1b<\/li>\n\n\n\n<li>\u5728 GIS \u4e2d\u901a\u5e38\u9700\u8981\u7528\u7814\u7a76\u533a\u8fb9\u754c\u6216\u77e9\u5f62\u6846\u628a\u5b83\u88c1\u526a\u6210\u6709\u9650\u533a\u57df\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-9027066068d33630122eeed870e62432\">\u4e09\u3001\u6cf0\u68ee\u591a\u8fb9\u5f62\u548c Delaunay \u4e09\u89d2\u7f51\u7684\u5173\u7cfb<\/h3>\n\n\n\n<h5 class=\"wp-block-heading\">1\u3001Delaunay \u4e09\u89d2\u7f51\u662f\u6cf0\u68ee\u591a\u8fb9\u5f62\u7684\u5bf9\u5076\u56fe<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u5982\u679c\u4e24\u4e2a\u70b9\u5728 Delaunay \u4e09\u89d2\u7f51\u4e2d\u6709\u8fb9\u76f8\u8fde\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u6cf0\u68ee\u591a\u8fb9\u5f62\u5171\u4eab\u4e00\u6761\u8fb9\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">2\u3001Delaunay \u4e09\u89d2\u5f62\u7684\u5916\u5fc3\u5c31\u662f\u6cf0\u68ee\u9876\u70b9<\/h5>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-253d76308d7dee4120b4ca644f6e254c\">\u56db\u3001Delaunay \u4e09\u89d2\u7f51\u7684\u6838\u5fc3\u51c6\u5219<\/h3>\n\n\n\n<h5 class=\"wp-block-heading\">1\u3001Delaunay \u4e09\u89d2\u7f51\u7684\u5173\u952e\u662f <strong>\u7a7a\u5916\u63a5\u5706\u51c6\u5219<\/strong>\u3002<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8e\u4e09\u89d2\u5f62 ABC\uff0c\u5982\u679c\u5b83\u7684\u5916\u63a5\u5706\u5185\u90e8\u4e0d\u5305\u542b\u5176\u4ed6\u70b9\uff0c\u90a3\u4e48\u8fd9\u4e2a\u4e09\u89d2\u5f62\u6ee1\u8db3 Delaunay \u6761\u4ef6\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">2\u3001\u6700\u5927\u6700\u5c0f\u89d2\u6027\u8d28<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b83\u503e\u5411\u4e8e\u907f\u514d\u7626\u957f\u4e09\u89d2\u5f62\uff0c\u80fd\u6700\u5927\u5316\u4e09\u89d2\u7f51\u4e2d\u7684\u6700\u5c0f\u89d2\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-3572577f748848eb6ba2d5524d8ae905\">\u4e94\u3001\u5982\u4f55\u6784\u9020\u6cf0\u68ee\u591a\u8fb9\u5f62\uff1f<\/h3>\n\n\n\n<h5 class=\"wp-block-heading\">1\u3001\u5148\u751f\u6210 Delaunay \u4e09\u89d2\u7f51\uff08\u5206\u5272\u5408\u5e76\u7b97\u6cd5\u3001\u4e09\u89d2\u7f51\u751f\u6210\u7b97\u6cd5\u3001Bowyer-Watson\u9010\u70b9\u63d2\u5165\u6cd5\uff09<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ea\u4ecb\u7ecd\u9010\u70b9\u63d2\u5165\u6cd5\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\uff081\uff09\u6784\u5efa\u8d85\u7ea7\u4e09\u89d2\u5f62<\/li>\n\n\n\n<li>\uff082\uff09\u5c06\u8d85\u7ea7\u4e09\u89d2\u5f62\u7684\u9876\u70b9\u52a0\u5165\u70b9\u96c6\u5185\uff0c\u5e76\u52a0\u5165\u4e34\u65f6\u4e09\u89d2\u5f62\u6570\u7ec4\u5185<\/li>\n\n\n\n<li>\uff083\uff09\u9488\u5bf9\u6bcf\u4e2a\u539f\u59cb\u751f\u6210\u70b9\u8fdb\u884c\u8ba8\u8bba\n<ul class=\"wp-block-list\">\n<li>    \uff084\uff09\u62ff\u5230\u8be5\u70b9A\uff0c\u904d\u5386\u6240\u6709\u4e34\u65f6\u4e09\u89d2\u5f62\uff0c\u5982\u679c\u8be5\u70b9\u5728\u4e34\u65f6\u4e09\u89d2\u5f62\u5185\uff0c\u5219\u8fd9\u4e2a\u4e34\u65f6\u4e09\u89d2\u5f62\u662f\u574f\u4e09\u89d2\u5f62<\/li>\n\n\n\n<li>    \uff085\uff09\u4ece\u4e34\u65f6\u4e09\u89d2\u5f62\u6570\u7ec4\u4e2d\u79fb\u9664\u574f\u4e09\u89d2\u5f62<\/li>\n\n\n\n<li>    \uff086\uff09\u5982\u679c\u574f\u4e09\u89d2\u5f62\u7684\u8fb9\u4e0d\u91cd\u5408\uff0c\u90a3\u4e48\u52a0\u5165\u6570\u7ec4<\/li>\n\n\n\n<li>    \uff087\uff09\u6784\u9020\u65b0\u7684\u4e34\u65f6\u4e09\u89d2\u5f62\uff0c\u5e76\u52a0\u5165\u4e34\u65f6\u4e09\u89d2\u5f62\u6570\u7ec4<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\uff088\uff09\u6700\u540e\u6392\u9664\u8d85\u7ea7\u4e09\u89d2\u5f62\u7684\u9876\u70b9\u6784\u6210\u7684\u4e09\u89d2\u5f62<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">points\u4e2d\u6bcf\u4e2a\u5143\u7d20\u662f\u4e00\u4e2a\u70b9\u5750\u6807\u7684\u5217\u8868\u5f62\u5f0f\uff0ctriangles\u4e2d\u6bcf\u4e2a\u5143\u7d20\u5b58\u50a8\u4e09\u89d2\u5f62\u9876\u70b9\u5728\u751f\u6210\u70b9\u5217\u8868\u4e2d\u7684\u7d22\u5f15\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>    def delaunay_(self,points):\n\n        # 1\u3001\u6784\u5efa\u8d85\u7ea7\u4e09\u89d2\u5f62\n        n = len(points)\n        min_x = min(&#91;p&#91;0] for p in points])\n        max_x = max(&#91;p&#91;0] for p in points])\n        min_y = min(&#91;p&#91;1] for p in points])\n        max_y = max(&#91;p&#91;1] for p in points])\n        dx = max_x - min_x\n        dy = max_y - min_y\n        t = max(dx, dy)*10\n        mid_x = (min_x + max_x) \/ 2\n        mid_y = (min_y + max_y) \/ 2\n        v_p1 = &#91;mid_x - t, mid_y - t]  # \u5de6\u4e0b\n        v_p = &#91;mid_x, mid_y + t]  # \u9876\u70b9\n        v_p2 = &#91;mid_x + t, mid_y - t]  # \u53f3\u4e0b\n\n        # 2\u3001\u5c06\u8d85\u7ea7\u4e09\u89d2\u5f62\u7684\u9876\u70b9\u52a0\u5165\u70b9\u96c6\u5185\uff0c\u5e76\u52a0\u5165\u4e34\u65f6\u4e09\u89d2\u5f62\u6570\u7ec4\u5185\n        all_points = points + &#91;v_p1, v_p, v_p2]\n        triangles = &#91;&#91;n, n+1, n+2]]\n\u9488\u5bf9\u6bcf\u4e2a\u539f\u59cb\u751f\u6210\u70b9\u8fdb\u884c\u8ba8\u8bba\n        # 3\u3001\u9488\u5bf9\u6bcf\u4e2a\u539f\u59cb\u751f\u6210\u70b9\u8fdb\u884c\u8ba8\u8bba\n        for i in range(n):\n            \n            # \u4e00\u3001\u6839\u636e\u8be5\u70b9\u5220\u9664\u5224\u65ad\u4e34\u65f6\u4e09\u89d2\u5f62\u6570\u7ec4\u4e2d\u7684\u574f\u4e09\u89d2\u5f62\u5e76\u4ece\u4e2d\u5220\u9664\n            # 4\u3001\u62ff\u5230\u8be5\u70b9\uff0c\u904d\u5386\u6240\u6709\u4e34\u65f6\u4e09\u89d2\u5f62\uff0c\u5982\u679c\u8be5\u70b9\u5728\u4e34\u65f6\u4e09\u89d2\u5f62\u5185\uff0c\u5219\u8fd9\u4e2a\u4e34\u65f6\u4e09\u89d2\u5f62\u662f\u574f\u4e09\u89d2\u5f62\n            point = points&#91;i]\n            bad_triangles = &#91;]\n            for triangle in triangles:\n                if self.point_in_circumcircle_extended(point, triangle, all_points):\n                    bad_triangles.append(triangle)\n\n            # 5\u3001\u4ece\u4e34\u65f6\u4e09\u89d2\u5f62\u6570\u7ec4\u4e2d\u79fb\u9664\u574f\u4e09\u89d2\u5f62\n            for triangle in bad_triangles:\n                triangles.remove(triangle)\n\n            # \u4e8c\u3001\u51c6\u5907\u57fa\u4e8e\u8be5\u70b9\u6784\u9020\u65b0\u7684\u4e09\u89d2\u5f62\n            # 6\u3001\u5982\u679c\u574f\u4e09\u89d2\u5f62\u7684\u8fb9\u4e0d\u91cd\u5408\uff0c\u90a3\u4e48\u52a0\u5165\u6570\u7ec4\n            polygon_edges = &#91;]\n            for triangle in bad_triangles:\n                for j in range(3):\n                    edge = &#91;triangle&#91;j], triangle&#91;(j+1) % 3]]\n                    edge.sort()\n                    flag = False\n                    for o_triangle in bad_triangles:\n                        if o_triangle == triangle:\n                            continue\n                        for k in range(3):\n                            o_edge = &#91;o_triangle&#91;k], o_triangle&#91;(k+1) % 3]]\n                            o_edge.sort()\n                            if o_edge == edge:\n                                flag = True\n                                break\n                        if flag:\n                            break\n                    if not flag:\n                        polygon_edges.append(edge)\n\n            # 7\u3001\u6784\u9020\u65b0\u7684\u4e34\u65f6\u4e09\u89d2\u5f62\uff0c\u5e76\u52a0\u5165\u4e34\u65f6\u4e09\u89d2\u5f62\u6570\u7ec4\n            for edge in polygon_edges:\n                triangles.append(&#91;i, edge&#91;0], edge&#91;1]])\n\n        final_triangles = &#91;]\n        # 8\u3001\u6700\u540e\u6392\u9664\u8d85\u7ea7\u4e09\u89d2\u5f62\u7684\u9876\u70b9\u6784\u6210\u7684\u4e09\u89d2\u5f62\n        for triangle in triangles:\n            if all(t&lt;n for t in triangle):\n                final_triangles.append(triangle)\n        return final_triangles<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u9644\u5f55point_in_circumcircle_extended\u51fd\u6570\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>def point_in_circumcircle_extended(self, point, triangle, all_points):\n        \"\"\"\u5224\u65ad\u70b9\u662f\u5426\u5728\u4e09\u89d2\u5f62\u7684\u5916\u63a5\u5706\u5185\"\"\"\n        px, py = point\n\n        # \u83b7\u53d6\u4e09\u89d2\u5f62\u4e09\u4e2a\u9876\u70b9\n        p1 = all_points&#91;triangle&#91;0]]\n        p2 = all_points&#91;triangle&#91;1]]\n        p3 = all_points&#91;triangle&#91;2]]\n\n        x1, y1 = p1\n        x2, y2 = p2\n        x3, y3 = p3\n\n        # \u8ba1\u7b97\u5916\u63a5\u5706\u5706\u5fc3\u548c\u534a\u5f84\n        d = 2 * ((x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1))\n\n        if abs(d) &lt; 1e-10:  # \u4e09\u70b9\u5171\u7ebf\n            return False\n\n        # \u514b\u83b1\u59c6\u6cd5\u5219\u6c42\u89e3\u5916\u63a5\u5706\u5706\u5fc3\n        ux = ((x1**2 + y1**2) * (y2 - y3) + (x2**2 + y2**2) * (y3 - y1) + (x3**2 + y3**2) * (y1 - y2)) \/ d\n        uy = ((x1**2 + y1**2) * (x3 - x2) + (x2**2 + y2**2) * (x1 - x3) + (x3**2 + y3**2) * (x2 - x1)) \/ d\n\n        # \u8ba1\u7b97\u534a\u5f84\u7684\u5e73\u65b9\n        radius_sq = (x1 - ux)**2 + (y1 - uy)**2\n\n        # \u8ba1\u7b97\u70b9\u5230\u5706\u5fc3\u7684\u8ddd\u79bb\u7684\u5e73\u65b9\n        dist_sq = (px - ux)**2 + (py - uy)**2\n\n        # \u5982\u679c\u8ddd\u79bb\u5c0f\u4e8e\u534a\u5f84\uff0c\u5219\u5728\u5706\u5185\n        return dist_sq &lt; radius_sq<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b64\u5916\uff0c\u5206\u5272\u5408\u5e76\u7b97\u6cd5\u7684\u57fa\u672c\u6b65\u9aa4\u4e3a\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5212\u5206\u70b9\u96c6<\/li>\n\n\n\n<li>\u9010\u4e2a\u70b9\u96c6\u8fdb\u884c\u4e09\u89d2\u5256\u5206\uff08\u4e00\u822c\u662f\u5212\u5206\u52303\u4e2a\u70b9\u76f4\u63a5\u51fa\u4e09\u89d2\u5f62\uff09<\/li>\n\n\n\n<li>\u5408\u5e76\u4e09\u89d2\u5256\u5206\u7ed3\u679c<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5408\u5e76\u4e09\u89d2\u5256\u5206\u7ed3\u679c\u601d\u8def\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"535\" src=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/486be3929ef69f83e19ca470b4733c24_720-1024x535.jpg\" alt=\"\" class=\"wp-image-194\" style=\"aspect-ratio:1.9140498017034002;width:503px;height:auto\" srcset=\"https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/486be3929ef69f83e19ca470b4733c24_720-1024x535.jpg 1024w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/486be3929ef69f83e19ca470b4733c24_720-300x157.jpg 300w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/486be3929ef69f83e19ca470b4733c24_720-768x401.jpg 768w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/486be3929ef69f83e19ca470b4733c24_720-421x220.jpg 421w, https:\/\/geocommunity.vip\/wp-content\/uploads\/2026\/05\/486be3929ef69f83e19ca470b4733c24_720.jpg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e09\u89d2\u7f51\u751f\u6210\u7b97\u6cd5\uff1a\u6838\u5fc3\u5206\u4e3a\u6536\u7f29\u751f\u957f\u4e0e\u6269\u5f20\u751f\u957f\u4e24\u7c7b\uff0c\u524d\u8005\u5148\u6784\u5efa\u70b9\u96c6\u7684\u51f8\u58f3\uff0c\u518d\u5411\u5185\u9010\u6b65\u751f\u6210\u4e09\u89d2\u7f51\u3002\u540e\u8005\u5219\u4ece\u521d\u59cb\u4e09\u89d2\u5f62\u51fa\u53d1\uff0c\u5229\u7528\u7a7a\u5916\u63a5\u5706\u6216\u5f20\u89d2\u6700\u5927\u51c6\u5219\u5411\u5916\u5c42\u5c42\u6269\u5c55\uff0c\u901a\u8fc7\u5c40\u90e8\u4f18\u5316\u4fdd\u8bc1\u4e09\u89d2\u7f51\u7684\u201c\u6700\u5706\u6da6\u201d\u7279\u6027\uff0c\u6700\u7ec8\u5f62\u6210\u8986\u76d6\u6574\u4e2a\u6570\u636e\u533a\u57df\u3001\u6ee1\u8db3Delaunay\u7279\u6027\u7684\u4e09\u89d2\u7f51\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5730\u5f62\u5efa\u6a21\u3001\u7a7a\u95f4\u5206\u6790\u7b49\u573a\u666f\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">2\u3001\u6c42\u6bcf\u4e2a\u4e09\u89d2\u5f62\u7684\u5916\u5fc3<\/h5>\n\n\n\n<h5 class=\"wp-block-heading\">3\u3001\u628a\u76f8\u90bb\u4e09\u89d2\u5f62\u7684\u5916\u5fc3\u8fde\u8d77\u6765<\/h5>\n\n\n\n<h5 class=\"wp-block-heading\">4\u3001\u5f97\u5230\u6cf0\u68ee\u8fb9<\/h5>\n\n\n\n<h5 class=\"wp-block-heading\">5\u3001\u5bf9\u51f8\u5305\u8fb9\u5411\u5916\u5ef6\u4f38\u5e76\u88c1\u526a<\/h5>\n\n\n\n<h5 class=\"wp-block-heading\">6\u3001\u5f62\u6210\u6cf0\u68ee\u591a\u8fb9\u5f62<\/h5>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u8282\u5305\u542b\uff1a\u57fa\u7840\u77e5\u8bc6\u3001\u683c\u6797\u5384\u59c6\u626b\u63cf\u6cd5\u751f\u6210\u51f8\u5305\uff08Pyt &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-190","post","type-post","status-publish","format-standard","hentry","category-gis"],"_links":{"self":[{"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/posts\/190","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/comments?post=190"}],"version-history":[{"count":10,"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/posts\/190\/revisions"}],"predecessor-version":[{"id":211,"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/posts\/190\/revisions\/211"}],"wp:attachment":[{"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/media?parent=190"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/categories?post=190"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/geocommunity.vip\/index.php\/wp-json\/wp\/v2\/tags?post=190"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}