{"id":1693,"date":"2022-05-03T17:12:44","date_gmt":"2022-05-03T09:12:44","guid":{"rendered":"https:\/\/www.caiqinyi.cn\/?p=1693"},"modified":"2025-02-26T11:03:50","modified_gmt":"2025-02-26T03:03:50","slug":"point_in_polygon_problem","status":"publish","type":"post","link":"https:\/\/www.caiqinyi.cn\/index.php\/2022\/05\/03\/point_in_polygon_problem\/","title":{"rendered":"\u6539\u8fdb\u7684Point In Polygon Problem\u7b97\u6cd5\u4ecb\u7ecd"},"content":{"rendered":"<p><script type=\"text\/javascript\" async src=\"https:\/\/www.caiqinyi.cn\/wp-content\/MathJax\/MathJax.js?config=TeX-AMS_CHTML\">\n<\/script><br \/>\n<script type=\"text\/x-mathjax-config\">\n    MathJax.Hub.Config({\n        tex2jax: {inlineMath: [['$','$']]},\n        TeX: {equationNumbers: {autoNumber: [\"AMS\"], useLabelIds: true}},\n        \"HTML-CSS\": {linebreaks: {automatic: true}},\n        SVG: {linebreaks: {automatic: true}}\n    });\n<\/script><\/p>\n<p>\u4eca\u5929\u603b\u7b97\u628a\u65b0\u7684\u623f\u95f4\u57fa\u672c\u6253\u626b\u5b8c\u6bd5\u4e86, \u5fc3\u60c5\u5341\u5206\u6109\u5feb~ \u4e0b\u5468\u5c31\u662f\u4e94\u4e00\u5047\u671f\u4e86, \u73b0\u5728\u676d\u5dde\u7684\u75ab\u60c5\u5f62\u52bf\u611f\u89c9\u662f\u6697\u6d41\u6d8c\u52a8, \u4f46\u613f\u80fd\u591f\u987a\u5229\u56de\u5bb6\u53ed=.= \u6700\u8fd1\u5728\u5b66\u4e60Jordan\u66f2\u7ebf\u5b9a\u7406, \u867d\u7136\u5176\u8bc1\u660e\u8fd8\u6ca1\u770b\u5b8c, \u4f46\u53d1\u73b0\u4e86\u4e00\u4e2a\u5f88\u6709\u8da3\u7684\u7b97\u6cd5\u5e94\u7528\u2014\u2014\u5224\u65ad\u70b9\u662f\u5426\u5728\u591a\u8fb9\u5f62\u5185\u90e8\u7684\u7b97\u6cd5, \u540c\u65f6\u8fd9\u4e5f\u662f\u6700\u8fd1\u5de5\u4f5c\u5185\u5bb9\u4e2d\u7528\u5230\u7684\u4e00\u4e2a\u7b97\u6cd5, \u56e0\u6b64\u60f3\u8981\u8bb0\u5f55\u4e00\u4e0b\u76f8\u5173\u7b97\u6cd5\u8981\u70b9.<\/p>\n<p><!--more--><\/p>\n<p><strong>\u53c2\u8003\u6750\u6599<\/strong><br \/>\n1. <a href=\"http:\/\/www.brionas.com\/2018\/07\/11\/%E6%94%B9%E8%BF%9B%E7%9A%84point-in-polygon-problem%E7%AE%97%E6%B3%95%E4%BB%8B%E7%BB%8D\/\">\u6539\u8fdb\u7684point in polygon problem\u7b97\u6cd5\u4ecb\u7ecd<\/a><\/p>\n\n<h3>\u80cc\u666f\u77e5\u8bc6<\/h3>\n<p>\u70b9\u548c\u591a\u8fb9\u5f62\u7684\u4f4d\u7f6e\u95ee\u9898(Point-In-Polygon(PIP) Problem), \u4e00\u822c\u6307\u7684\u662f\u7ed9\u5b9a\u4e8c\u7ef4\u5e73\u9762\u4e0a\u7684\u4e00\u4e2a\u70b9$Q$\u4ee5\u53ca\u4e00\u4e2a\u591a\u8fb9\u5f62$P$\uff0c\u600e\u6837\u5224\u65ad\u70b9$Q$\u662f\u4f4d\u4e8e\u591a\u8fb9\u5f62$P$\u5185\u90e8\u8fd8\u662f\u5916\u90e8. \u8be5\u7b97\u6cd5\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66, \u5730\u7406\u7a7a\u95f4\u4fe1\u606f\u5b66\u7b49\u9886\u57df\u6709\u5e7f\u6cdb\u7684\u5e94\u7528. \u76ee\u524d\u6709\u4e24\u79cd\u901a\u7528\u7684\u7b97\u6cd5\u5b9e\u73b0: Ray Casting Algorithm(\u53c8\u79f0Even-Odd\u7b97\u6cd5) \u548cWinding Number Algorithm.<\/p>\n<h4>$\\cdot$ Ray Casting Algorithm<\/h4>\n<p>\u4ece$Q$\u5411\u65e0\u7a77\u8fdc\u70b9\u53d1\u5c04\u4e00\u6761\u5c04\u7ebf, \u8ba1\u7b97\u8be5\u5c04\u7ebf\u548c\u591a\u8fb9\u5f62\u7684\u8fb9\u76f8\u4ea4\u7684\u6b21\u6570, \u5982\u679c\u662f\u5947\u6570\u6b21, \u5219\u70b9\u5728\u591a\u8fb9\u5f62\u5185\u90e8; \u5982\u679c\u662f\u5076\u6570\u6b21, \u5219\u70b9\u5728\u591a\u8fb9\u5f62\u5916\u90e8. \u8be5\u7b97\u6cd5\u7684\u7406\u8bba\u4f9d\u636e\u662fJordan\u66f2\u7ebf\u5b9a\u7406: \u8bbe$\\gamma: S^1 \\to E^2$\u662f\u4e00\u4e2a\u5d4c\u5165, \u5219$E^2 \\backslash \\gamma(S^1)$\u5b58\u5728\u552f\u4e00\u4e00\u4e2a\u6709\u754c\u9053\u8def\u5206\u652f$U$, \u5e76\u4e14$U$\u4ee5$\\gamma(S^1)$\u4e3a\u8fb9\u754c, \u5373$\\overline{U} \\backslash U^{\\circ} = \\gamma(S^1)$.<br \/>\n\u6839\u636eJordan\u66f2\u7ebf\u5b9a\u7406, \u53ef\u4ee5\u5bf9\u7b97\u6cd5\u6709\u76f4\u89c2\u7684\u89e3\u91ca: \u5bf9\u4e8e\u7ed9\u5b9a\u70b9$Q$\u548c\u65e0\u7a77\u8fdc\u70b9\u95f4$S$\u7684\u8fde\u7ebf$QS$\uff0c\u7531\u4e8e$S$\u5fc5\u7136\u4f4d\u4e8e\u591a\u8fb9\u5f62$P$\u5916\u90e8, \u800c$QS$\u548c\u591a\u8fb9\u5f62\u7684\u6bcf\u4e2a\u4ea4\u70b9$K$\u90fd\u662f\u4e00\u4e2a\u5916\u90e8\u548c\u5185\u90e8\u5207\u6362\u7684\u4e34\u754c\u70b9:<br \/>\n1. \u5982\u679c\u662f\u5947\u6570\u4e2a\u4ea4\u70b9, \u4ece$S$\u51fa\u53d1, \u5207\u6362\u8fc7\u7a0b\u5fc5\u7136\u662f: $S$(\u5916\u90e8) \u2013>(\u5185\u90e8) \u2013>(\u5916\u90e8) $\\cdots$\u2013>(\u5185\u90e8\uff09\u2013>$Q$, \u8fd9\u6837$Q$\u5fc5\u7136\u4f4d\u4e8e$P$\u5185\u90e8.<br \/>\n2. \u5982\u679c\u662f\u5076\u6570\u4e2a\u4ea4\u70b9, \u4ece$S$\u51fa\u53d1, \u5207\u6362\u8fc7\u7a0b\u5fc5\u7136\u662f: $S$(\u5916\u90e8) \u2013>(\u5185\u90e8) \u2013>(\u5916\u90e8) $\\cdots$\u2013>(\u5916\u90e8) \u2013>$Q$, \u8fd9\u6837$Q$\u5fc5\u7136\u4f4d\u4e8e$P$\u5916\u90e8.<\/p>\n<h4>$\\cdot$ Winding Number Algorithm<\/h4>\n<p>Winding Number Algorithm\u53c8\u79f0\u4e3a\u8f6c\u89d2\u7d2f\u52a0\u6cd5, <a href=\"https:\/\/www.zhihu.com\/question\/28416085\/answer\/40757108\">\u77e5\u4e4e<\/a>\u4e0a\u6709\u4e00\u4e2a\u6bd4\u8f83\u76f4\u89c2\u7684\u89e3\u91ca\u5982\u4e0b:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2022\/05\/Winding-Number-Algorithm.png\" alt=\"\" width=\"498\" height=\"211\" class=\"aligncenter size-full wp-image-1703\" srcset=\"https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2022\/05\/Winding-Number-Algorithm.png 498w, https:\/\/www.caiqinyi.cn\/wp-content\/uploads\/2022\/05\/Winding-Number-Algorithm-300x127.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p><em>\u7ed9\u591a\u8fb9\u5f62\u7684\u9876\u70b9\u4f9d\u6b21\u7f16\u53f7(\u5982\u4e0a\u56fe\u4e2d\u4e3a$A, B, C, D, E$), \u79f0\u5f85\u5224\u65ad\u7684\u70b9\u4e3a$O$. \u4f9d\u6b21\u8003\u5bdf\u89d2$AOB, BOC, COD, DOE, EOA$. \u8fd9\u91cc\u7684\u89d2\u5747\u53d6\u5c0f\u4e8e180\u5ea6\u7684\u90a3\u4e00\u4fa7, \u5e76\u5747\u4e3a\u6709\u5411\u89d2, \u6211\u4eec\u89c4\u5b9a\u9006\u65f6\u9488\u4e3a\u6b63, \u987a\u65f6\u9488\u4e3a\u8d1f. \u4e0a\u9762\u5de6\u56fe\u4e2d, \u4e94\u4e2a\u89d2\u90fd\u662f\u6b63\u7684; \u53f3\u56fe\u4e2d, \u89d2DOE\u662f\u8d1f\u7684. \u628a\u6240\u6709\u7684\u89d2\u7d2f\u52a0\u8d77\u6765, \u6211\u4eec\u53d1\u73b0\u5de6\u56fe\u4e2d\u89d2\u5ea6\u4e4b\u548c\u4e3a360\u5ea6, \u53f3\u56fe\u4e3a\u96f6.<br \/>\n\u5f62\u8c61\u4e00\u70b9\u513f\u7406\u89e3, \u5c31\u662f\u4f60\u7ad9\u5728$O$\u5904, \u8f6c\u8eab\u7528\u76ee\u5149\u628a\u6574\u4e2a\u591a\u8fb9\u5f62\u626b\u63cf\u4e00\u904d. \u82e5\u4f60\u8f6c\u4e86\u5947\u6570\u5708, \u5219\u4f60\u5728\u591a\u8fb9\u5f62\u5185; \u82e5\u4f60\u8f6c\u4e86\u5076\u6570\u5708, \u5219\u4f60\u5728\u591a\u8fb9\u5f62\u5916.<\/em><\/p>\n<p>\u5bf9\u4e8e\u7b80\u5355\u591a\u8fb9\u5f62(\u8fb9\u4e0d\u81ea\u4ea4\u7684\u591a\u8fb9\u5f62), \u62d3\u6251\u4e0a\u5373\u4e3a\u4e0e$S^1$\u540c\u80da\u7684\u56fe\u5f62, \u4e0a\u9762\u7684\u4e24\u79cd\u7b97\u6cd5\u901a\u5e38\u80fd\u5f97\u5230\u76f8\u540c\u7684\u7ed3\u679c. \u5bf9\u4e8e\u8fb9\u76f8\u4ea4\u7684\u975e\u7b80\u5355\u591a\u8fb9\u5f62(\u6b64\u65f6\u4e5f\u65e0\u6cd5\u76f4\u63a5\u4f7f\u7528Jordan\u66f2\u7ebf\u5b9a\u7406), \u5185\u90e8\u4e0e\u5916\u90e8\u901a\u5e38\u6709\u4e0d\u540c\u7684\u5b9a\u4e49: \u6709\u7684\u628a\u91cd\u53e0\u90e8\u5206\u6839\u636e\u5f02\u6216(XOR) \u539f\u5219\u5b9a\u4e49\u4e3a\u5916\u90e8, \u6709\u7684\u5219\u628a\u91cd\u53e0\u90e8\u5206\u6839\u636e\u6216(OR) \u539f\u5219\u5b9a\u4e49\u4e3a\u5185\u90e8. \u7531\u4e8e\u4e00\u822c\u7684Ray Casting\u7b97\u6cd5\u4e0d\u80fd\u591f\u5904\u7406\u5c04\u7ebf\u548c\u9876\u70b9\u76f8\u4ea4\u7684\u60c5\u5f62\u4ee5\u53ca\u5c04\u7ebf\u548c\u591a\u53d8\u5f62\u8fb9\u91cd\u5408\u7b49\u7279\u6b8a\u60c5\u5f62, \u56e0\u6b64\u63a5\u4e0b\u6765\u7b80\u8981\u4ecb\u7ecd\u4e00\u79cd\u7b80\u5355\u6709\u6548\u7684\u6539\u8fdb\u4e86\u7684Ray Casting\u7b97\u6cd5.<\/p>\n<h3>\u7b97\u6cd5\u4ecb\u7ecd<\/h3>\n<p>\u8be5\u7b97\u6cd5\u7531Michael Galetzka\u548cPatrick Glauner\u4e8e2012\u5e74\u63d0\u51fa, 2017\u5e74\u53d1\u8868\u4e8eProceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications(VISIGRAPP 2017). \u503c\u5f97\u4e00\u63d0\u7684\u662f, Michael Galetzka\u8fd8\u5c31\u804c\u4e8eEpic Games, \u4fdd\u4e0d\u51c6\u4ed6\u63d0\u51fa\u7684\u8fd9\u4e2a\u7b97\u6cd5\u5df2\u7ecf\u5e94\u7528\u5728UE\u4e0a\u4e86~<br \/>\n\u7531\u4e8e\u70b9$Q$\u4e0e\u591a\u8fb9\u5f62$P$(\u9876\u70b9\u4e3a$p_1, p_2, \\cdots, p_n$) \u4f4d\u4e8e\u4e8c\u7ef4\u5e73\u9762\u4e0a, \u53ef\u4ee5\u8003\u8651\u5c06$Q$\u548c$P$\u901a\u8fc7\u5750\u6807\u5e73\u79fb, \u4f7f$Q$\u5e73\u79fb\u5230\u5750\u6807\u539f\u70b9\u800c\u5176\u548c$P$\u7684\u76f8\u5bf9\u4f4d\u7f6e\u4e0d\u53d8, \u663e\u7136\u5e73\u79fb\u4e0d\u4f1a\u6539\u53d8\u70b9$Q$\u4e0e\u591a\u8fb9\u5f62$P$\u7684\u4f4d\u7f6e\u5173\u7cfb(\u5728\u591a\u8fb9\u5f62\u5185\u6216\u5916), \u4e0b\u9762\u7b97\u6cd5\u4e3b\u8981\u662f\u9488\u5bf9\u5e73\u79fb\u540e\u7684\u60c5\u5f62\u8fdb\u884c\u8bf4\u660e, \u7b97\u6cd5\u6b65\u9aa4\u5982\u4e0b:<br \/>\n1. \u5224\u65ad$Q$\u662f\u5426\u4f4d\u4e8e\u662f$P$\u7684\u9876\u70b9\u6216\u8005\u4f4d\u4e8e$P$\u7684\u8fb9\u4e0a, \u5982\u679c\u662f, \u70b9$Q$\u5728\u591a\u8fb9\u5f62\u5185\u90e8.<br \/>\n2. \u5728\u9876\u70b9\u96c6\u5408$P$\u4e2d\u5bfb\u627e\u4e0d\u5728$x$\u8f74\u4e0a\u7684\u9876\u70b9, \u5982\u679c\u627e\u4e0d\u5230, \u70b9$Q$\u5728\u591a\u8fb9\u5f62\u5916\u90e8. (\u6ce8: \u6839\u636e\u6b65\u9aa41, $Q$\u4e0d\u5728$P$\u7684\u9876\u70b9\u6216\u8005\u8fb9\u4e0a, \u800c\u627e\u4e0d\u5230\u4e0d\u5728$x$\u8f74\u4e0a\u7684\u70b9\u8bf4\u660e\u591a\u8fb9\u5f62$P$\u7684\u70b9\u90fd\u5728$x$\u8f74\u4e0a, \u800c$Q$\u4f4d\u4e8e\u539f\u70b9, \u8bf4\u660e$Q$\u5728$P$\u7684\u5916\u90e8.)<br \/>\n3. \u8bbe$i = 1$, \u4ece\u70b9$p_s$\u5f00\u59cb\u901a\u8fc7\u91cd\u590d\u4e0b\u9762\u6b65\u9aa4\u76f4\u5230\u6240\u6709\u7684\u9876\u70b9\u90fd\u88ab\u8bbf\u95ee\u5230:<br \/>\n$\\quad$a) \u5224\u65ad\u70b9$p_{s + i}$\u662f\u5426\u4f4d\u4e8e$x$\u8f74\u4e0a, \u5982\u679c\u5728, \u9012\u589e$i$, \u5982\u679c$s + i > n$, \u90a3\u4e48\u5c06$i$\u8bbe\u7f6e\u4e3a$-s$, \u4ece$p_0$\u5f00\u59cb\u7ee7\u7eed\u5bfb\u627e, \u76f4\u5230\u627e\u5230\u4e00\u4e2a\u4e0d\u4f4d\u4e8e$x$\u8f74\u4e0a\u7684\u70b9$p_{s + i}$\u4e3a\u6b62.<br \/>\n$\\quad$b) \u6839\u636e\u6b65\u9aa4a\u4e2d\u7684\u67e5\u627e\u8fc7\u7a0b, \u91c7\u53d6\u4e0b\u9762\u7684\u64cd\u4f5c:<br \/>\n$\\quad \\quad$i) \u5982\u679c\u6b65\u9aa4a\u4e2d\u627e\u65f6\u6ca1\u6709Skip\u6389\u4efb\u4f55\u9876\u70b9, \u90a3\u4e48\u5224\u65ad\u4ece$p_s$\u5230$p_{s + i}$\u7684\u7ebf\u6bb5\u662f\u5426\u548c$x$\u8f74\u7684\u6b63\u534a\u8f74\u76f8\u4ea4, \u5982\u76f8\u4ea4, \u4ea4\u70b9\u4e2a\u6570\u52a01;<br \/>\n$\\quad \\quad$ii) \u5982\u679c\u6b65\u9aa4a\u4e2d\u627e\u65f6Skip\u6389\u81f3\u5c11\u4e00\u4e2a$x$\u8f74\u5750\u6807\u4e3a\u6b63\u7684\u9876\u70b9, \u90a3\u4e48\u5224\u65ad\u4ece$p_s$\u5230$p_{s + i}$\u7684\u7ebf\u6bb5\u662f\u5426\u548c\u6574\u4e2a$x$\u8f74\u76f8\u4ea4, \u5982\u76f8\u4ea4, \u4ea4\u70b9\u4e2a\u6570\u52a01;<br \/>\n$\\quad \\quad$iii)  \u5982\u679c\u6b65\u9aa4a\u4e2d\u627e\u65f6Skip\u6389\u81f3\u5c11\u4e00\u4e2a$x$\u8f74\u5750\u6807\u4e3a\u8d1f\u7684\u9876\u70b9, \u4e0d\u505a\u4efb\u4f55\u64cd\u4f5c; (\u6ce8: \u4e0d\u53ef\u80fd\u540c\u65f6Skip\u6389\u4f4d\u4e8e$x$\u8f74\u6b63\u534a\u8f74\u548c$x$\u8f74\u8d1f\u534a\u8f74\u7684\u70b9, \u5982\u679c\u6709, \u8bf4\u660e$Q$\u4f4d\u4e8e\u591a\u8fb9\u5f62\u7684\u8fb9\u4e0a, \u6b65\u9aa41\u5c31\u8fd4\u56de\u4e86)<br \/>\n$\\quad$c) $p_{s + i}$\u4e3a\u4e0b\u4e00\u8f6e\u8fed\u4ee3\u7684\u8d77\u70b9.<br \/>\n4. \u5224\u65ad\u4ea4\u70b9\u4e2a\u6570\u662f\u5947\u6570\u8fd8\u662f\u5076\u6570, \u5982\u679c\u662f\u5947\u6570, \u8bf4\u660e\u70b9$Q$\u4f4d\u4e8e\u591a\u8fb9\u5f62$P$\u5185\u90e8; \u5982\u679c\u662f\u5076\u6570, \u8bf4\u660e\u70b9$Q$\u4f4d\u4e8e\u591a\u8fb9\u5f62$P$\u5916\u90e8.<\/p>\n<p>\u81f3\u4e8e\u7b97\u6cd5\u7684\u6b63\u786e\u6027\u8bc1\u660e, \u53ef\u53c2\u8003\u8bba\u6587<a href=\"https:\/\/arxiv.org\/pdf\/1207.3502.pdf\">A Simple and Correct Even-Odd Algorithm for the Point-in-Polygon Problem for Complex Polygons<\/a><\/p>\n<p>\u4e0d\u96be\u53d1\u73b0, \u6240\u6709\u70b9\u5747\u53ea\u8bbf\u95ee\u4e00\u904d, \u65f6\u95f4\u590d\u6742\u5ea6\u4e3a$O(n)$, \u4f5c\u8005\u4e5f\u5728<a href=\"https:\/\/github.com\/pglauner\/point_in_polygon\">\u8fd9\u91cc<\/a>\u7ed9\u51fa\u4e86\u5728\u70b9\u7684\u6570\u503c\u7c7b\u578b\u4e3a\u6574\u578b\u60c5\u5f62\u4e0b\u7684\u4e00\u4e2a\u5b9e\u73b0, \u82e5\u540e\u9762\u6709\u7a7a, \u81ea\u5df1\u53ef\u4ee5\u5c1d\u8bd5\u5c06\u5176\u6269\u5c55\u5230\u6d6e\u70b9\u6570\u4e0b\u7684\u60c5\u5f62.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4eca\u5929\u603b\u7b97\u628a\u65b0\u7684\u623f\u95f4\u57fa\u672c\u6253\u626b\u5b8c\u6bd5\u4e86, \u5fc3\u60c5\u5341\u5206\u6109\u5feb~ \u4e0b\u5468\u5c31\u662f\u4e94\u4e00\u5047\u671f\u4e86, \u73b0\u5728\u676d\u5dde\u7684\u75ab\u60c5\u5f62\u52bf\u611f\u89c9\u662f\u6697\u6d41\u6d8c\u52a8,  &hellip; <a href=\"https:\/\/www.caiqinyi.cn\/index.php\/2022\/05\/03\/point_in_polygon_problem\/\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u6539\u8fdb\u7684Point In Polygon Problem\u7b97\u6cd5\u4ecb\u7ecd<\/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":[5],"tags":[],"_links":{"self":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/1693"}],"collection":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/comments?post=1693"}],"version-history":[{"count":19,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/1693\/revisions"}],"predecessor-version":[{"id":3609,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/posts\/1693\/revisions\/3609"}],"wp:attachment":[{"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/media?parent=1693"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/categories?post=1693"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.caiqinyi.cn\/index.php\/wp-json\/wp\/v2\/tags?post=1693"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}