{"id":10132,"date":"2022-11-05T17:29:00","date_gmt":"2022-11-05T09:29:00","guid":{"rendered":"http:\/\/139.9.1.231\/?p=10132"},"modified":"2022-11-04T17:30:16","modified_gmt":"2022-11-04T09:30:16","slug":"marching-cubes","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/11\/05\/marching-cubes\/","title":{"rendered":"Marching Cubes \u7b97\u6cd5"},"content":{"rendered":"\n

\u3000Marching Cubes\u7b97\u6cd5\u662f\u4e09\u7ef4\u79bb\u6563\u6570\u636e\u573a\u4e2d\u63d0\u53d6\u7b49\u503c\u9762<\/strong>\u7684\u7ecf\u5178\u7b97\u6cd5\uff0c\u5176\u4e3b\u8981\u5e94\u7528\u4e8e\u533b\u5b66\u9886\u57df\u7684\u53ef\u89c6\u5316\u573a\u666f\uff0c\u4f8b\u5982CT\u626b\u63cf\u548cMRI\u626b\u63cf\u76843D\u91cd\u5efa\u7b49\u3002<\/p>\n\n\n\n

Marching Cube \u9996\u5148\u5c06\u7a7a\u95f4\u5206\u6210\u4f17\u591a\u7684\u516d\u9762\u4f53\u7f51\u683c\uff0c\u7c7b\u4f3c\u5c06\u7a7a\u95f4\u5206\u6210\u5f88\u591a\u7684\u5c0f\u5757<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

\u6211\u4eec\u6709\u5f88\u591a\u7684\u5df2\u77e5\u91c7\u6837\u70b9\uff0c\u5e76\u4e14\u77e5\u9053\u8fd9\u4e9b\u70b9\u5728\u7a7a\u95f4\u4e2d\u7684\u7a7a\u95f4\u573a\u503c\uff0c\u73b0\u5728\u6211\u4eec\u5c06\u7a7a\u95f4\u5206\u4e3a\u5f88\u591a\u4e2a\u5c0f\u683c\u5b50\uff0c\u6bcf\u4e2a\u5c0f\u683c\u5b50\u90fd\u67098\u4e2a\u9876\u70b9\uff0c\u6211\u4eec\u901a\u8fc7\u8ba1\u7b978\u4e2a\u9876\u70b9\u5468\u56f4\uff08\u8303\u56f4\u4e0e\u516d\u9762\u4f53\u7684\u5927\u5c0f\u76f8\u5173\uff09\u7684\u91c7\u6837\u70b9\uff0c\u8fd1\u4f3c\u8ba1\u7b97\u51fa8\u4e2a\u9876\u70b9\u7684\u7a7a\u95f4\u573a\u503c\uff08\u52a0\u6743\u8bc4\u4ef7\u7b49\u65b9\u6cd5\uff09\u3002\u3000<\/p>\n\n\n\n

\u4ee50\u7b49\u503c\u9762\u4e3a\u4f8b:\u5982\u4f55\u627e\u52300\u7b49\u503c\u9762\u7ecf\u8fc7\u7684\u516d\u9762\u4f53\u7f51\u683c\uff1f\u3000<\/strong><\/p>\n\n\n\n

\u7b97\u6cd5\u4e3b\u8981\u7684\u601d\u60f3\u662f\u5728\u4e09\u7ef4\u79bb\u6563\u6570\u636e\u573a\u4e2d\u901a\u8fc7\u7ebf\u6027\u63d2\u503c\u6765\u903c\u8fd1\u7b49\u503c\u9762\uff0c\u5177\u4f53\u5982\u4e0b\uff1a\u4e09\u7ef4\u79bb\u6563\u6570\u636e\u573a\u4e2d\u6bcf\u4e2a\u6805\u683c\u5355\u5143\u4f5c\u4e3a\u4e00\u4e2a\u4f53\u7d20\uff0c\u4f53\u7d20\u7684\u6bcf\u4e2a\u9876\u70b9\u90fd\u5b58\u5728\u5bf9\u5e94\u7684\u6807\u91cf\u503c\u3002\u5982\u679c\u4f53\u7d20\u9876\u70b9\u4e0a\u7684\u503c\u5927\u4e8e\u6216\u7b49\u4e8e\u7b49\u503c\u9762\u503c\uff0c\u5219\u5b9a\u4e49\u8be5\u9876\u70b9\u4f4d\u4e8e\u7b49\u503c\u9762\u4e4b\u5916\uff0c\u6807\u8bb0\u4e3a\u201c0\u201d\uff1b\u800c\u5982\u679c\u4f53\u7d20\u9876\u70b9\u4e0a\u7684\u503c\u5c0f\u4e8e\u7b49\u503c\u9762\u503c\uff0c\u5219\u5b9a\u4e49\u8be5\u9876\u70b9\u4f4d\u4e8e\u7b49\u503c\u9762\u4e4b\u5185\uff0c\u6807\u8bb0\u4e3a\u201c1\u201d\u3002\u7531\u4e8e\u6bcf\u4e2a\u4f53\u7d20\u5355\u5143\u67098\u4e2a\u9876\u70b9\uff0c\u90a3\u4e48\u5171\u5b58\u57282^8 = 256\u79cd\u60c5\u5f62\uff0c\u4e0b\u56fe\u662fMarching Cubes\u7b97\u6cd5\u768415\u79cd\u57fa\u672c\u60c5\u5f62\uff0c\u5176\u4ed6241\u79cd\u60c5\u5f62\u53ef\u4ee5\u901a\u8fc7\u8fd915\u79cd\u57fa\u672c\u60c5\u5f62\u7684\u65cb\u8f6c\u3001\u6620\u5c04\u7b49\u65b9\u5f0f\u5b9e\u73b0\u3002<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u3000\u6bcf\u4e2a\u4f53\u7d20\u5355\u5143\u4e0a\u9876\u70b9\u548c\u8fb9\u7684\u7d22\u5f15\u89c4\u5219\u5982\u4e0b\u56fe\u5de6\u6240\u793a\uff0c\u5047\u5982\u4f53\u7d20\u4e0b\u65b9\u7684\u9876\u70b93\u7684\u503c\u5c0f\u4e8e\u7b49\u503c\u9762\u503c\uff0c\u5176\u4ed6\u9876\u70b9\u4e0a\u7684\u503c\u90fd\u5927\u4e8e\u7b49\u503c\u9762\u503c\uff08\u5982\u4e0b\u56fe\u53f3\u6240\u793a\uff09\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u751f\u6210\u4e00\u4e2a\u4e0e\u4f53\u7d20\u8fb92\uff0c3\uff0c11\u76f8\u4ea4\u7684\u4e09\u89d2\u9762\u7247\uff0c\u800c\u4e09\u89d2\u9762\u7247\u9876\u70b9\u7684\u5177\u4f53\u4f4d\u7f6e\u5219\u9700\u8981\u6839\u636e\u7b49\u503c\u9762\u503c\u548c\u8fb9\u9876\u70b93-2\uff0c3-0\uff0c3-7\u7684\u503c\u7ebf\u6027\u63d2\u503c\u8ba1\u7b97\u5f97\u5230\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5bf9\u4e8e\u4e0e\u7b49\u503c\u9762\u5b58\u5728\u4ea4\u70b9\u7684\u4f53\u7d20\u8fb9\uff0c\u4ea4\u70b9\u5750\u6807\u7528P\u8868\u793a\uff0cP1<\/sub>\u3001P2<\/sub>\u4ee3\u8868\u8fb9\u4e0a\u4e24\u4e2a\u7aef\u70b9\u7684\u5750\u6807\uff0cV1<\/sub>\u3001V2<\/sub>\u4ee3\u8868\u8fd9\u4e24\u4e2a\u7aef\u70b9\u4e0a\u7684\u503c\uff0cV\u4ee3\u8868\u7b49\u503c\u9762\u503c\uff0c\u90a3\u4e48\u4ea4\u70b9\u5750\u6807\u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n\n\n\n

P = P1<\/sub> + (V \u2013 V1<\/sub>)\u00b7(P2<\/sub> \u2013 P1<\/sub>)\/(V2<\/sub> \u2013 V1<\/sub>)<\/p>\n\n\n\n

\u3000\u3000\u7b97\u6cd5\u7b2c\u4e00\u6b65\uff1a<\/strong>\u901a\u8fc7edgeTable\u8868\u5224\u65ad\u7b49\u503c\u9762\u548c\u4f53\u7d20\u5355\u5143\u54ea\u4e00\u6761\u8fb9\u76f8\u4ea4<\/p>\n\n\n\n

\u3000\u3000\u4f53\u7d20\u5355\u5143\u9876\u70b9\u72b6\u6001\u7684\u7d22\u5f15\u53f7\u5b9a\u4e49\u89c4\u5219\u5982\u4e0b\uff1a<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
cubeindex = 0;\nif (V[0] < isolevel) cubeindex |= 1;\nif (V[1] < isolevel) cubeindex |= 2;\nif (V[2] < isolevel) cubeindex |= 4;\nif (V[3] < isolevel) cubeindex |= 8;\nif (V[4] < isolevel) cubeindex |= 16;\nif (V[5] < isolevel) cubeindex |= 32;\nif (V[6] < isolevel) cubeindex |= 64;\nif (V[7] < isolevel) cubeindex |= 128;<\/pre>\n\n\n\n
\u4ee5\u4e0a\u56fe\u6240\u793a\u4e3a\u4f8b\uff0c\u4ec5\u9876\u70b93\u6807\u8bb0\u4e3a\u201c1\u201d\uff0c\u5176\u4ed6\u9876\u70b9\u6807\u8bb0\u4e3a\u201c0\u201d\uff0c\u90a3\u4e48\u4f53\u7d20\u5355\u5143\u7684\u9876\u70b9\u72b6\u6001\u4e3a0000 1000\u6216\u80058\uff0c\u901a\u8fc7\u67e5\u627e\u8868\u5f97\u5230edgeTable[8] = 1000 0000 1100\uff0c\u610f\u5473\u7740\u4f53\u7d20\u5355\u5143\u7684\u8fb92\uff0c3\uff0c11\u548c\u7b49\u503c\u9762\u76f8\u4ea4\uff0c\u7136\u540e\u901a\u8fc7\u7ebf\u6027\u63d2\u503c\u8ba1\u7b97\u5404\u4e2a\u4ea4\u70b9\u7684\u4f4d\u7f6e\u3002<\/p>\n\n\n\n
\u7b97\u6cd5\u7b2c\u4e8c\u6b65\uff1a<\/strong>\u901a\u8fc7triTable\u8868\u751f\u6210\u5bf9\u5e94\u4e09\u89d2\u9762\u7247\u7684\u7ec4\u6210\u60c5\u51b5<\/p>\n\n\n\n
\u3000\u3000\u8fd8\u662f\u4ee5\u4e0a\u56fe\u6240\u793a\u4e3a\u4f8b\uff0c\u901a\u8fc7\u67e5\u627e\u8868\u5f97\u5230triTable[8] = {3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}\uff0c\u610f\u5473\u7740\u8be5\u79cd\u9876\u70b9\u72b6\u6001\u53ef\u4ee5\u751f\u6210\u4e09\u89d2\u9762\u7247(3, 11, 2)\uff0c\u4ee3\u8868\u4e09\u89d2\u9762\u7247\u76843\u4e2a\u9876\u70b9\u4e3a\u8fb93\uff0c11\uff0c2\u548c\u7b49\u503c\u9762\u76f8\u4ea4\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n
\u3000\u3000\u7ecf\u8fc7\u4e0a\u8ff0\u6b65\u9aa4\u4e4b\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u7b49\u503c\u9762\u7684\u70b9\u9762\u4fe1\u606f\u3002\u4e3a\u4e86\u8fdb\u4e00\u6b65\u5b8c\u5584\u663e\u793a\u6548\u679c\uff0c\u9700\u8981\u8c03\u6574\u9876\u70b9\u6cd5\u5411\u3002\u5047\u8bbe\u9876\u70b9(i, j, k)\u4e0a\u7684\u503c\u4e3af(i, j, k)\uff0c\u91c7\u7528\u4e2d\u5fc3\u5dee\u5206\u65b9\u6cd5\u53ef\u4ee5\u8ba1\u7b97\u8be5\u70b9\u5904\u7684\u68af\u5ea6\u77e2\u91cf\uff1a<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u5bf9G\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u5f97\u5230\u9876\u70b9(i, j, k)\u4e0a\u7684\u5355\u4f4d\u6cd5\u5411\u91cf\uff0c\u7136\u540e\u5bf9\u4f53\u7d20\u5355\u5143\u4e0a8\u4e2a\u9876\u70b9\u7684\u6cd5\u5411\u91cf\u8fdb\u884c\u7ebf\u6027\u63d2\u503c\u5c31\u53ef\u5f97\u5230\u4e09\u89d2\u9762\u7247\u5404\u4e2a\u9876\u70b9\u7684\u663e\u793a\u6cd5\u5411\u91cf\u3002<\/p>\n\n\n\n
\"\"\/<\/figure><\/div>\n\n\n\n
\"\"\/<\/figure>\n\n\n\n
\u53c2\u8003\uff1ahttp:\/\/graphics.stanford.edu\/~mdfisher\/MarchingCubes.html<\/p>\n\n\n\n
Marching Cube\u7684\u95ee\u9898<\/h2>\n\n\n\n
\u5f53\u7136\u6700\u521d\u7684Marching Cube \u6709\u5f88\u591a\u95ee\u9898\uff0c\u4f8b\u5982\u62d3\u6251\u8fde\u63a5\u4e8c\u4e49\u6027\uff0c\u4e00\u79cd\u72b6\u6001\u53ef\u4ee5\u6709\u591a\u79cd\u8fde\u63a5\u5173\u7cfb<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
\u800c\u4e14Marching Cube\u7684\u6548\u7387\u4e0d\u662f\u7279\u522b\u9ad8\uff0c\u9700\u8981\u501f\u52a9\u5206\u5c42\u7ed3\u6784\u548c\u5e76\u884c\u8ba1\u7b97\u3002
\u800c\u4e14Marching Cube\u751f\u6210\u9762\u7247\u7684\u5927\u5c0f\u4e0e\u516d\u9762\u4f53\u7684\u5927\u5c0f\u76f8\u5173\uff0c\u8fc7\u5927\u5219\u4f1a\u5bfc\u81f4\u6a21\u578b\u6a21\u7cca\uff0c\u7ec6\u8282\u6d88\u5931\uff0c\u8fc7\u5c0f\u4f1a\u5bfc\u81f4\u9762\u7247\u7684\u6570\u76ee\u8fc7\u591a\u3002<\/p>\n\n\n\n
\u4f46\u662f\u4ece1987\u5e74\u63d0\u51faMarching Cube\u81f3\u4eca\uff0c\u5df2\u7ecf\u5bf9\u5176\u6709\u4e86\u5f88\u591a\u7684\u6539\u8fdb\u548c\u4f18\u5316\u7b97\u6cd5\uff0c\u5728\u5904\u7406\u65f6\u95f4\uff0c\u51cf\u5c11\u5185\u5b58\u5f00\u9500\uff0c\u5206\u8fa8\u7387\u65b9\u9762\u90fd\u6709\u5f88\u5927\u7684\u4f18\u5316\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u3000Marching Cubes\u7b97\u6cd5\u662f\u4e09\u7ef4\u79bb\u6563\u6570\u636e\u573a\u4e2d\u63d0\u53d6\u7b49\u503c\u9762\u7684\u7ecf\u5178\u7b97\u6cd5\uff0c\u5176\u4e3b\u8981\u5e94\u7528\u4e8e\u533b\u5b66\u9886\u57df\u7684\u53ef\u89c6\u5316\u573a\u666f\uff0c\u4f8b … \u7ee7\u7eed\u9605\u8bfbMarching Cubes \u7b97\u6cd5<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[31,33],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/10132"}],"collection":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/comments?post=10132"}],"version-history":[{"count":18,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/10132\/revisions"}],"predecessor-version":[{"id":10157,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/10132\/revisions\/10157"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=10132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=10132"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=10132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}