{"id":99556,"date":"2026-09-02T19:58:01","date_gmt":"2026-09-02T11:58:01","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/99556.html"},"modified":"2026-09-02T19:58:01","modified_gmt":"2026-09-02T11:58:01","slug":"%e5%ad%97%e5%8d%8a%e8%89%b2%e8%b0%83%e5%8e%9f%e7%90%86%e8%af%a6%e8%a7%a3%ef%bc%88%e5%9b%9b%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/99556.html","title":{"rendered":"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09"},"content":{"rendered":"<p id=\"main-toc\">\u76ee\u5f55<\/p>\n<p id=\"-toc\" style=\"margin-left:0px\">\n<p id=\"12.3%20%E5%9B%BE%E6%A1%88%E6%8A%96%E5%8A%A8-toc\" style=\"margin-left:0px\">12.3 \u56fe\u6848\u6296\u52a8<\/p>\n<p id=\"12.4%20%E9%9D%9E%E5%91%A8%E6%9C%9F%E6%8A%96%E5%8A%A8-toc\" style=\"margin-left:0px\">12.4 \u975e\u5468\u671f\u6296\u52a8<\/p>\n<p id=\"12.4.1%20%E5%BC%97%E6%B4%9B%E4%BC%8A%E5%BE%B7%E2%80%91%E6%96%AF%E5%9D%A6%E4%BC%AF%E6%A0%BC%E7%AE%97%E6%B3%95-toc\" style=\"margin-left:40px\">12.4.1 \u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5<\/p>\n<p id=\"%E5%BD%A9%E8%89%B2%E5%9B%BE%E5%83%8F%E7%9A%84%E6%8A%96%E5%8A%A8%E5%A4%84%E7%90%86-toc\" style=\"margin-left:80px\">\u5f69\u8272\u56fe\u50cf\u7684\u6296\u52a8\u5904\u7406<\/p>\n<p id=\"12.4.2%20%E5%9F%BA%E4%BA%8E%E7%A9%BA%E9%97%B4%E5%A1%AB%E5%85%85%E6%9B%B2%E7%BA%BF%E7%9A%84%E6%8A%96%E5%8A%A8%E7%AE%97%E6%B3%95-toc\" style=\"margin-left:40px\">12.4.2 \u57fa\u4e8e\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7684\u6296\u52a8\u7b97\u6cd5<\/p>\n<p id=\"%E5%83%8F%E7%B4%A0%E9%81%8D%E5%8E%86%E6%8E%92%E5%BA%8F-toc\" style=\"margin-left:80px\">\u50cf\u7d20\u904d\u5386\u6392\u5e8f<\/p>\n<p id=\"%E5%9F%BA%E4%BA%8E%E7%9A%AE%E4%BA%9A%E8%AF%BA%E6%9B%B2%E7%BA%BF%E7%9A%84%E5%9B%BE%E5%83%8F%E5%8C%BA%E5%9F%9F%E5%88%92%E5%88%86-toc\" style=\"margin-left:80px\">\u57fa\u4e8e\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u56fe\u50cf\u533a\u57df\u5212\u5206<\/p>\n<p id=\"%E8%87%AA%E9%80%82%E5%BA%94%E5%88%86%E5%89%B2-toc\" style=\"margin-left:80px\">\u81ea\u9002\u5e94\u5206\u5272<\/p>\n<p id=\"%E8%87%AA%E9%80%82%E5%BA%94%E5%88%86%E5%89%B2%E8%AE%A1%E7%AE%97%E6%B5%81%E7%A8%8B-toc\" style=\"margin-left:80px\">\u81ea\u9002\u5e94\u5206\u5272\u8ba1\u7b97\u6d41\u7a0b<\/p>\n<p id=\"%E6%8A%96%E5%8A%A8%E5%8D%95%E5%85%83%E9%87%8F%E5%8C%96-toc\" style=\"margin-left:80px\">\u6296\u52a8\u5355\u5143\u91cf\u5316<\/p>\n<p id=\"%E9%BB%91%E7%82%B9%E7%B0%87%E4%BD%8D%E7%BD%AE%E5%BE%AE%E8%B0%83-toc\" style=\"margin-left:80px\">\u9ed1\u70b9\u7c07\u4f4d\u7f6e\u5fae\u8c03<\/p>\n<p id=\"%E5%AE%8C%E6%95%B4%E6%8A%96%E5%8A%A8%E7%AE%97%E6%B3%95%E6%B5%81%E7%A8%8B-toc\" style=\"margin-left:80px\">\u5b8c\u6574\u6296\u52a8\u7b97\u6cd5\u6d41\u7a0b<\/p>\n<hr id=\"hr-toc\" \/>\n<h2 id=\"12.3%20%E5%9B%BE%E6%A1%88%E6%8A%96%E5%8A%A8\">12.3 \u56fe\u6848\u6296\u52a8<\/h2>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6709\u5e8f\u6296\u52a8\u5e38\u5e38\u4f1a\u548c\u4e00\u79cd\u540d\u4e3a\u56fe\u6848\u6296\u52a8&#xff08;Pattern Dithering&#xff09;\u7684\u6280\u672f\u76f8\u6df7\u6dc6\u3002\u8be5\u65b9\u6cd5\u5c06\u56fe\u50cf\u5212\u5206\u4e3a\u82e5\u5e72\u5927\u5c0f\u4e3a\u202fN\u00d7N\u202f\u7684\u6296\u52a8\u5355\u5143&#xff0c;\u8fd9\u4e00\u70b9\u548c\u6709\u5e8f\u6296\u52a8\u7684\u5904\u7406\u65b9\u5f0f\u7c7b\u4f3c\u3002\u6bcf\u4e2a\u6296\u52a8\u5355\u5143\u4e00\u5171\u53ef\u4ee5\u751f\u6210 <img decoding=\"async\" alt=\"(N^2+1)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115759-6a980f47e317b.png\" \/> \u4e2a\u91cf\u5316\u7070\u5ea6\u7b49\u7ea7\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u7b97\u6cd5\u6267\u884c\u6d41\u7a0b\u5982\u4e0b&#xff1a;\u4f7f\u7528\u8fd9<img decoding=\"async\" alt=\"(N^2+1)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115759-6a980f47e317b.png\" \/> \u4e2a\u91cf\u5316\u7b49\u7ea7\u4f5c\u4e3a\u7d22\u5f15&#xff0c;\u8bfb\u53d6\u4e00\u5f20\u6296\u52a8\u56fe\u6848\u67e5\u627e\u8868&#xff1b;\u9488\u5bf9\u6bcf\u4e00\u4e2a\u5355\u5143&#xff0c;\u5229\u7528\u5f0f (12.1) \u8ba1\u7b97\u5355\u5143\u5185\u56fe\u50cf\u7684\u5e73\u5747\u4eae\u5ea6&#xff0c;\u518d\u5c06\u8be5\u5e73\u5747\u503c\u91cf\u5316\u81f3 <img decoding=\"async\" alt=\"(N^2+1)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115759-6a980f47e317b.png\" \/> \u4e2a\u7b49\u7ea7\u4e2d\u7684\u67d0\u4e00\u7ea7\u3002\u6700\u540e\u4ee5\u91cf\u5316\u540e\u7684\u7b49\u7ea7\u503c\u4e3a\u7d22\u5f15&#xff0c;\u53d6\u51fa\u67e5\u627e\u8868\u4e2d\u5bf9\u5e94\u7684\u6296\u52a8\u56fe\u6848\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u9700\u8981\u6ce8\u610f&#xff1a;\u5982\u679c\u6296\u52a8\u56fe\u6848\u67e5\u627e\u8868\u76f4\u63a5\u9009\u7528 12.2 \u8282\u7b97\u51fa\u7684\u6709\u5e8f\u6296\u52a8\u6240\u5bf9\u5e94\u7684<img decoding=\"async\" alt=\"(N^2+1)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115759-6a980f47e317b.png\" \/>\u5957\u56fe\u6848&#xff0c;\u90a3\u4e48\u56fe\u6848\u6296\u52a8\u7b97\u6cd5\u751f\u6210\u7684\u6548\u679c\u4e0e\u6709\u5e8f\u6296\u52a8\u76f8\u8fd1\u4f46\u5e76\u4e0d\u5b8c\u5168\u7b49\u540c\u3002\u4e8b\u5b9e\u4e0a&#xff0c;\u5bf9\u4e8e\u540c\u4e00\u4e2a\u5e73\u5747\u4eae\u5ea6&#xff0c;\u56fe\u6848\u6296\u52a8\u6c38\u8fdc\u67e5\u8868\u8f93\u51fa\u5b8c\u5168\u76f8\u540c\u7684\u56fe\u6848&#xff1b;\u800c\u6709\u5e8f\u6296\u52a8\u5219\u4f1a\u6839\u636e\u6296\u52a8\u5355\u5143\u5185\u90e8\u50cf\u7d20\u4eae\u5ea6\u7684\u5b9e\u9645\u5206\u5e03&#xff0c;\u751f\u6210\u4e0d\u4e00\u6837\u7684\u4e8c\u503c\u70b9\u9635\u56fe\u6848\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6296\u52a8\u56fe\u6848\u67e5\u627e\u8868\u7684\u9009\u53d6\u81ea\u7531\u5ea6\u5f88\u9ad8\u3002\u6b63\u56e0\u5982\u6b64&#xff0c;\u56fe\u6848\u6296\u52a8\u53ef\u7528\u6765\u4e3a\u56fe\u50cf\u751f\u6210\u591a\u79cd\u7279\u6b8a\u6e32\u67d3\u6548\u679c\u3002\u8be5\u6280\u672f\u4e00\u4e2a\u7ecf\u5178\u7684\u5b9e\u4f8b\u5c31\u662f\u884c\u5f0f\u6253\u5370\u673a\u8f93\u51fa\u7684\u56fe\u50cf&#xff08;\u89c1\u56fe 12\u201118&#xff09;&#xff1a;\u8fd9\u7c7b\u6548\u679c\u7684\u5b9e\u73b0\u539f\u7406\u5c31\u662f\u6784\u9020\u4e00\u5f20\u6296\u52a8\u8868&#xff0c;\u8ba9\u6bcf\u4e00\u4e2a\u91cf\u5316\u7b49\u7ea7\u90fd\u5bf9\u5e94\u4e00\u7ec4\u7cbe\u5fc3\u6311\u9009\u3001\u53ef\u91cd\u53e0\u6253\u5370\u7684\u5b57\u7b26\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5373\u4fbf\u5728\u8fd9\u7c7b\u7279\u6b8a\u6548\u679c\u573a\u666f\u4e0b&#xff0c;\u57fa\u4e8e\u9608\u503c\u51fd\u6570\u7684\u6296\u52a8&#xff08;\u6709\u5e8f\u6296\u52a8&#xff09;\u4ecd\u7136\u6bd4\u56fe\u6848\u6296\u52a8\u7075\u6d3b\u5f97\u591a\u3002\u518d\u6b21\u63d0\u9192\u8bfb\u8005&#xff1a;\u6709\u5e8f\u6296\u52a8\u751f\u6210\u7684\u70b9\u7c07\u5f62\u72b6\u7531\u9608\u503c\u51fd\u6570\u7684\u7b49\u503c\u7ebf\u51e0\u4f55\u5f62\u6001\u51b3\u5b9a&#xff0c;\u800c\u9608\u503c\u51fd\u6570\u672c\u8eab\u53ef\u4ee5\u8bbe\u8ba1\u6210\u4efb\u610f\u5f62\u72b6\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115759-6a980f47ecfeb.png\" \/><\/p>\n<h2 id=\"12.4%20%E9%9D%9E%E5%91%A8%E6%9C%9F%E6%8A%96%E5%8A%A8\">12.4 \u975e\u5468\u671f\u6296\u52a8<\/h2>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5728\u5404\u7c7b\u975e\u5468\u671f\u6296\u52a8\u7b97\u6cd5\u5f53\u4e2d&#xff0c;\u6700\u65e9\u51fa\u73b0\u7684\u4e00\u6279\u7b97\u6cd5\u5305\u542b\u968f\u673a\u8c03\u5236\u6296\u52a8&#xff1b;\u4e0d\u8fc7\u73b0\u5982\u4eca&#xff0c;\u8be5\u7b97\u6cd5\u5df2\u7ecf\u5927\u591a\u88ab\u6548\u679c\u66f4\u4f18\u7684\u65b9\u6848\u6240\u53d6\u4ee3\u3002\u800c\u53e6\u4e00\u79cd\u95ee\u4e16\u7a0d\u665a\u3001\u73b0\u5df2\u6210\u4e3a\u7ecf\u5178\u4e14\u5e7f\u4e3a\u6d41\u884c\u7684\u7b97\u6cd5\u4fbf\u662f\u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c&#xff08;Floyd\u2011Steinberg&#xff09;\u8bef\u5dee\u6269\u6563\u7b97\u6cd5\u3002\u8be5\u7b97\u6cd5\u6700\u521d\u9762\u5411\u7070\u5ea6\u56fe\u50cf\u63d0\u51fa&#xff0c;\u4e5f\u80fd\u591f\u5f88\u65b9\u4fbf\u5730\u62d3\u5c55\u5e94\u7528\u4e8e\u5f69\u8272\u56fe\u50cf\u3002<\/p>\n<h3 id=\"12.4.1%20%E5%BC%97%E6%B4%9B%E4%BC%8A%E5%BE%B7%E2%80%91%E6%96%AF%E5%9D%A6%E4%BC%AF%E6%A0%BC%E7%AE%97%E6%B3%95\">12.4.1 \u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5<\/h3>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5\u4f1a\u8ba1\u7b97\u5f53\u524d\u50cf\u7d20\u91cf\u5316\u540e\u4ea7\u751f\u7684\u8bef\u5dee&#xff0c;\u5e76\u5c06\u8be5\u8bef\u5dee\u8865\u507f\u5206\u644a\u5230\u5468\u8fb9\u76f8\u90bb\u50cf\u7d20\u4e0a&#xff0c;\u4ee5\u6b64\u5c06\u6574\u5e45\u56fe\u50cf\u7684\u603b\u91cf\u5316\u8bef\u5dee\u964d\u5230\u6700\u4f4e\u3002 \u5177\u4f53\u6765\u8bf4&#xff0c;\u5047\u8bbe\u6211\u4eec\u8981\u5bf9\u7531\u56fe\u50cf\u51fd\u6570<img decoding=\"async\" alt=\"(f(x,y))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f4809ec6.png\" \/>\u5b9a\u4e49\u7684\u56fe\u50cf\u6267\u884c 1\u2011bit \u4e8c\u503c\u91cf\u5316\u3002\u4ece\u5750\u6807<img decoding=\"async\" alt=\"((x,y))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f480ec34.png\" \/> \u5904\u7684\u50cf\u7d20\u5f00\u59cb&#xff0c;\u628a\u539f\u59cb\u50cf\u7d20\u503c<img decoding=\"async\" alt=\"(f(x,y))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f4809ec6.png\" \/> \u66ff\u6362\u4e3a\u91cf\u5316\u7ed3\u679c<img decoding=\"async\" alt=\"(\\\\bar{f}(x,y))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f4813ba3.png\" \/>&#xff1b;\u9608\u503c\u4e00\u822c\u53d6 50%&#xff0c;\u9ad8\u4e8e\u9608\u503c\u8f93\u51fa 1&#xff0c;\u4f4e\u4e8e\u9608\u503c\u8f93\u51fa 0\u3002\u968f\u540e\u8ba1\u7b97\u91cf\u5316\u8bef\u5dee&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"(\\\\delta=f(x,y)-\\\\bar{f}(x,y))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f4818998.png\" \/> \u8bef\u5dee\u6309\u5982\u4e0b\u89c4\u5219\u6269\u6563&#xff08;\u89c1\u56fe 12\u201119&#xff09;&#xff1a;<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f481e77c.png\" \/><\/p>\n<ul>\n<li>\u5c06<img decoding=\"async\" alt=\"(\\\\displaystyle \\\\frac{3}{8}\\\\delta)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f482bbce.png\" \/>\u52a0\u5230\u53f3\u90bb\u50cf\u7d20<img decoding=\"async\" alt=\"(f(x+1,y))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f48309a1.png\" \/>&#xff1b;<\/li>\n<li>\u5c06 <img decoding=\"async\" alt=\"(\\\\displaystyle \\\\frac{3}{8}\\\\delta)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f482bbce.png\" \/> \u52a0\u5230\u4e0b\u90bb\u50cf\u7d20<img decoding=\"async\" alt=\"(f(x,y+1))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f4835421.png\" \/>&#xff1b;<\/li>\n<li>\u5c06 <img decoding=\"async\" alt=\"(\\\\displaystyle \\\\frac{1}{4}\\\\delta)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f483a13e.png\" \/>\u52a0\u5230\u53f3\u4e0b\u5bf9\u89d2\u50cf\u7d20 <img decoding=\"async\" alt=\"(f(x+1,y+1))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f483edb9.png\" \/>\u3002<\/li>\n<\/ul>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u63a5\u7740\u79fb\u52a8\u81f3\u540c\u4e00\u884c\u7684\u4e0b\u4e00\u4e2a\u50cf\u7d20<img decoding=\"async\" alt=\"((x+1,y))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f48439a6.png\" \/>&#xff0c;\u53d6\u66f4\u65b0\u540e\u7684\u503c <img decoding=\"async\" alt=\"(f(x+1,y)+\\\\frac{3}{8}\\\\delta)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f48481f6.png\" \/>&#xff0c;\u91cd\u590d\u4e0a\u8ff0\u91cf\u5316\u2011\u8bef\u5dee\u6269\u6563\u6d41\u7a0b\u3002\u4e00\u884c\u5904\u7406\u5b8c\u6bd5\u540e\u518d\u5207\u6362\u81f3\u4e0b\u4e00\u884c&#xff0c;\u5faa\u73af\u5f80\u590d\u3002<\/p>\n<p>\u8fb9\u754c\u5904\u7406\u89c4\u5219&#xff1a;\u4e00\u884c\u6700\u53f3\u4fa7\u50cf\u7d20\u4e0d\u518d\u5411\u53f3\u3001\u5411\u53f3\u4e0b\u6269\u6563\u8bef\u5dee&#xff1b;\u56fe\u50cf\u6700\u540e\u4e00\u884c\u7684\u50cf\u7d20\u4e0d\u518d\u5411\u4e0b\u3001\u5411\u53f3\u4e0b\u6269\u6563\u8bef\u5dee\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u8be5\u6296\u52a8\u7b97\u6cd5\u5b58\u5728\u4e00\u4e2a\u660e\u663e\u7f3a\u9677&#xff1a;\u8bef\u5dee\u4f1a\u6cbf\u7740\u5bf9\u89d2\u7ebf\u65b9\u5411\u4f20\u9012\u6269\u6563&#xff0c;\u6700\u7ec8\u56fe\u50cf\u4e0a\u4f1a\u51fa\u73b0\u5e26\u6709\u65b9\u5411\u6027\u7684\u4f2a\u5f71\u3002\u56fe 12\u201120 \u5c55\u793a\u4e86\u6d4b\u8bd5\u56fe\u50cf\u7ecf\u8fc7\u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5\u5904\u7406\u540e\u7684\u7ed3\u679c&#xff0c;\u53ef\u4ee5\u6e05\u6670\u89c2\u5bdf\u5230\u5bf9\u89d2\u7ebf\u8bef\u5dee\u6269\u6563\u5e26\u6765\u7684\u62d6\u5f71\u6548\u679c\u3002\u5b66\u672f\u754c\u5df2\u7ecf\u63d0\u51fa\u4e86\u8be5\u7b97\u6cd5\u7684\u591a\u79cd\u6539\u8fdb\u53d8\u4f53&#xff0c;\u7528\u6765\u6d88\u9664\u8fd9\u7c7b\u65b9\u5411\u4f2a\u5f71&#xff0c;\u66f4\u591a\u5185\u5bb9\u53ef\u53c2\u9605 12.5 \u8282\u3002<\/p>\n<h4 id=\"%E5%BD%A9%E8%89%B2%E5%9B%BE%E5%83%8F%E7%9A%84%E6%8A%96%E5%8A%A8%E5%A4%84%E7%90%86\">\u5f69\u8272\u56fe\u50cf\u7684\u6296\u52a8\u5904\u7406<\/h4>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u524d\u9762\u4e3b\u8981\u4ecb\u7ecd\u4e86\u7070\u5ea6\u56fe\u50cf\u7684 1\u2011bit \u4e8c\u503c\u6296\u52a8&#xff1b;\u4f46\u540c\u6837\u7684\u6296\u52a8\u6280\u672f\u4e5f\u9002\u7528\u4e8e\u5f69\u8272\u56fe\u50cf\u91cf\u5316&#xff0c;\u53ef\u4ee5\u907f\u514d\u6216\u5927\u5e45\u51cf\u8f7b\u8272\u5e26&#xff08;\u91cf\u5316\u8f6e\u5ed3&#xff09;\u73b0\u8c61\u3002\u4f8b\u5982\u56fe 12\u201121 \u5de6\u4fa7\u56fe\u50cf\u76f4\u63a5\u4ece 24\u2011bit \u91cf\u5316\u538b\u7f29\u5230 8\u2011bit&#xff0c;\u672a\u5f00\u542f\u6296\u52a8&#xff1b;\u53f3\u4fa7\u56fe\u50cf\u540c\u6837\u91cf\u5316\u4e3a 8\u2011bit&#xff0c;\u4f46\u662f\u542f\u7528\u4e86\u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u6296\u52a8\u7b97\u6cd5\u3002\u5bf9\u6bd4\u53ef\u89c1&#xff0c;\u7ecf\u8fc7\u6296\u52a8\u5904\u7406\u7684\u56fe\u50cf\u51e0\u4e4e\u770b\u4e0d\u5230\u4eba\u773c\u53ef\u611f\u77e5\u7684\u8272\u5e26\u75d5\u8ff9\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f484caf2.png\" \/><\/p>\n<h3 id=\"12.4.2%20%E5%9F%BA%E4%BA%8E%E7%A9%BA%E9%97%B4%E5%A1%AB%E5%85%85%E6%9B%B2%E7%BA%BF%E7%9A%84%E6%8A%96%E5%8A%A8%E7%AE%97%E6%B3%95\">12.4.2 \u57fa\u4e8e\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7684\u6296\u52a8\u7b97\u6cd5<\/h3>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6b63\u5f0f\u5c55\u5f00\u8bb2\u89e3\u524d&#xff0c;\u6211\u4eec\u5148\u56de\u987e\u6296\u52a8\u7b97\u6cd5\u7684\u5206\u7c7b\u6846\u67b6&#xff08;\u56fe 12\u20114&#xff09;&#xff0c;\u5b9a\u4f4d\u4e00\u4e0b\u76ee\u524d\u6240\u4ecb\u7ecd\u7b97\u6cd5\u6240\u5904\u7684\u7c7b\u522b&#xff0c;\u5206\u7c7b\u7ed3\u679c\u5982\u56fe 12\u201122 \u6240\u793a\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f485f608.png\" \/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4ece\u5206\u7c7b\u56fe\u4e2d\u53ef\u4ee5\u770b\u51fa&#xff1a;\u622a\u81f3\u76ee\u524d\u6211\u4eec\u8fd8\u6ca1\u6709\u4ecb\u7ecd\u8fc7\u975e\u5468\u671f\u7c07\u72b6\u6296\u52a8\u7b97\u6cd5\u3002\u7406\u8bba\u4e0a\u8fd9\u7c7b\u7b97\u6cd5\u53ef\u4ee5\u751f\u6210\u975e\u5e38\u4f18\u79c0\u7684\u534a\u8272\u8c03\u6548\u679c&#xff0c;\u56e0\u4e3a\u5b83\u80fd\u591f\u6a21\u62df\u611f\u5149\u80f6\u7247\u4e73\u5242\u7684\u6210\u50cf\u673a\u7406\u3002\u5728\u9ed1\u767d\u80f6\u7247\u6444\u5f71\u5f53\u4e2d&#xff0c;\u80f6\u7247\u8868\u9762\u6d82\u6ee1\u5927\u91cf\u968f\u673a\u5206\u5e03\u3001\u4e92\u4e0d\u91cd\u590d\u7684\u5fae\u5c0f\u611f\u5149\u9897\u7c92&#xff1b;\u6bcf\u4e00\u9897\u611f\u5149\u9897\u7c92\u90fd\u5360\u636e\u4e00\u5757\u6709\u9650\u9762\u79ef&#xff0c;\u66dd\u5149\u540e\u6574\u7c07\u9897\u7c92\u7edf\u4e00\u70b9\u4eae\u6216\u7184\u706d&#xff0c;\u6700\u7ec8\u751f\u6210\u7167\u7247\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u56fe 12\u201122 \u5f53\u4e2d\u7a7a\u7f3a\u7684\u5206\u7c7b\u4f4d\u7f6e&#xff0c;\u5c31\u7531\u4e00\u7c7b\u91cd\u8981\u7684\u975e\u5468\u671f\u6570\u5b57\u534a\u8272\u8c03\u7b97\u6cd5\u586b\u8865\u3002\u8fd9\u7c7b\u7b97\u6cd5\u4f7f\u7528\u4e00\u7c7b\u5206\u5f62\u66f2\u7ebf&#xff0c;\u7edf\u79f0\u4e3a\u76ae\u4e9a\u8bfa\u66f2\u7ebf&#xff08;Peano curve&#xff09;&#xff0c;\u4e5f\u5e38\u88ab\u79f0\u4f5c\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u3002\u76f8\u8f83\u4e8e\u524d\u9762\u4ecb\u7ecd\u8fc7\u7684\u7b97\u6cd5&#xff0c;\u5b83\u5177\u5907\u591a\u9879\u4f18\u52bf&#xff1a;<\/p>\n<ul>\n<li>\u901a\u8fc7\u8ba1\u7b97\u6bcf\u4e2a\u6296\u52a8\u5355\u5143\u7684\u5e73\u5747\u91cf\u5316\u8bef\u5dee\u5e76\u5411\u5916\u6269\u6563&#xff0c;\u540c\u65f6\u517c\u987e\u70b9\u7c07\u805a\u5408\u4e0e\u7f51\u70b9\u79bb\u6563\u5206\u5e03\u4e24\u79cd\u7279\u6027&#xff1b;<\/li>\n<li>\u5e73\u5747\u91cf\u5316\u8bef\u5dee\u6269\u6563\u6ca1\u6709\u56fa\u5b9a\u7684\u4f20\u64ad\u65b9\u5411&#xff0c;\u4e0d\u4f1a\u51fa\u73b0\u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5\u7684\u65b9\u5411\u6027\u4f2a\u5f71&#xff1b;<\/li>\n<li>\u8f93\u51fa\u5c5e\u4e8e\u975e\u5468\u671f\u7eb9\u7406&#xff0c;\u56fe\u50cf\u4e0d\u4f1a\u4ea7\u751f\u591a\u4f59\u3001\u89c4\u6574\u7684\u5468\u671f\u6027\u6469\u5c14\u7eb9\u8def&#xff1b;<\/li>\n<li>\u8fd0\u884c\u8fc7\u7a0b\u4e2d\u53ef\u4ee5\u52a8\u6001\u4fee\u6539\u6296\u52a8\u5355\u5143\u5c3a\u5bf8&#xff0c;\u8ba9\u56fe\u50cf\u7ec6\u8282\u5f97\u5230\u66f4\u597d\u8fd8\u539f\u3002<\/li>\n<\/ul>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5728\u6570\u5b57\u51fa\u7248\u9886\u57df&#xff0c;\u7c07\u72b6\u805a\u5408\u7b97\u6cd5\u79f0\u4e3a\u8c03\u5e45&#xff08;AM\u2011Amplitude Modulation&#xff09;\u7b97\u6cd5&#xff0c;\u539f\u7406\u662f\u6539\u53d8\u9ed1\u70b9\u7c07\u7684\u5927\u5c0f&#xff1b;\u7f51\u70b9\u79bb\u6563\u6269\u6563\u7b97\u6cd5\u79f0\u4e3a\u8c03\u9891&#xff08;FM\u2011Frequency Modulation&#xff09;\u7b97\u6cd5&#xff0c;\u539f\u7406\u662f\u5206\u6563\u9ed1\u70b9\u5e76\u63a7\u5236\u70b9\u7684\u5206\u5e03\u5bc6\u5ea6\u3002\u672c\u6587\u4ecb\u7ecd\u7684\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u6296\u52a8\u7b97\u6cd5\u6548\u679c\u4ecb\u4e8e\u8c03\u5e45\u4e0e\u8c03\u9891\u534a\u8272\u8c03\u4e4b\u95f4&#xff1b;\u56e0\u6b64\u53ef\u4ee5\u7075\u6d3b\u9002\u914d\u4e00\u5927\u6279\u7f51\u70b9\u5b9a\u4f4d\u7cbe\u5ea6\u5404\u4e0d\u76f8\u540c\u7684\u6253\u5370\u8f93\u51fa\u8bbe\u5907\u3002<\/p>\n<h4 id=\"%E5%83%8F%E7%B4%A0%E9%81%8D%E5%8E%86%E6%8E%92%E5%BA%8F\">\u50cf\u7d20\u904d\u5386\u6392\u5e8f<\/h4>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u56fe\u50cf <img decoding=\"async\" alt=\"(f:U\\\\subset\\\\mathbb{R}^2\\\\to\\\\mathbb{C})\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f486b91f.png\" \/> \u7684\u50cf\u7d20\u904d\u5386\u5e8f\u5217&#xff0c;\u662f\u4e00\u6761\u4e00\u5bf9\u4e00\u6620\u5c04\u8def\u5f84 <img decoding=\"async\" alt=\"(c:I\\\\subset\\\\mathbb{R}\\\\to U)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f487065b.png\" \/>\u3002\u8be5\u8def\u5f84\u5b9a\u4e49\u5728\u5b9e\u6570\u57df\u5b50\u96c6 I \u4e0a&#xff0c;\u8def\u5f84\u626b\u8fc7\u7684\u533a\u57df <img decoding=\"async\" alt=\"(c(I))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f48750c3.png\" \/> \u8986\u76d6\u56fe\u50cf\u5b9a\u4e49\u57df\u5185\u6240\u6709\u50cf\u7d20\u3002\u4e5f\u5c31\u662f\u8bf4&#xff0c;\u904d\u5386\u5e8f\u5217 c \u4f1a\u7ed9\u5750\u6807 <img decoding=\"async\" alt=\"((i,j))\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115800-6a980f4879a9f.png\" \/> \u7684\u6bcf\u4e00\u4e2a\u50cf\u7d20\u5206\u914d\u552f\u4e00\u5e8f\u53f7 k&#xff0c;\u6ee1\u8db3 <img decoding=\"async\" alt=\"(c(k)=(i,j))\" class=\"mathcode\" src=\"2026-09-02bo1o35rb0mc.png\" \/>\u3002\u76f4\u89c2\u6765\u8bb2&#xff0c;\u50cf\u7d20\u904d\u5386\u5c31\u662f\u6309\u7167\u4e00\u5957\u56fa\u5b9a\u987a\u5e8f&#xff0c;\u4e0d\u91cd\u590d\u5730\u8d70\u5b8c\u56fe\u50cf\u5f53\u4e2d\u6240\u6709\u50cf\u7d20\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u77e9\u9635\u5b58\u50a8\u683c\u5f0f\u56fe\u50cf\u6700\u5e38\u7528\u7684\u904d\u5386\u65b9\u5f0f\u5c31\u662f\u9010\u884c\u626b\u63cf&#xff08;\u89c1\u56fe 12\u201123&#xff09;\u3002 \u9010\u884c\u904d\u5386\u867d\u7136\u7b80\u5355\u9ad8\u6548&#xff0c;\u4f46\u7528\u4e8e\u6296\u52a8\u7b97\u6cd5\u65f6\u6709\u4e24\u4e2a\u7f3a\u70b9&#xff1a;\u4e00\u662f\u5b58\u5728\u6c34\u5e73\u65b9\u5411\u904d\u5386\u503e\u5411\u6027&#xff1b;\u4e8c\u662f\u6bcf\u884c\u626b\u63cf\u7ed3\u675f\u8df3\u8f6c\u81f3\u4e0b\u4e00\u884c\u65f6\u8def\u5f84\u51fa\u73b0\u65ad\u88c2\u3002 \u5f80\u8fd4\u5f0f&#xff08;\u725b\u8015\u5f0f&#xff09;\u904d\u5386&#xff08;\u89c1\u56fe 12\u201124&#xff09;\u867d\u7136\u6d88\u9664\u4e86\u6362\u884c\u8def\u5f84\u65ad\u88c2\u95ee\u9898&#xff0c;\u4f46\u662f\u904d\u5386\u65b9\u5411\u503e\u5411\u6027\u95ee\u9898\u4f9d\u65e7\u5b58\u5728\u3002\u800c\u6b63\u662f\u8fd9\u79cd\u65b9\u5411\u503e\u5411\u6027&#xff0c;\u9020\u6210\u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5\u5bb9\u6613\u51fa\u73b0\u5bf9\u89d2\u7ebf\u4f2a\u5f71\u3002 \u6211\u4eec\u53ef\u4ee5\u91c7\u7528\u8fd1\u4f3c\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7684\u904d\u5386\u8def\u5f84&#xff0c;\u4e00\u6b21\u6027\u6d88\u9664\u4e0a\u8ff0\u4e24\u4e2a\u7f3a\u9677\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02yabvonbpt4p.png\" \/><\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02x25fmq4txb1.png\" \/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4e00\u6761\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u662f\u8fde\u7eed\u6ee1\u5c04\u6620\u5c04&#xff1a;<img decoding=\"async\" alt=\"(\\\\phi:[0,1]\\\\to[0,1]\\\\times[0,1])\" class=\"mathcode\" src=\"2026-09-02tffksp0wqo2.png\" \/>\u3002\u8be5\u66f2\u7ebf\u53ef\u4ee5\u8fde\u7eed\u904d\u5386\u5355\u4f4d\u6b63\u65b9\u5f62\u5185\u7684\u6bcf\u4e00\u4e2a\u70b9\u3002\u7ecf\u8fc7\u7f29\u653e\u53d8\u6362\u540e&#xff0c;\u5c31\u53ef\u4ee5\u751f\u6210\u5e73\u9762\u4efb\u610f\u77e9\u5f62\u533a\u57df\u4e0a\u7684\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u3002\u6211\u4eec\u7684\u76ee\u6807\u5c31\u662f\u9009\u53d6\u4e00\u6761\u8fd1\u4f3c\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u65e0\u91cd\u590d\u8def\u5f84&#xff0c;\u7528\u6765\u751f\u6210\u6570\u5b57\u56fe\u50cf\u50cf\u7d20\u7684\u904d\u5386\u987a\u5e8f\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7531\u6570\u5b66\u5bb6\u6731\u585e\u4f69\u30fb\u76ae\u4e9a\u8bfa\u4e8e 19 \u4e16\u7eaa\u672b\u9996\u6b21\u53d1\u73b0\u3002\u76ae\u4e9a\u8bfa\u6784\u9020\u51fa\u4e86\u4e00\u6761\u53ef\u4ee5\u904d\u5386\u5355\u4f4d\u6b63\u65b9\u5f62\u6240\u6709\u70b9\u7684\u8fde\u7eed\u66f2\u7ebf&#xff0c;\u540e\u4eba\u4fbf\u5c06\u5176\u547d\u540d\u4e3a\u76ae\u4e9a\u8bfa\u66f2\u7ebf&#xff1b;\u5982\u4eca\u6240\u6709\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u4e5f\u5e38\u6cdb\u79f0\u4e3a\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u3002 \u56fe 12\u201125 \u5c55\u793a\u4e86\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf&#xff08;Hilbert curve&#xff09;\u9012\u5f52\u6784\u9020\u8fc7\u7a0b\u5f53\u4e2d\u7684 4 \u4e2a\u8fed\u4ee3\u6b65\u9aa4\u3002 \u4e0d\u96be\u770b\u51fa&#xff1a;\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u6bcf\u4e00\u6b21\u8fed\u4ee3\u751f\u6210\u7684\u6298\u7ebf&#xff0c;\u90fd\u4f1a\u6070\u597d\u904d\u5386\u89c4\u6574\u7f51\u683c\u4e0a\u6240\u6709\u9876\u70b9&#xff0c;\u5e76\u4e14\u6bcf\u4e2a\u9876\u70b9\u4ec5\u8bbf\u95ee\u4e00\u6b21\u3002\u4e0d\u65ad\u8fed\u4ee3\u5373\u53ef\u751f\u6210\u4efb\u610f\u5206\u8fa8\u7387\u56fe\u50cf\u5bf9\u5e94\u7684\u50cf\u7d20\u904d\u5386\u5e8f\u5217&#xff1b;\u7531\u6b64\u5f97\u5230\u7684\u904d\u5386\u8def\u5f84\u65e2\u4e0d\u5b58\u5728\u65ad\u70b9&#xff0c;\u4e5f\u6ca1\u6709\u4f18\u5148\u65b9\u5411\u3002\u56fe 12\u201126 \u7ed9\u51fa\u4e86 4\u202f\u00d7\u202f4 \u5206\u8fa8\u7387\u56fe\u50cf\u57fa\u4e8e\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u751f\u6210\u7684\u50cf\u7d20\u904d\u5386\u987a\u5e8f\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u4e4d\u4e00\u770b\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u904d\u5386\u4ec5\u9002\u7528\u4e8e\u5206\u8fa8\u7387\u4e3a<img decoding=\"async\" alt=\"(2^p\\\\times2^p)\" class=\"mathcode\" src=\"2026-09-02qiba0zanuy0.png\" \/>&#xff08;p \u4e3a\u6b63\u6574\u6570&#xff09;\u7684\u56fe\u50cf\u3002\u4e0d\u8fc7\u4efb\u610f <img decoding=\"async\" alt=\"(m\\\\times n)\" class=\"mathcode\" src=\"2026-09-02byxb335wl1v.png\" \/>\u5c3a\u5bf8\u56fe\u50cf\u5bf9\u5e94\u7684\u7f51\u683c\u90fd\u53ef\u4ee5\u5d4c\u5165\u4e00\u4e2a\u8fb9\u957f\u4e3a 2 \u7684\u6574\u6570\u6b21\u5e42\u7684\u6b63\u65b9\u5f62\u7f51\u683c&#xff1b;\u6211\u4eec\u53ef\u4ee5\u5148\u5bf9\u6b63\u65b9\u5f62\u7f51\u683c\u751f\u6210\u5e0c\u5c14\u4f2f\u7279\u904d\u5386\u5e8f\u5217&#xff0c;\u518d\u4ece\u4e2d\u622a\u53d6\u5f97\u5230\u539f\u56fe\u7684\u904d\u5386\u987a\u5e8f\u3002\u8fd9\u79cd\u5b9e\u73b0\u65b9\u6848\u6bd4\u76f4\u63a5\u6784\u9020\u77e9\u5f62\u533a\u57df\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u904d\u5386\u66f4\u52a0\u7b80\u4fbf\u9ad8\u6548\u3002 \u9664\u6b64\u4e4b\u5916\u8fd8\u6709\u8bb8\u591a\u5176\u4ed6\u9012\u5f52\u6784\u9020\u7684\u6298\u7ebf\u578b\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf&#xff0c;\u5747\u53ef\u7528\u6765\u751f\u6210\u79bb\u6563\u56fe\u50cf\u50cf\u7d20\u904d\u5386\u5e8f\u5217&#xff1b;\u4e0b\u6587\u793a\u4f8b\u7edf\u4e00\u9009\u7528\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02ebgpwh2mw3z.png\" \/><\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02fe30qcz50fn.png\" \/><\/p>\n<h4 id=\"%E5%9F%BA%E4%BA%8E%E7%9A%AE%E4%BA%9A%E8%AF%BA%E6%9B%B2%E7%BA%BF%E7%9A%84%E5%9B%BE%E5%83%8F%E5%8C%BA%E5%9F%9F%E5%88%92%E5%88%86\">\u57fa\u4e8e\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u56fe\u50cf\u533a\u57df\u5212\u5206<\/h4>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u60f3\u8981\u7406\u89e3\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u534a\u8272\u8c03\u7b97\u6cd5&#xff0c;\u5148\u8981\u7406\u89e3\u8be5\u904d\u5386\u66f2\u7ebf\u5982\u4f55\u5c06\u56fe\u50cf\u5b9a\u4e49\u57df\u5206\u5272\u6210\u591a\u4e2a\u5b50\u533a\u57df\u3002 \u8bbe<img decoding=\"async\" alt=\"(c:I\\\\to U\\\\subset\\\\mathbb{R}^2)\" class=\"mathcode\" src=\"2026-09-02mxkooswt0xp.png\" \/> \u4e3a\u57fa\u4e8e\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u56fe\u50cf\u50cf\u7d20\u904d\u5386\u5e8f\u5217&#xff0c;\u5c06\u533a\u95f4 I \u62c6\u5206\u4e3a n \u4e2a\u5b50\u533a\u95f4&#xff1a;<img decoding=\"async\" alt=\"(I_1\\\\cup I_2\\\\cup\\\\cdots\\\\cup I_n)\" class=\"mathcode\" src=\"2026-09-02xndbwx0mbia.png\" \/>\u3002\u7531\u4e8e\u50cf\u7d20\u904d\u5386\u5c5e\u4e8e\u4e00\u4e00\u6620\u5c04&#xff0c;\u533a\u95f4\u7684\u5206\u5272\u4f1a\u6620\u5c04\u6210\u56fe\u50cf\u533a\u57df\u7684\u5206\u5272&#xff1a;<img decoding=\"async\" alt=\"(c(I_1)\\\\cup c(I_2)\\\\cup\\\\cdots\\\\cup c(I_n))\" class=\"mathcode\" src=\"2026-09-0241jyehpp432.png\" \/>\u3002\u5176\u4e2d\u6620\u5c04<img decoding=\"async\" alt=\"(c|_{I_j}:I_j\\\\to R_j=c(I_j))\" class=\"mathcode\" src=\"2026-09-0255vktyk45cu.png\" \/> \u5373\u4e3a\u5b50\u533a\u57df <img decoding=\"async\" alt=\"(R_j)\" class=\"mathcode\" src=\"2026-09-02bevz5tpmzy0.png\" \/>\u5185\u90e8\u50cf\u7d20\u7684\u904d\u5386\u5e8f\u5217\u3002\u56fe 12\u201127 \u5c55\u793a\u4e00\u5757 4\u202f\u00d7\u202f4 \u50cf\u7d20\u533a\u5757&#xff0c;\u88ab\u5212\u5206\u4e3a\u50cf\u7d20\u6570\u91cf\u5206\u522b\u4e3a 5\u30014\u30017 \u7684\u4e09\u5757\u5b50\u533a\u57df&#xff08;\u6bcf\u4e2a\u5b50\u533a\u57df\u4f7f\u7528\u4e0d\u540c\u7070\u5ea6\u5e95\u8272\u6807\u6ce8&#xff09;\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02fyhusp1megu.png\" \/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u503c\u5f97\u5f3a\u8c03&#xff1a;\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u751f\u6210\u7684\u5206\u5272\u533a\u5757\u5929\u7136\u5e26\u6709\u5148\u540e\u987a\u5e8f\u3002\u6cbf\u7740\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u5b8c\u6574\u904d\u5386\u4e00\u904d&#xff0c;\u5c31\u4f1a\u6309\u6b21\u5e8f\u3001\u4e0d\u91cd\u590d\u5730\u8bbf\u95ee\u6bcf\u4e00\u5757\u5b50\u533a\u57df\u3002 \u76ae\u4e9a\u8bfa\u66f2\u7ebf\u5212\u5206\u51fa\u6765\u7684\u5b50\u533a\u5757\u5728\u7b97\u6cd5\u4e2d\u7684\u4f5c\u7528\u7b49\u4ef7\u4e8e\u6709\u5e8f\u6296\u52a8\u91cc\u7684\u6296\u52a8\u5355\u5143&#xff0c;\u56e0\u6b64\u8fd9\u4e9b\u5b50\u533a\u57df\u540c\u6837\u88ab\u79f0\u4e3a\u6296\u52a8\u5355\u5143&#xff0c;\u7b80\u79f0\u5355\u5143\u3002<\/p>\n<h4 id=\"%E8%87%AA%E9%80%82%E5%BA%94%E5%88%86%E5%89%B2\">\u81ea\u9002\u5e94\u5206\u5272<\/h4>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u524d\u6587\u5df2\u7ecf\u63d0\u5230&#xff0c;\u975e\u5468\u671f\u7c07\u72b6\u6296\u52a8\u7b97\u6cd5\u53ef\u4ee5\u7c97\u7565\u6a21\u62df\u80f6\u7247\u4e73\u5242\u534a\u8272\u8c03\u6210\u50cf&#xff1b;\u800c\u5982\u679c\u5141\u8bb8\u6296\u52a8\u5355\u5143\u5927\u5c0f\u52a8\u6001\u53d8\u5316&#xff0c;\u6a21\u62df\u6548\u679c\u8fd8\u80fd\u8fdb\u4e00\u6b65\u63d0\u5347&#xff0c;\u8fd9\u5c31\u5bf9\u5e94\u80f6\u7247\u611f\u5149\u9897\u7c92\u5c3a\u5bf8\u7684\u53d8\u5316\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u56fe\u50cf\u4e2d\u6bcf\u4e00\u4e2a\u50cf\u7d20\u90fd\u4f1a\u5f52\u5c5e\u67d0\u4e00\u4e2a\u6296\u52a8\u5355\u5143&#xff0c;\u4f46\u4e00\u4e2a\u6296\u52a8\u5355\u5143\u53ef\u5305\u542b\u591a\u4e2a\u50cf\u7d20&#xff0c;\u4e8c\u8005\u5e76\u4e0d\u662f\u4e00\u4e00\u5bf9\u5e94\u5173\u7cfb\u3002\u5355\u5143\u5c3a\u5bf8\u51fd\u6570\u4f1a\u4e3a\u6bcf\u4e00\u4e2a\u50cf\u7d20\u5206\u914d\u4e00\u4e2a\u6570\u503c&#xff0c;\u4ee3\u8868\u5176\u6240\u5c5e\u6296\u52a8\u5355\u5143\u5305\u542b\u7684\u50cf\u7d20\u603b\u6570\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u60f3\u8981\u5728\u6296\u52a8\u8fc7\u7a0b\u4e2d\u65e2\u4fdd\u8bc1\u7070\u5ea6\u8fc7\u6e21\u81ea\u7136&#xff0c;\u53c8\u7cbe\u7ec6\u8fd8\u539f\u56fe\u50cf\u7ec6\u8282&#xff0c;\u5c31\u5e94\u5f53\u4f9d\u636e\u50cf\u7d20\u90bb\u57df\u5185\u4eae\u5ea6\u53d8\u5316\u5feb\u6162\u52a8\u6001\u8c03\u6574\u6296\u52a8\u5355\u5143\u5c3a\u5bf8&#xff1a;\u50cf\u7d20\u5468\u56f4\u4eae\u5ea6\u53d8\u5316\u5267\u70c8&#xff08;\u9ad8\u9891\u7ec6\u8282\u533a\u57df&#xff09;\u9009\u7528\u8f83\u5c0f\u6296\u52a8\u5355\u5143&#xff1b;\u4eae\u5ea6\u5e73\u7f13\u533a\u57df\u9009\u7528\u8f83\u5927\u6296\u52a8\u5355\u5143\u3002 \u8be5\u53d8\u5316\u91cf\u53ef\u4ee5\u6cbf\u7740\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u904d\u5386\u65b9\u5411&#xff0c;\u6c42\u53d6\u50cf\u7d20\u70b9\u4eae\u5ea6\u65b9\u5411\u5bfc\u6570\u7684\u7edd\u5bf9\u503c\u5f97\u5230\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5b9e\u9645\u4e0a&#xff0c;\u5355\u5143\u5c3a\u5bf8\u4e0e\u65b9\u5411\u5bfc\u6570\u5e45\u503c\u4e4b\u95f4\u7684\u5339\u914d\u5173\u7cfb&#xff0c;\u8fd8\u8981\u8003\u8651\u5230\u4eba\u773c\u5bf9\u4eae\u5ea6\u53d8\u5316\u7684\u54cd\u5e94\u7b26\u5408\u5bf9\u6570\u611f\u77e5\u7279\u6027\u3002\u56e0\u6b64\u5355\u5143\u5c3a\u5bf8\u51fd\u6570\u53d6\u65b9\u5411\u5bfc\u6570\u5e45\u503c\u7684\u6307\u6570\u51fd\u6570&#xff1b;\u8be5\u89c4\u5219\u80fd\u591f\u4fdd\u8bc1\u6bcf\u4e2a\u6296\u52a8\u5355\u5143\u5185\u90e8\u7684\u89c6\u89c9\u4eae\u5ea6&#xff0c;\u4e0e\u56fe\u50cf\u4eae\u5ea6\u6cbf\u7740\u904d\u5386\u66f2\u7ebf\u65b9\u5411\u7684\u53d8\u5316\u659c\u7387\u7ef4\u6301\u7ebf\u6027\u5173\u7cfb\u3002 \u56fe 12\u201128 \u7ed9\u51fa\u4e00\u5e45\u7070\u5ea6\u56fe\u50cf&#xff0c;\u4ee5\u53ca\u91c7\u7528\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u904d\u5386\u751f\u6210\u7684\u81ea\u9002\u5e94\u5206\u5272\u6548\u679c\u56fe\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02gfnsqr4kmzf.png\" \/><\/p>\n<h4 id=\"%E8%87%AA%E9%80%82%E5%BA%94%E5%88%86%E5%89%B2%E8%AE%A1%E7%AE%97%E6%B5%81%E7%A8%8B\">\u81ea\u9002\u5e94\u5206\u5272\u8ba1\u7b97\u6d41\u7a0b<\/h4>\n<p>\u501f\u52a9\u5355\u5143\u5c3a\u5bf8\u51fd\u6570 s&#xff0c;\u5c31\u53ef\u4ee5\u5bf9\u56fe\u50cf\u5b9a\u4e49\u57df\u6267\u884c\u81ea\u9002\u5e94\u533a\u5757\u5212\u5206&#xff0c;\u5212\u5206\u6b65\u9aa4\u5982\u4e0b&#xff1a;<\/p>\n<li>\u8bbe\u7f6e\u7528\u6237\u7ed9\u5b9a\u7684\u6700\u5927\u5355\u5143\u5c3a\u5bf8&#xff0c;\u4f5c\u4e3a\u5f53\u524d\u5355\u5143\u5c3a\u5bf8\u521d\u59cb\u503c<img decoding=\"async\" alt=\"(s_0)\" class=\"mathcode\" src=\"2026-09-02msfntsb0lnd.png\" \/>&#xff1b;<\/li>\n<li>\u6309\u7167\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u904d\u5386\u987a\u5e8f\u4f9d\u6b21\u626b\u63cf\u56fe\u50cf\u5185\u6240\u6709\u50cf\u7d20&#xff1b;<\/li>\n<li>\u5bf9\u5f53\u524d\u50cf\u7d20 p&#xff0c;\u8ba1\u7b97\u5176\u76ee\u6807\u5355\u5143\u5c3a\u5bf8 <img decoding=\"async\" alt=\"(s(p))\" class=\"mathcode\" src=\"2026-09-02kzb5myzm3ju.png\" \/>&#xff1b;<\/li>\n<li>\u5c06 <img decoding=\"async\" alt=\"(s(p))\" class=\"mathcode\" src=\"2026-09-02kzb5myzm3ju.png\" \/> \u4e0e\u5f53\u524d\u5355\u5143\u5c3a\u5bf8<img decoding=\"async\" alt=\"(s_0)\" class=\"mathcode\" src=\"2026-09-02msfntsb0lnd.png\" \/> \u5bf9\u6bd4&#xff1b;\u82e5<img decoding=\"async\" alt=\"(s(p)&lt;s_0)\" class=\"mathcode\" src=\"2026-09-02msc1fiddg4n.png\" \/>&#xff0c;\u66f4\u65b0\u5f53\u524d\u5355\u5143\u5c3a\u5bf8\u4e3a<img decoding=\"async\" alt=\"(s(p))\" class=\"mathcode\" src=\"2026-09-02kzb5myzm3ju.png\" \/>&#xff0c;\u7136\u540e\u7ee7\u7eed\u626b\u63cf\u4e0b\u4e00\u4e2a\u50cf\u7d20<img decoding=\"async\" alt=\"(p+1)\" class=\"mathcode\" src=\"2026-09-02gy00gyru41l.png\" \/>\u3002<\/li>\n<h4 id=\"%E6%8A%96%E5%8A%A8%E5%8D%95%E5%85%83%E9%87%8F%E5%8C%96\">\u6296\u52a8\u5355\u5143\u91cf\u5316<\/h4>\n<p>\u6bcf\u4e2a\u6296\u52a8\u5355\u5143\u7684\u91cf\u5316\u5904\u7406&#xff0c;\u9700\u8981\u4f9d\u6258\u5355\u5143\u5185\u90e8\u50cf\u7d20\u7684\u904d\u5386\u987a\u5e8f\u5b8c\u6210&#xff08;\u89c1\u56fe 12\u201129&#xff09;&#xff0c;\u8be6\u7ec6\u6d41\u7a0b&#xff1a;<\/p>\n<li>\u4f7f\u7528\u5f0f (12.1) \u8ba1\u7b97\u6296\u52a8\u5355\u5143\u5185\u90e8\u50cf\u7d20\u7684\u5e73\u5747\u4eae\u5ea6&#xff1b;<\/li>\n<li>\u901a\u8fc7\u5f00\u542f\u3001\u5173\u95ed\u5355\u5143\u5185\u90e8\u5206\u50cf\u7d20&#xff0c;\u751f\u6210\u4e00\u5f20\u4e8c\u503c\u70b9\u9635\u56fe\u6848&#xff0c;\u8ba9\u8be5\u70b9\u9635\u7684\u7b49\u6548\u5e73\u5747\u4eae\u5ea6\u5c3d\u53ef\u80fd\u63a5\u8fd1\u5355\u5143\u539f\u59cb\u5e73\u5747\u4eae\u5ea6&#xff1b;\u4e8c\u8005\u4e4b\u95f4\u7684\u5dee\u503c\u79f0\u4e3a\u5355\u5143\u91cf\u5316\u8bef\u5dee&#xff1b;<\/li>\n<li>\u5728\u751f\u6210\u4e8c\u503c\u70b9\u9635\u65f6&#xff0c;\u5c3d\u91cf\u5c06\u6240\u6709\u70b9\u4eae\u7684\u9ed1\u70b9\u805a\u96c6\u5728\u4e00\u8d77&#xff0c;\u5f62\u6210\u9ed1\u70b9\u7c07\u3002<\/li>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u56fe 12\u201129 (a) \u662f\u4e00\u5757\u5305\u542b 16 \u4e2a\u50cf\u7d20\u3001\u4f7f\u7528\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf\u904d\u5386\u7684\u6296\u52a8\u5355\u5143&#xff1b;\u56fe 12\u201129 (b) \u5c55\u793a\u4e86\u8be5\u7b97\u6cd5\u751f\u6210\u7684\u9ed1\u70b9\u7c07&#xff0c;\u5206\u522b\u5bf9\u5e94\u8be5\u533a\u57df\u9664\u53bb\u4eae\u5ea6 0 \u4ee5\u5916\u7684 16 \u4e2a\u7070\u5ea6\u7b49\u7ea7\u3002 \u56fe 12\u201130 \u5de6\u4fa7\u662f\u56fe 12\u201128 \u5f53\u4e2d\u7070\u5ea6\u56fe\u50cf&#xff0c;\u6bcf\u4e2a\u6296\u52a8\u5355\u5143\u76f4\u63a5\u586b\u5145\u4e3a\u533a\u5757\u5e73\u5747\u7070\u5ea6&#xff1b;\u53f3\u4fa7\u4e3a\u91c7\u7528\u4e0a\u8ff0\u91cf\u5316\u65b9\u6cd5\u751f\u6210\u7684\u6296\u52a8\u6548\u679c\u56fe\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02cfbnoqv1fze.png\" \/><\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02prari4ff1m0.png\" \/><\/p>\n<h4 id=\"%E9%BB%91%E7%82%B9%E7%B0%87%E4%BD%8D%E7%BD%AE%E5%BE%AE%E8%B0%83\">\u9ed1\u70b9\u7c07\u4f4d\u7f6e\u5fae\u8c03<\/h4>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02xfqeiux0kdw.png\" \/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u5b8c\u6210\u6296\u52a8\u5355\u5143\u91cf\u5316\u540e&#xff0c;\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u5757\u9ed1\u70b9\u7c07\u3002\u6cbf\u7740\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7684\u8d70\u5411\u6ed1\u52a8\u9ed1\u70b9\u7c07&#xff0c;\u5c31\u62e5\u6709\u4e86\u4e00\u4e2a\u4f4d\u7f6e\u8c03\u6574\u7684\u81ea\u7531\u5ea6\u3002\u4e00\u79cd\u6548\u679c\u8f83\u597d\u7684\u7b56\u7565&#xff1a;\u5c06\u9ed1\u70b9\u7c07\u7684\u4e2d\u5fc3\u50cf\u7d20\u5bf9\u9f50\u6296\u52a8\u5355\u5143\u7684\u4e2d\u5fc3\u50cf\u7d20\u3002\u8be5\u5c45\u4e2d\u64cd\u4f5c\u4f1a\u4e3a\u6700\u7ec8\u6296\u52a8\u56fe\u50cf\u5f15\u5165\u4e00\u5b9a\u968f\u673a\u6027&#xff0c;\u4ece\u89c6\u89c9\u89c2\u611f\u4e0a\u63d0\u5347\u534a\u8272\u8c03\u753b\u8d28&#xff0c;\u5904\u7406\u8fc7\u7a0b\u89c1\u56fe 12\u201131&#xff1a;<\/p>\n<p>(a) \u7ed9\u51fa\u4e00\u5757 4\u202f\u00d7\u202f4 \u6296\u52a8\u5355\u5143&#xff1b;<\/p>\n<p>(b) \u5b9a\u4f4d\u5355\u5143\u5185\u4eae\u5ea6\u6700\u6df1\u7684\u50cf\u7d20&#xff1b;<\/p>\n<p>(c) \u751f\u6210\u4e00\u5757 5 \u50cf\u7d20\u5927\u5c0f\u7684\u9ed1\u70b9\u7c07&#xff1b;<\/p>\n<p>(d) \u5b8c\u6210\u9ed1\u70b9\u7c07\u5c45\u4e2d\u653e\u7f6e\u3002<\/p>\n<h4 id=\"%E5%AE%8C%E6%95%B4%E6%8A%96%E5%8A%A8%E7%AE%97%E6%B3%95%E6%B5%81%E7%A8%8B\">\u5b8c\u6574\u6296\u52a8\u7b97\u6cd5\u6d41\u7a0b<\/h4>\n<p>\u7b80\u800c\u8a00\u4e4b&#xff0c;\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u6296\u52a8\u7b97\u6cd5\u6838\u5fc3\u601d\u8def\u6e05\u6670\u3002\u9009\u5b9a\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u5b8c\u6210\u50cf\u7d20\u904d\u5386\u4e4b\u540e&#xff0c;\u4f9d\u6b21\u6267\u884c\u4e0b\u9762\u6b65\u9aa4&#xff1a;<\/p>\n<li>\u6309\u7167\u524d\u6587\u89c4\u5219&#xff0c;\u5c06\u56fe\u50cf\u5206\u5272\u6210\u4e00\u7cfb\u5217\u6296\u52a8\u5355\u5143&#xff1b;<\/li>\n<li>\u4f7f\u7528\u5f0f (12.1)&#xff0c;\u8ba1\u7b97\u6bcf\u4e00\u5757\u6296\u52a8\u5355\u5143\u5185\u90e8\u56fe\u50cf\u7684\u5e73\u5747\u4eae\u5ea6&#xff1b;<\/li>\n<li>\u4e3a\u6bcf\u4e00\u4e2a\u6296\u52a8\u5355\u5143\u751f\u6210\u5bf9\u5e94\u7684\u9ed1\u70b9\u7c07&#xff0c;\u4fdd\u8bc1\u751f\u6210\u4e8c\u503c\u56fe\u6848\u7684\u7b49\u6548\u4eae\u5ea6\u8fd1\u4f3c\u7b49\u4e8e\u5355\u5143\u5e73\u5747\u4eae\u5ea6&#xff1b;<\/li>\n<li>\u5728\u6296\u52a8\u5355\u5143\u5185\u90e8\u653e\u7f6e\u3001\u5c45\u4e2d\u5bf9\u9f50\u9ed1\u70b9\u7c07&#xff1b;<\/li>\n<li>\u6cbf\u7740\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u524d\u8fdb\u81f3\u4e0b\u4e00\u4e2a\u6296\u52a8\u5355\u5143&#xff1b;\u8ba1\u7b97\u4e0b\u4e00\u5757\u5355\u5143\u5e73\u5747\u4eae\u5ea6\u65f6&#xff0c;\u53e0\u52a0\u4e0a\u4e00\u5757\u5355\u5143\u9057\u7559\u7684\u91cf\u5316\u8bef\u5dee&#xff1b;\u91cd\u590d\u4ee5\u4e0a\u5168\u90e8\u6d41\u7a0b\u3002<\/li>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02kze1ezjrr3m.png\" \/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u8be5\u7b97\u6cd5\u6267\u884c\u6548\u7387\u5f88\u9ad8&#xff0c;\u56fe\u50cf\u533a\u5757\u5206\u5272\u4e0e\u5404\u5355\u5143\u5e73\u5747\u4eae\u5ea6\u8ba1\u7b97\u53ef\u540c\u6b65\u5b8c\u6210\u3002 \u56fe 12\u201132 \u4e3a\u6d4b\u8bd5\u56fe\u50cf\u7ecf\u8fc7\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u6296\u52a8\u5904\u7406\u540e\u7684\u7ed3\u679c&#xff1b;\u672c\u4f8b\u4f7f\u7528\u56fe 12\u201125 \u4e2d\u7684\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf&#xff0c;\u6296\u52a8\u5355\u5143\u56fa\u5b9a\u5927\u5c0f\u4e3a 7 \u50cf\u7d20\u3002\u56fe 12\u201133 \u4f7f\u7528\u540c\u4e00\u5957\u7b97\u6cd5&#xff0c;\u5f00\u542f\u81ea\u9002\u5e94\u5355\u5143\u6a21\u5f0f&#xff0c;\u5355\u5143\u6700\u5927\u5c3a\u5bf8\u9650\u5b9a\u4e3a 7 \u50cf\u7d20\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-02oswr3ojn1cd.png\" \/><\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u53ef\u4ee5\u770b\u5230\u8be5\u7b97\u6cd5\u6cbf\u7740\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u8def\u5f84\u4f20\u9012\u91cf\u5316\u8bef\u5dee&#xff1a;\u5f53\u6bcf\u4e2a\u6296\u52a8\u5355\u5143\u4ec5\u5305\u542b\u5355\u4e2a\u50cf\u7d20&#xff0c;\u7b97\u6cd5\u7b49\u4ef7\u4e8e\u6cbf\u7740\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u505a\u50cf\u7d20\u7ea7\u8bef\u5dee\u6269\u6563&#xff1b;\u5f53\u6296\u52a8\u5355\u5143\u5c3a\u5bf8\u66f4\u5927\u65f6&#xff0c;\u5219\u5148\u5728\u5355\u5143\u5185\u90e8\u751f\u6210\u9ed1\u70b9\u7c07&#xff0c;\u518d\u5c06\u8bef\u5dee\u6269\u6563\u4f20\u9012\u7ed9\u540e\u7eed\u5355\u5143\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u6709\u5e8f\u6296\u52a8\u5f53\u4e2d&#xff0c;\u4e00\u65e6\u9009\u5b9a\u6296\u52a8\u5355\u5143\u5c3a\u5bf8&#xff0c;\u70b9\u9635\u805a\u7c7b\u56fe\u6848\u5c31\u7531\u6296\u52a8\u77e9\u9635\u6c38\u4e45\u56fa\u5b9a\u3002 \u800c\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u6296\u52a8\u7b97\u6cd5&#xff0c;\u9ed1\u70b9\u7c07\u7684\u5c3a\u5bf8\u5b8c\u5168\u53d6\u51b3\u4e8e\u56fe\u50cf\u5206\u5272\u7ed3\u679c&#xff0c;\u7a0b\u5e8f\u8fd0\u884c\u671f\u95f4\u5c31\u53ef\u4ee5\u968f\u65f6\u4fee\u6539\u3002<\/p>\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u56fe 12\u201134 \u622a\u53d6\u4e86\u4e00\u5e45\u5361\u901a\u56fe\u50cf&#xff0c;\u753b\u9762\u5305\u542b\u7ebf\u6761\u8f6e\u5ed3\u4ee5\u53ca\u5927\u7247\u7070\u5ea6\u5747\u5300\u533a\u57df&#xff1b;\u80cc\u666f\u5899\u9762\u9634\u5f71\u4f7f\u7528\u89c4\u5219\u7f51\u70b9\u6a21\u62df\u4f20\u7edf\u5370\u5237\u534a\u8272\u8c03\u7f51\u5c4f\u6548\u679c\u3002\u56fe\u50cf\u5206\u522b\u7ecf\u8fc7\u56fa\u5b9a\u5355\u5143\u5c3a\u5bf8\u3001\u81ea\u9002\u5e94\u5355\u5143\u5c3a\u5bf8\u4e24\u79cd\u76ae\u4e9a\u8bfa\u6296\u52a8\u7b97\u6cd5\u5904\u7406&#xff1b;\u81ea\u9002\u5e94\u65b9\u6848\u753b\u8d28\u63d0\u5347\u6548\u679c\u5341\u5206\u660e\u663e\u3002\u6539\u8fdb\u7684\u6839\u6e90\u6765\u81ea\u56fe\u50cf\u9ad8\u9891\u8fb9\u7f18\u533a\u57df\u7684\u5904\u7406\u4f18\u5316&#xff0c;\u81ea\u9002\u5e94\u7b97\u6cd5\u65e2\u80fd\u5b8c\u7f8e\u5bf9\u9f50\u7ebf\u6761\u8f6e\u5ed3\u8fb9\u7f18&#xff0c;\u53c8\u80fd\u5229\u7528\u5747\u5300\u7f51\u70b9\u7cbe\u51c6\u8fd8\u539f\u51fa\u5404\u4e2a\u7070\u5ea6\u5c42\u6b21\u3002<\/p>\n<p class=\"img-center\"><img decoding=\"async\" alt=\"\" src=\"2026-09-023nee5jl0ljj.png\" \/><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u5f55 12.3 \u56fe\u6848\u6296\u52a8<br \/>\n12.4 \u975e\u5468\u671f\u6296\u52a8<br \/>\n12.4.1 \u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5<br \/>\n\u5f69\u8272\u56fe\u50cf\u7684\u6296\u52a8\u5904\u7406<br \/>\n12.4.2 \u57fa\u4e8e\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7684\u6296\u52a8\u7b97\u6cd5<br \/>\n\u50cf\u7d20\u904d\u5386\u6392\u5e8f<br \/>\n\u57fa\u4e8e\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u56fe\u50cf\u533a\u57df\u5212\u5206<br \/>\n\u81ea\u9002\u5e94\u5206\u5272<br \/>\n\u81ea\u9002\u5e94\u5206\u5272\u8ba1\u7b97\u6d41\u7a0b<br \/>\n\u6296\u52a8\u5355\u5143\u91cf\u5316<br \/>\n\u9ed1\u70b9\u7c07\u4f4d\u7f6e\u5fae\u8c03<br \/>\n\u5b8c\u6574\u6296\u52a8\u7b97\u6cd5\u6d41\u7a0b 12.3 \u56fe\u6848\u6296\u52a8 \u6709\u5e8f\u6296\u52a8\u5e38\u5e38\u4f1a\u548c\u4e00\u79cd\u540d\u4e3a\u56fe\u6848\u6296\u52a8&#xff08;Pattern Dithering&#xff09;\u7684\u6280\u672f\u76f8\u6df7\u6dc6\u3002\u8be5\u65b9\u6cd5\u5c06\u56fe\u50cf\u5212\u5206\u4e3a\u82e5\u5e72\u5927\u5c0f\u4e3a\u202fN\u00d7N\u202f\u7684\u6296\u52a8\u5355\u5143&amp;#x<\/p>\n","protected":false},"author":2,"featured_media":99536,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[50,427,523],"topic":[],"class_list":["post-99556","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-server","tag-50","tag-427","tag-523"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/99556.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u76ee\u5f55 12.3 \u56fe\u6848\u6296\u52a8 12.4 \u975e\u5468\u671f\u6296\u52a8 12.4.1 \u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5 \u5f69\u8272\u56fe\u50cf\u7684\u6296\u52a8\u5904\u7406 12.4.2 \u57fa\u4e8e\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7684\u6296\u52a8\u7b97\u6cd5 \u50cf\u7d20\u904d\u5386\u6392\u5e8f \u57fa\u4e8e\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u56fe\u50cf\u533a\u57df\u5212\u5206 \u81ea\u9002\u5e94\u5206\u5272 \u81ea\u9002\u5e94\u5206\u5272\u8ba1\u7b97\u6d41\u7a0b \u6296\u52a8\u5355\u5143\u91cf\u5316 \u9ed1\u70b9\u7c07\u4f4d\u7f6e\u5fae\u8c03 \u5b8c\u6574\u6296\u52a8\u7b97\u6cd5\u6d41\u7a0b 12.3 \u56fe\u6848\u6296\u52a8 \u6709\u5e8f\u6296\u52a8\u5e38\u5e38\u4f1a\u548c\u4e00\u79cd\u540d\u4e3a\u56fe\u6848\u6296\u52a8&#xff08;Pattern Dithering&#xff09;\u7684\u6280\u672f\u76f8\u6df7\u6dc6\u3002\u8be5\u65b9\u6cd5\u5c06\u56fe\u50cf\u5212\u5206\u4e3a\u82e5\u5e72\u5927\u5c0f\u4e3a\u202fN\u00d7N\u202f\u7684\u6296\u52a8\u5355\u5143&amp;#x\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/99556.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-09-02T11:58:01+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115759-6a980f47e317b.png\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/99556.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/99556.html\",\"name\":\"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"isPartOf\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\"},\"datePublished\":\"2026-09-02T11:58:01+00:00\",\"dateModified\":\"2026-09-02T11:58:01+00:00\",\"author\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\"},\"breadcrumb\":{\"@id\":\"https:\/\/www.wsisp.com\/helps\/99556.html#breadcrumb\"},\"inLanguage\":\"zh-Hans\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.wsisp.com\/helps\/99556.html\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/99556.html#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u9996\u9875\",\"item\":\"https:\/\/www.wsisp.com\/helps\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#website\",\"url\":\"https:\/\/www.wsisp.com\/helps\/\",\"name\":\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\",\"description\":\"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"zh-Hans\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"zh-Hans\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"contentUrl\":\"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery\",\"caption\":\"admin\"},\"sameAs\":[\"http:\/\/wp.wsisp.com\"],\"url\":\"https:\/\/www.wsisp.com\/helps\/author\/admin\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.wsisp.com\/helps\/99556.html","og_locale":"zh_CN","og_type":"article","og_title":"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","og_description":"\u76ee\u5f55 12.3 \u56fe\u6848\u6296\u52a8 12.4 \u975e\u5468\u671f\u6296\u52a8 12.4.1 \u5f17\u6d1b\u4f0a\u5fb7\u2011\u65af\u5766\u4f2f\u683c\u7b97\u6cd5 \u5f69\u8272\u56fe\u50cf\u7684\u6296\u52a8\u5904\u7406 12.4.2 \u57fa\u4e8e\u7a7a\u95f4\u586b\u5145\u66f2\u7ebf\u7684\u6296\u52a8\u7b97\u6cd5 \u50cf\u7d20\u904d\u5386\u6392\u5e8f \u57fa\u4e8e\u76ae\u4e9a\u8bfa\u66f2\u7ebf\u7684\u56fe\u50cf\u533a\u57df\u5212\u5206 \u81ea\u9002\u5e94\u5206\u5272 \u81ea\u9002\u5e94\u5206\u5272\u8ba1\u7b97\u6d41\u7a0b \u6296\u52a8\u5355\u5143\u91cf\u5316 \u9ed1\u70b9\u7c07\u4f4d\u7f6e\u5fae\u8c03 \u5b8c\u6574\u6296\u52a8\u7b97\u6cd5\u6d41\u7a0b 12.3 \u56fe\u6848\u6296\u52a8 \u6709\u5e8f\u6296\u52a8\u5e38\u5e38\u4f1a\u548c\u4e00\u79cd\u540d\u4e3a\u56fe\u6848\u6296\u52a8&#xff08;Pattern Dithering&#xff09;\u7684\u6280\u672f\u76f8\u6df7\u6dc6\u3002\u8be5\u65b9\u6cd5\u5c06\u56fe\u50cf\u5212\u5206\u4e3a\u82e5\u5e72\u5927\u5c0f\u4e3a\u202fN\u00d7N\u202f\u7684\u6296\u52a8\u5355\u5143&amp;#x","og_url":"https:\/\/www.wsisp.com\/helps\/99556.html","og_site_name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","article_published_time":"2026-09-02T11:58:01+00:00","og_image":[{"url":"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/09\/20260902115759-6a980f47e317b.png"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"\u4f5c\u8005":"admin","\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4":"2 \u5206"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.wsisp.com\/helps\/99556.html","url":"https:\/\/www.wsisp.com\/helps\/99556.html","name":"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","isPartOf":{"@id":"https:\/\/www.wsisp.com\/helps\/#website"},"datePublished":"2026-09-02T11:58:01+00:00","dateModified":"2026-09-02T11:58:01+00:00","author":{"@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41"},"breadcrumb":{"@id":"https:\/\/www.wsisp.com\/helps\/99556.html#breadcrumb"},"inLanguage":"zh-Hans","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.wsisp.com\/helps\/99556.html"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/www.wsisp.com\/helps\/99556.html#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u9996\u9875","item":"https:\/\/www.wsisp.com\/helps"},{"@type":"ListItem","position":2,"name":"\u5b57\u534a\u8272\u8c03\u539f\u7406\u8be6\u89e3\uff08\u56db\uff09"}]},{"@type":"WebSite","@id":"https:\/\/www.wsisp.com\/helps\/#website","url":"https:\/\/www.wsisp.com\/helps\/","name":"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3","description":"\u9999\u6e2f\u670d\u52a1\u5668_\u9999\u6e2f\u4e91\u670d\u52a1\u5668\u8d44\u8baf_\u670d\u52a1\u5668\u5e2e\u52a9\u6587\u6863_\u670d\u52a1\u5668\u6559\u7a0b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.wsisp.com\/helps\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"zh-Hans"},{"@type":"Person","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/358e386c577a3ab51c4493330a20ad41","name":"admin","image":{"@type":"ImageObject","inLanguage":"zh-Hans","@id":"https:\/\/www.wsisp.com\/helps\/#\/schema\/person\/image\/","url":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","contentUrl":"https:\/\/gravatar.wp-china-yes.net\/avatar\/?s=96&d=mystery","caption":"admin"},"sameAs":["http:\/\/wp.wsisp.com"],"url":"https:\/\/www.wsisp.com\/helps\/author\/admin"}]}},"_links":{"self":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/99556","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/comments?post=99556"}],"version-history":[{"count":0,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/posts\/99556\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media\/99536"}],"wp:attachment":[{"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/media?parent=99556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/categories?post=99556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/tags?post=99556"},{"taxonomy":"topic","embeddable":true,"href":"https:\/\/www.wsisp.com\/helps\/wp-json\/wp\/v2\/topic?post=99556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}