Loop\u7ec6\u5206\u53ea\u80fd\u5bf9\u4e09\u89d2\u5f62\u7684\u6a21\u578b\u8fdb\u884c\u7ec6\u5206<\/p>\n\n\n\n
\u53d6\u6bcf\u4e2a\u4e09\u89d2\u5f62\u7684\u6bcf\u4e00\u4e2a\u8fb9\u7684\u4e2d\u70b9\uff0c\u5e76\u76f8\u4e92\u8fde\u63a5\u8d77\u6765\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u79fb\u52a8\u9876\u70b9<\/h4>\n\n\n\n\u9876\u70b9\u5206\u4e3a\u65b0\u9876\u70b9\u548c\u8001\u9876\u70b9\uff1a<\/p>\n\n\n\n\u5bf9\u4e8e\u65b0\u9876\u70b9\uff1a\u65b0\u9876\u70b9\u6240\u5728\u8fb9\u7684\u4e24\u4e2a\u8001\u9876\u70b9\u5206\u522b\u4e58[latex]\\frac{3}{8}[\/latex]\uff0c\u518d\u5c06\u8be5\u8fb9\u6240\u5728\u4e09\u89d2\u5f62\u7684\u53e6\u5916\u4e24\u4e2a\u9876\u70b9\u5206\u522b\u4e58[latex]\\frac{1}{8}[\/latex]\uff0c\u6700\u540e\u76f8\u52a0\uff0c\u5373\uff1a[latex]\\frac{3}{8}(A+B)+\\frac{1}{8}(C+D)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u8001\u9876\u70b9\uff0c\u9700\u8981\u5148\u8ba1\u7b97\u4e24\u4e2a\u503cn\uff1a\u9876\u70b9\u5ea6\u6570\uff08\u9876\u70b9\u6240\u8fde\u8fb9\u7684\u4e2a\u6570\uff09\uff0cu\uff1a\u5982\u679cn=3\uff0c[latex]u=\\frac{3}{16}[\/latex]\uff0c\u5426\u5219[latex]u=\\frac{3}{8n}[\/latex]\u3002<\/p>\n\n\n\n\u7136\u540e\u5c06\u88ab\u4fee\u6539\u9876\u70b9\u7684\u503c\u4e58[latex](1-n*u)[\/latex]\uff0c\u5c06\u5468\u56f4\u6240\u6709\u7684\u8001\u9876\u70b9\u76f8\u52a0\u518d\u4e58[latex]u[\/latex]\uff0c\u6700\u540e\u76f8\u52a0\uff0c\u5373\uff1a[latex](1-n*u)*original-position+u*neighbor-position-sum[\/latex]<\/p>\n\n\n\nCatmull-Clark\u7ec6\u5206<\/h3>\n\n\n\nCatmull-Clark\u7ec6\u5206\u53ef\u4ee5\u5bf9\u6240\u6709\u7684\u6a21\u578b\u8fdb\u884c\u7ec6\u5206\u3002\u5728\u8be5\u7ec6\u5206\u4e2d\uff0c\u9700\u8981\u5c06\u9762\u5206\u4e3a\u56db\u8fb9\u5f62\u9762\u548c\u975e\u56db\u8fb9\u5f62\u9762\u3002\u5c06\u9876\u70b9\u5206\u4e3a\u5947\u5f02\u70b9\uff08\u9876\u70b9\u5ea6\u6570\u4e0d\u7b49\u4e8e4\uff09\u548c\u975e\u5947\u5f02\u70b9\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5f15\u5165\u65b0\u9876\u70b9<\/h4>\n\n\n\n\u53d6\u6bcf\u4e2a\u8fb9\u7684\u4e2d\u70b9\u548c\u6bcf\u4e2a\u7c73\u9762\u7684\u4e2d\u70b9\uff0c\u5e76\u8fde\u63a5\u8d77\u6765\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u4f1a\u53d1\u73b0\u7ec6\u5206\u65f6\u6240\u6709\u7684\u975e\u56db\u8fb9\u5f62\u9762\u90fd\u4f1a\u6d88\u5931\uff0c\u800c\u5947\u5f02\u70b9\u4f1a\u589e\u52a0\uff0c\u4e14\u6bcf\u4e00\u4e2a\u975e\u56db\u8fb9\u5f62\u9762\u90fd\u4f1a\u589e\u52a0\u4e00\u4e2a\u5947\u5f02\u70b9\u3002<\/p>\n\n\n\n\u79fb\u52a8\u9876\u70b9<\/h4>\n\n\n\n\u5c06\u9876\u70b9\u5206\u4e3a\uff1a\u8001\u9876\u70b9v\u3001\u5728\u9762\u4e2d\u95f4\u7684\u65b0\u9876\u70b9f\u3001\u5728\u8fb9\u4e0a\u7684\u65b0\u9876\u70b9e\u3002<\/p>\n\n\n\n\u5bf9\u4e8e\u5728\u9762\u4e2d\u95f4\u7684\u65b0\u9876\u70b9\uff1a[latex]f=\\frac{v_1+v_2+v_3+v_4}{4}[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u5728\u8fb9\u4e0a\u7684\u65b0\u9876\u70b9\uff1a[latex]=\\frac{v_1+v_2+f_1+f_2}{4}[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u8001\u9876\u70b9\uff1a[latex]v=\\frac{f_1+f_2+f_3+f_4+2(m_1+m_2+m_3+m_4)+4p}{16}[\/latex]\uff0c\u5176\u4e2dm\u4e3a\u8fb9\u4e0a\u7684\u70b9\uff0cp\u4e3a\u88ab\u79fb\u52a8\u7684\u9876\u70b9\u672c\u8eab\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u7f51\u683c\u7b80\u5316<\/h2>\n\n\n\n\u2f06\u6b21\u8bef\u5dee\u5ea6\u91cf<\/h3>\n\n\n\n\u5b83\u7528\u6765\u8868\u793a\u7f51\u683c\u7b80\u5316\u5e26\u6765\u7684\u8bef\u5dee\u7684\u5927\u5c0f\u3002\u4e8c\u6b21\u8bef\u5dee\uff1a\u65b0\u7684\u70b9\u5e94\u8be5\u4e0e\u5b83\u76f8\u5173\u8054\u7684\u9762\u7684\u8ddd\u79bb\u7684\u5e73\u65b9\u548c\u6700\u5c0f\u3002<\/p>\n\n\n\n\u8fb9\u574d\u7f29<\/h3>\n\n\n\n\u5c06\u4e00\u4e2a\u8fb9\u7684\u4e24\u4e2a\u9876\u70b9\u8fdb\u884c\u5408\u5e76\u3002<\/p>\n\n\n\n\u5047\u8bbe\u574d\u7f29\u6bcf\u4e00\u6761\u8fb9\uff0c\u7136\u540e\u5206\u522b\u8ba1\u7b97\u5b83\u4eec\u7684\u4e8c\u6b21\u8bef\u5dee\u3002\u7136\u540e\u6bcf\u6b21\u9009\u62e9\u4e8c\u6b21\u8bef\u5dee\u6700\u5c0f\u7684\u8fb9\u8fdb\u884c\u574d\u7f29\uff0c\u7136\u540e\u66f4\u65b0\u88ab\u5f71\u54cd\u7684\u8fb9\u7684\u4e8c\u6b21\u8bef\u5dee\u3002\u53ef\u4ee5\u4f7f\u7528\u5806\u6216\u4f18\u5148\u961f\u5217\u3002\u901a\u8fc7\u5c40\u90e8\u6700\u4f18\u89e3\u6c42\u53d6\u5168\u5c40\u6700\u4f18\u89e3\uff0c\u5373\u8d2a\u5fc3\u7b97\u6cd5\u3002<\/p>\n\n\n\n\u9634\u5f71\u6620\u5c04<\/h2>\n\n\n\n\u4ece\u706f\u5149\u6e32\u67d3\uff1a<\/p>\n\n\n\n\u5c06\u706f\u5149\u4f5c\u4e3a\u76f8\u673a\uff0c\u4ece\u706f\u5149\u5904\u89c2\u5bdf\u573a\u666f\uff0c\u8bb0\u5f55\u4e0b\u6df1\u5ea6\u56fe\u3002<\/p>\n\n\n\n<\/figure 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\u9876\u70b9\u5206\u4e3a\u65b0\u9876\u70b9\u548c\u8001\u9876\u70b9\uff1a<\/p>\n\n\n\n
\u5bf9\u4e8e\u65b0\u9876\u70b9\uff1a\u65b0\u9876\u70b9\u6240\u5728\u8fb9\u7684\u4e24\u4e2a\u8001\u9876\u70b9\u5206\u522b\u4e58[latex]\\frac{3}{8}[\/latex]\uff0c\u518d\u5c06\u8be5\u8fb9\u6240\u5728\u4e09\u89d2\u5f62\u7684\u53e6\u5916\u4e24\u4e2a\u9876\u70b9\u5206\u522b\u4e58[latex]\\frac{1}{8}[\/latex]\uff0c\u6700\u540e\u76f8\u52a0\uff0c\u5373\uff1a[latex]\\frac{3}{8}(A+B)+\\frac{1}{8}(C+D)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5bf9\u4e8e\u8001\u9876\u70b9\uff0c\u9700\u8981\u5148\u8ba1\u7b97\u4e24\u4e2a\u503cn\uff1a\u9876\u70b9\u5ea6\u6570\uff08\u9876\u70b9\u6240\u8fde\u8fb9\u7684\u4e2a\u6570\uff09\uff0cu\uff1a\u5982\u679cn=3\uff0c[latex]u=\\frac{3}{16}[\/latex]\uff0c\u5426\u5219[latex]u=\\frac{3}{8n}[\/latex]\u3002<\/p>\n\n\n\n\u7136\u540e\u5c06\u88ab\u4fee\u6539\u9876\u70b9\u7684\u503c\u4e58[latex](1-n*u)[\/latex]\uff0c\u5c06\u5468\u56f4\u6240\u6709\u7684\u8001\u9876\u70b9\u76f8\u52a0\u518d\u4e58[latex]u[\/latex]\uff0c\u6700\u540e\u76f8\u52a0\uff0c\u5373\uff1a[latex](1-n*u)*original-position+u*neighbor-position-sum[\/latex]<\/p>\n\n\n\nCatmull-Clark\u7ec6\u5206<\/h3>\n\n\n\nCatmull-Clark\u7ec6\u5206\u53ef\u4ee5\u5bf9\u6240\u6709\u7684\u6a21\u578b\u8fdb\u884c\u7ec6\u5206\u3002\u5728\u8be5\u7ec6\u5206\u4e2d\uff0c\u9700\u8981\u5c06\u9762\u5206\u4e3a\u56db\u8fb9\u5f62\u9762\u548c\u975e\u56db\u8fb9\u5f62\u9762\u3002\u5c06\u9876\u70b9\u5206\u4e3a\u5947\u5f02\u70b9\uff08\u9876\u70b9\u5ea6\u6570\u4e0d\u7b49\u4e8e4\uff09\u548c\u975e\u5947\u5f02\u70b9\u3002<\/p>\n\n\n\n<\/figure 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