{"id":407,"date":"2017-11-30T22:26:33","date_gmt":"2017-11-30T14:26:33","guid":{"rendered":"http:\/\/www.whudj.cn\/?p=407"},"modified":"2017-12-19T12:09:26","modified_gmt":"2017-12-19T04:09:26","slug":"bezier%e6%9b%b2%e7%ba%bf%ef%bc%88%e4%ba%8c%ef%bc%89%ef%bc%9a%e7%bb%99%e5%ae%9a%e5%8f%82%e6%95%b0u%e6%b1%82%e7%82%b9","status":"publish","type":"post","link":"http:\/\/www.whudj.cn\/?p=407","title":{"rendered":"Bezier\u66f2\u7ebf\uff08\u4e8c\uff09\uff1a\u7ed9\u5b9a\u53c2\u6570u\u6c42\u70b9"},"content":{"rendered":"

\u8d1d\u585e\u5c14\u66f2\u7ebf\u6700\u5e38\u89c1\u7684\u529f\u80fd\u5c31\u662f\u7ed9\u5b9a\u53c2\u6570\u70b9u,\u8ba1\u7b97\u5bf9\u5e94\u66f2\u7ebf\u4e0a\u7684\u70b9C(u)\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u6b63\u7b97\u8fc7\u7a0b\uff0c\u5373\u7ed9\u5b9a\u53c2\u6570\u6c42\u8868\u8fbe\u5f0f\u7684\u503c\u3002\u6700\u7b80\u5355\u7684\u65b9\u6cd5\u662f\u6839\u636e\u516c\u5f0f\uff0c\u9996\u5148\u8ba1\u7b97\u5404\u57fa\u51fd\u6570\u7684\u503c\uff0c\u7136\u540e\u4e0e\u76f8\u5e94\u7684\u63a7\u5236\u70b9\u76f8\u4e58\uff0c\u76f8\u52a0\u3002\u4f46\u662f\u8fd9\u6837\u4f1a\u8ba1\u7b97u\u7684n\u6b21\u5e42\uff0c\u6709\u53ef\u80fd\u662f\u6570\u503c\u4e0d\u7a33\u5b9a\u7684\u3002\u672c\u6587\u4ecb\u7ecd\u7684\u5fb7\u5361\u65af\u7279\u91cc\u5965(De Casteljau’s)\u7b97\u6cd5\uff0c\u662f\u4e00\u79cd\u6570\u503c\u7a33\u5b9a\u7684\u65b9\u6cd5\u3002<\/p>\n

De Casteljau’s \u7b97\u6cd5\u7684\u601d\u60f3\u662f:\u5047\u8bbebezier\u66f2\u7ebf\u7684\u63a7\u5236\u70b9\u5e8f\u5217\u4e3a\\(P_{00},P_{01},\\cdots,P_{0n}\\)\uff0c\u786e\u5b9a\u70b9\u5e8f\u5217\\(P_{10},P_{11},\\cdots,P_{1n-1}\\)\uff0c\u5176\u4e2d\\(P_{ji} = uP_{j-1i} + (1-u)P_{j-1i+1}\\)\u5171n\u4e2a\u70b9\uff0c\u7136\u540e\u91cd\u590d\u8fed\u4ee3\uff0c\u76f4\u81f3n\u6b21\u8fed\u4ee3\u540e\uff0c\u53ea\u5269\u4e0b\u4e00\u4e2a\u70b9\uff0c\u5373\u4e3a\u6240\u6c42\u70b9\u3002\u5982\u4e0b\u56fe\uff1a<\/p>\n

\"\"<\/p>\n

5\u9636bezier\u66f2\u7ebf\u7684\u63a7\u5236\u70b9\u4e3a\\(0,1,…,5\\)\uff0c\u6b32\u6c42u=0.4\u65f6\u7684\u70b9\uff0c\u9996\u5148\u5bf9\u63a7\u5236\u591a\u8fb9\u5f62\u8fdb\u884c\u201c\u5207\u89d2\u201d,\u5f97\u52305\u4e2a\u65b0\u70b9\\(10,11,…,14\\)\uff0c\u7ecf\u8fc75\u6b21\u5207\u89d2\u540e\uff0c\u5f97\u5230\u7684\u70b950\u5373\u4e3au=0.4\u65f6\u7684\u503c\u3002<\/p>\n

\u4e00\u79cd\u9012\u5f52\u7684\u89e3\u6cd5\uff1a<\/p>\n

\u6709\u4e86\u8fed\u4ee3\u516c\u5f0f\uff0c\u6211\u4eec\u5c31\u77e5\u9053\u4e86\u7b97\u6cd5\u53ef\u4ee5\u901a\u8fc7\u9012\u5f52\u5b9e\u73b0\u3002<\/p>\n

Point deCasteljau(int i,int j,double u)\r\n{\r\n   if(0==j)\r\n    return Pi;\r\n   else\r\n    return (1.0-u)*deCasteljau(i,j-1,u) + u*deCasteljau(i+1,j-1,u);\r\n}\r\n\r\nPoint Evalute(double u)\r\n{\r\n   return deCasteljau(0,n,u);\r\n}<\/pre>\n
\u4f46\u662f\u4f60\u5f88\u5feb\u4f1a\u53d1\u73b0\uff0c\u9012\u5f52\u6709\u4e2a\u6bd4\u8f83\u4e25\u91cd\u7684\u95ee\u9898\uff0c\u5c31\u662f\u51fa\u73b0\u4e86\u5927\u91cf\u7684\u91cd\u590d\u8ba1\u7b97\u3002\u4ed6\u7684\u6a21\u5f0f\u4e0eFibonacci \u201c\u80a5\u4e0d\u62ff\u4e03\u201d\u51fd\u6570\u662f\u4e00\u6837\u7684\uff0c\u5176\u9012\u5f52\u8def\u5f84\u6784\u6210\u4e86\u4e00\u4e2a\u6709\u5411\u56fe\uff0c\u800c\u975e\u6811\u7ed3\u6784\uff0c\u5927\u90e8\u5206\u7684\u4e2d\u4ecb\u8282\u70b9\u8981\u88ab\u91cd\u590d\u8ba1\u7b97\u82e5\u5e72\u904d\u3002\u5982\u4e0b\u56fe\uff1a<\/p>\n
\"\"<\/p>\n
\u975e\u9012\u5f52\u89e3\u6cd5\uff1a<\/p>\n
\u6309\u7167\u8fed\u4ee3\u516c\u5f0f\uff0c\u9996\u5148\u6784\u9020\u4e00\u4e2an+1\u7684\u6570\u7ec4A\uff0c\u5c06\u63a7\u5236\u70b9\u5e8f\u5217\\(p_0,p_1,…,p_n\\)\u5b58\u5165\uff0c\u7136\u540e\u6267\u884cn\u6b21\u8fed\u4ee3\uff0c\u53d6\u6700\u540e\u4e00\u6b21\u8fed\u4ee3\u8ba1\u7b97\u51fa\u7684\u70b9A[0]\u5373\u4e3a\u6240\u6c42\u70b9\u3002<\/p>\n
Point Evaluate(Point A[],int n,double u)\r\n{\r\n\tfor(int i=0;i<n;++i)\r\n\t{\r\n\t\tfor(int j=0;j<n-i;++j)\r\n\t\t\tA[j] = (1.0-u)*A[j]+u*A[j+1];\r\n\t}\r\n\treturn A[0];\r\n}<\/pre>\n
\u4e0a\u8ff0\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n),\u7a7a\u95f4\u590d\u6742\u5ea6\u4e3aO(n)\u3002\u5177\u5907\u6570\u503c\u7a33\u5b9a\u7684\u7279\u6027\u3002<\/p>\n
\n
\u672c\u6587\u53c2\u8003Introduction to Computing with Geometry<\/a> \u7684\u7b2c\u4e94\u7ae0 Bezier Curves \u7684\u524d\u4e09\u8282\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u8d1d\u585e\u5c14\u66f2\u7ebf\u6700\u5e38\u89c1\u7684\u529f\u80fd\u5c31\u662f\u7ed9\u5b9a\u53c2\u6570\u70b9u,\u8ba1\u7b97\u5bf9\u5e94\u66f2\u7ebf\u4e0a\u7684\u70b9C(u)\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u662f\u6b63 … Continue reading →<\/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":[23],"tags":[],"_links":{"self":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/407"}],"collection":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=407"}],"version-history":[{"count":11,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/407\/revisions"}],"predecessor-version":[{"id":600,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/407\/revisions\/600"}],"wp:attachment":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=407"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=407"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}