\u8d1d\u585e\u5c14\u66f2\u7ebf\u662f\u7531\u591a\u4e2a\u70b9\u786e\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u5176\u4e2d\uff0c\u66f2\u7ebf\u4e00\u5b9a\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u70b9\u3002<\/p>\n\n\n\n
\u5047\u8bbe\u6709\u4e09\u4e2a\u70b9[latex]b_0[\/latex]\u3001[latex]b_1[\/latex]\u3001[latex]b_2[\/latex]\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5047\u8bbe\u4e00\u4e2a\u65f6\u95f4t\uff0c\u53d6\u503c\u4e3a[latex][0,1][\/latex]\u3002\u5728\u65f6\u95f4t\u65f6\uff0c\u5728\u7ebf\u6bb5[latex]b_0 b_1[\/latex]\u4e0a\u53d6\u4e00\u70b9[latex]b_0^1[\/latex]\uff0c\u4f7f\u5f97[latex]b_0 b_0^1:b_0^1 b_1=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u540c\u65f6\uff0c\u5728\u7ebf\u6bb5[latex]b_1 b_2[\/latex]\u4e0a\u505a\u540c\u6837\u7684\u64cd\u4f5c\uff0c\u627e\u5230\u4e00\u70b9[latex]b_1^1[\/latex]\uff0c\u4f7f\u5f97[latex]b_1 b_1^1:b_1^1 b_2=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u7136\u540e\u518d\u5c06[latex]b_0^1 b_1^1[\/latex]\u8fde\u8d77\u6765\uff0c\u5e76\u5728[latex]b_0^1 b_1^1[\/latex]\u4e0a\u627e\u5230\u4e00\u70b9[latex]b_0^2[\/latex]\uff0c\u4f7f\u5f97[latex]b_0^1 b_0^2:b_0^2 b_1^1=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5f97\u5230\u7684[latex]b_0^2[\/latex]\u5c31\u662f\u6240\u6c42\u66f2\u7ebf\u4e0a\u7684\u4e00\u70b9\u3002\u5c06\u6240\u6709t\u53d6\u503c\u6240\u5f97\u5230\u7684\u70b9\u8fde\u8d77\u6765\uff0c\u4fbf\u662f\u6240\u6c42\u66f2\u7ebf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u4e2a\u66f2\u7ebf\u662f\u7531\u4e09\u4e2a\u70b9\u6240\u51b3\u5b9a\u7684\uff0c\u6240\u4ee5\u53eb\u505a\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/p>\n\n\n\n\u4e5f\u53ef\u4ee5\u7531\u591a\u4e2a\u70b9\u6765\u51b3\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u6bd4\u5982\u4e09\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u4ee3\u6570\u516c\u5f0f<\/h3>\n\n\n\nde Casteljau\u7b97\u6cd5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cfb\u6570\u91d1\u5b57\u5854\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\nn\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n[latex]\\mathbf{b}^n[\/latex]\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u9636\u6570n\uff08n\u6b21\u5411\u91cf\u591a\u9879\u5f0f\uff09[latex]\\mathbf{b}_j[\/latex]\uff1a\u8d1d\u585e\u5c14\u63a7\u5236\u70b9[latex]B_j^n(t)[\/latex]\uff1a\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f<\/p>\n\n\n\n\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n\u8be5\u516c\u5f0f\u4e0d\u4ec5\u80fd\u7528\u5728\u4e8c\u7ef4\u5e73\u9762\uff0c\u4e5f\u53ef\u7528\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u3002<\/p>\n\n\n\n\u6027\u8d28<\/h3>\n\n\n\n\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u5fc5\u5b9a\u7ecf\u8fc7[latex]b_0[\/latex]\u548c[latex]b_n[\/latex]<\/p>\n\n\n\n\u5176\u5f00\u59cb\u548c\u7ed3\u5c3e\u5904\u4e0e\u521d\u672b\u7aef\u7ebf\u6bb5\u76f8\u5207<\/p>\n\n\n\n\u63a7\u5236\u70b9\u7ecf\u8fc7\u4eff\u5c04\u53d8\u6362\u540e\uff0c\u4ecd\u80fd\u5f97\u5230\u6b63\u786e\u8d1d\u585e\u5c14\u66f2\u7ebf<\/p>\n\n\n\n\u66f2\u7ebf\u5728\u63a7\u5236\u70b9\u7684\u51f8\u5305\u5185<\/p>\n\n\n\n\u5206\u6bb5\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n\n\n\n\u5f53\u63a7\u5236\u70b9\u53d8\u591a\u65f6\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u96be\u4ee5\u63a7\u5236\uff0c\u5fae\u5c0f\u5730\u6539\u53d8\u4e00\u4e2a\u63a7\u5236\u70b9\u90fd\u4f1a\u5f71\u54cd\u5230\u6574\u4e2a\u66f2\u7ebf\u3002\u6240\u4ee5\u6bcf\u56db\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5206\u522b\u8ba1\u7b97\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002\u56db\u4e2a\u63a7\u5236\u70b9\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u63a7\u5236\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u4f4d\u7f6e\uff0c\u4e2d\u95f4\u4e24\u4e2a\u63a7\u5236\u70b9\u63a7\u5236\u66f2\u7ebf\u7684\u5f62\u72b6\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u5728\u6bcf\u7ec4\u8fde\u63a5\u7684\u4f4d\u7f6e\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u4e0d\u5e73\u6ed1\u3002<\/p>\n\n\n\n\u53d1\u73b0\u5982\u679c\u5728\u8fde\u63a5\u5904\u7684\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u7b49\uff0c\u66f2\u7ebf\u5c06\u5728\u8be5\u5904\u53d8\u5f97\u5e73\u6ed1\uff0c\u5373\u8be5\u5904\u7684\u5bfc\u6570\u4e5f\u8fde\u7eed\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nC0\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u8fde\u7eed\uff0c\u5373\u4e24\u70b9\u76f8\u8fde [latex]a_n=b_0[\/latex]C1\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e00\u9636\u5bfc\u8fde\u7eed [latex]a_n=b_0=\\frac{1}{2}(a_{n-1} + b_1)[\/latex]C2\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e8c\u9636\u5bfc\u8fde\u7eed\u4ee5\u6b64\u7c7b\u63a8<\/p>\n\n\n\n\u66f2\u9762<\/h2>\n\n\n\n\u5c06\u8d1d\u585e\u5c14\u66f2\u7ebf\u6269\u5c55\u5230\u66f2\u9762\uff0c\u752816\u4e2a\u63a7\u5236\u70b9\uff0c\u53734*4\u4e2a\u63a7\u5236\u70b9\u6765\u751f\u6210\u4e00\u4e2a\u66f2\u9762\u3002\u7c7b\u4f3c\u53cc\u7ebf\u6027\u63d2\u503c\uff0c\u6bcf4\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5148\u8ba1\u7b97\u51fat\u65f6\u523b4\u6761\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u70b9\uff0c\u518d\u5c06\u8fd94\u4e2a\u70b9\u4f5c\u4e3a\u63a7\u5236\u70b9\uff0c\u518d\u753b\u51fa\u4e00\u6761\u66f2\u7ebf\u3002 \u5c06\u4e0d\u540ct\u53d6\u503c\u5f97\u5230\u7684\u6240\u6709\u66f2\u7ebf\u8fde\u8d77\u6765\uff0c\u5c31\u80fd\u5f97\u5230\u66f2\u9762\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"\u8d1d\u585e\u5c14\u66f2\u7ebf \u8d1d\u585e\u5c14\u66f2\u7ebf\u662f\u7531\u591a\u4e2a\u70b9\u786e\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u5176\u4e2d\uff0c\u66f2\u7ebf\u4e00\u5b9a\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u70b9\u3002 de Casteljau\u7b97\u6cd5 \u5047\u8bbe\u6709\u4e09\u4e2a\u70b9[ …<\/p>","protected":false},"author":1,"featured_media":1089,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-1063","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=1063"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions"}],"predecessor-version":[{"id":1751,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions\/1751"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1089"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u5047\u8bbe\u4e00\u4e2a\u65f6\u95f4t\uff0c\u53d6\u503c\u4e3a[latex][0,1][\/latex]\u3002\u5728\u65f6\u95f4t\u65f6\uff0c\u5728\u7ebf\u6bb5[latex]b_0 b_1[\/latex]\u4e0a\u53d6\u4e00\u70b9[latex]b_0^1[\/latex]\uff0c\u4f7f\u5f97[latex]b_0 b_0^1:b_0^1 b_1=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u540c\u65f6\uff0c\u5728\u7ebf\u6bb5[latex]b_1 b_2[\/latex]\u4e0a\u505a\u540c\u6837\u7684\u64cd\u4f5c\uff0c\u627e\u5230\u4e00\u70b9[latex]b_1^1[\/latex]\uff0c\u4f7f\u5f97[latex]b_1 b_1^1:b_1^1 b_2=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u7136\u540e\u518d\u5c06[latex]b_0^1 b_1^1[\/latex]\u8fde\u8d77\u6765\uff0c\u5e76\u5728[latex]b_0^1 b_1^1[\/latex]\u4e0a\u627e\u5230\u4e00\u70b9[latex]b_0^2[\/latex]\uff0c\u4f7f\u5f97[latex]b_0^1 b_0^2:b_0^2 b_1^1=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5f97\u5230\u7684[latex]b_0^2[\/latex]\u5c31\u662f\u6240\u6c42\u66f2\u7ebf\u4e0a\u7684\u4e00\u70b9\u3002\u5c06\u6240\u6709t\u53d6\u503c\u6240\u5f97\u5230\u7684\u70b9\u8fde\u8d77\u6765\uff0c\u4fbf\u662f\u6240\u6c42\u66f2\u7ebf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u4e2a\u66f2\u7ebf\u662f\u7531\u4e09\u4e2a\u70b9\u6240\u51b3\u5b9a\u7684\uff0c\u6240\u4ee5\u53eb\u505a\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/p>\n\n\n\n\u4e5f\u53ef\u4ee5\u7531\u591a\u4e2a\u70b9\u6765\u51b3\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u6bd4\u5982\u4e09\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u4ee3\u6570\u516c\u5f0f<\/h3>\n\n\n\nde Casteljau\u7b97\u6cd5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cfb\u6570\u91d1\u5b57\u5854\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\nn\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n[latex]\\mathbf{b}^n[\/latex]\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u9636\u6570n\uff08n\u6b21\u5411\u91cf\u591a\u9879\u5f0f\uff09[latex]\\mathbf{b}_j[\/latex]\uff1a\u8d1d\u585e\u5c14\u63a7\u5236\u70b9[latex]B_j^n(t)[\/latex]\uff1a\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f<\/p>\n\n\n\n\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n\u8be5\u516c\u5f0f\u4e0d\u4ec5\u80fd\u7528\u5728\u4e8c\u7ef4\u5e73\u9762\uff0c\u4e5f\u53ef\u7528\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u3002<\/p>\n\n\n\n\u6027\u8d28<\/h3>\n\n\n\n\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u5fc5\u5b9a\u7ecf\u8fc7[latex]b_0[\/latex]\u548c[latex]b_n[\/latex]<\/p>\n\n\n\n\u5176\u5f00\u59cb\u548c\u7ed3\u5c3e\u5904\u4e0e\u521d\u672b\u7aef\u7ebf\u6bb5\u76f8\u5207<\/p>\n\n\n\n\u63a7\u5236\u70b9\u7ecf\u8fc7\u4eff\u5c04\u53d8\u6362\u540e\uff0c\u4ecd\u80fd\u5f97\u5230\u6b63\u786e\u8d1d\u585e\u5c14\u66f2\u7ebf<\/p>\n\n\n\n\u66f2\u7ebf\u5728\u63a7\u5236\u70b9\u7684\u51f8\u5305\u5185<\/p>\n\n\n\n\u5206\u6bb5\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n\n\n\n\u5f53\u63a7\u5236\u70b9\u53d8\u591a\u65f6\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u96be\u4ee5\u63a7\u5236\uff0c\u5fae\u5c0f\u5730\u6539\u53d8\u4e00\u4e2a\u63a7\u5236\u70b9\u90fd\u4f1a\u5f71\u54cd\u5230\u6574\u4e2a\u66f2\u7ebf\u3002\u6240\u4ee5\u6bcf\u56db\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5206\u522b\u8ba1\u7b97\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002\u56db\u4e2a\u63a7\u5236\u70b9\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u63a7\u5236\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u4f4d\u7f6e\uff0c\u4e2d\u95f4\u4e24\u4e2a\u63a7\u5236\u70b9\u63a7\u5236\u66f2\u7ebf\u7684\u5f62\u72b6\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u5728\u6bcf\u7ec4\u8fde\u63a5\u7684\u4f4d\u7f6e\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u4e0d\u5e73\u6ed1\u3002<\/p>\n\n\n\n\u53d1\u73b0\u5982\u679c\u5728\u8fde\u63a5\u5904\u7684\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u7b49\uff0c\u66f2\u7ebf\u5c06\u5728\u8be5\u5904\u53d8\u5f97\u5e73\u6ed1\uff0c\u5373\u8be5\u5904\u7684\u5bfc\u6570\u4e5f\u8fde\u7eed\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nC0\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u8fde\u7eed\uff0c\u5373\u4e24\u70b9\u76f8\u8fde [latex]a_n=b_0[\/latex]C1\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e00\u9636\u5bfc\u8fde\u7eed [latex]a_n=b_0=\\frac{1}{2}(a_{n-1} + b_1)[\/latex]C2\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e8c\u9636\u5bfc\u8fde\u7eed\u4ee5\u6b64\u7c7b\u63a8<\/p>\n\n\n\n\u66f2\u9762<\/h2>\n\n\n\n\u5c06\u8d1d\u585e\u5c14\u66f2\u7ebf\u6269\u5c55\u5230\u66f2\u9762\uff0c\u752816\u4e2a\u63a7\u5236\u70b9\uff0c\u53734*4\u4e2a\u63a7\u5236\u70b9\u6765\u751f\u6210\u4e00\u4e2a\u66f2\u9762\u3002\u7c7b\u4f3c\u53cc\u7ebf\u6027\u63d2\u503c\uff0c\u6bcf4\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5148\u8ba1\u7b97\u51fat\u65f6\u523b4\u6761\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u70b9\uff0c\u518d\u5c06\u8fd94\u4e2a\u70b9\u4f5c\u4e3a\u63a7\u5236\u70b9\uff0c\u518d\u753b\u51fa\u4e00\u6761\u66f2\u7ebf\u3002 \u5c06\u4e0d\u540ct\u53d6\u503c\u5f97\u5230\u7684\u6240\u6709\u66f2\u7ebf\u8fde\u8d77\u6765\uff0c\u5c31\u80fd\u5f97\u5230\u66f2\u9762\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"\u8d1d\u585e\u5c14\u66f2\u7ebf \u8d1d\u585e\u5c14\u66f2\u7ebf\u662f\u7531\u591a\u4e2a\u70b9\u786e\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u5176\u4e2d\uff0c\u66f2\u7ebf\u4e00\u5b9a\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u70b9\u3002 de Casteljau\u7b97\u6cd5 \u5047\u8bbe\u6709\u4e09\u4e2a\u70b9[ …<\/p>","protected":false},"author":1,"featured_media":1089,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-1063","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=1063"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions"}],"predecessor-version":[{"id":1751,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions\/1751"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1089"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u540c\u65f6\uff0c\u5728\u7ebf\u6bb5[latex]b_1 b_2[\/latex]\u4e0a\u505a\u540c\u6837\u7684\u64cd\u4f5c\uff0c\u627e\u5230\u4e00\u70b9[latex]b_1^1[\/latex]\uff0c\u4f7f\u5f97[latex]b_1 b_1^1:b_1^1 b_2=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u7136\u540e\u518d\u5c06[latex]b_0^1 b_1^1[\/latex]\u8fde\u8d77\u6765\uff0c\u5e76\u5728[latex]b_0^1 b_1^1[\/latex]\u4e0a\u627e\u5230\u4e00\u70b9[latex]b_0^2[\/latex]\uff0c\u4f7f\u5f97[latex]b_0^1 b_0^2:b_0^2 b_1^1=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5f97\u5230\u7684[latex]b_0^2[\/latex]\u5c31\u662f\u6240\u6c42\u66f2\u7ebf\u4e0a\u7684\u4e00\u70b9\u3002\u5c06\u6240\u6709t\u53d6\u503c\u6240\u5f97\u5230\u7684\u70b9\u8fde\u8d77\u6765\uff0c\u4fbf\u662f\u6240\u6c42\u66f2\u7ebf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u4e2a\u66f2\u7ebf\u662f\u7531\u4e09\u4e2a\u70b9\u6240\u51b3\u5b9a\u7684\uff0c\u6240\u4ee5\u53eb\u505a\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/p>\n\n\n\n\u4e5f\u53ef\u4ee5\u7531\u591a\u4e2a\u70b9\u6765\u51b3\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u6bd4\u5982\u4e09\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u4ee3\u6570\u516c\u5f0f<\/h3>\n\n\n\nde Casteljau\u7b97\u6cd5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cfb\u6570\u91d1\u5b57\u5854\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\nn\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n[latex]\\mathbf{b}^n[\/latex]\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u9636\u6570n\uff08n\u6b21\u5411\u91cf\u591a\u9879\u5f0f\uff09[latex]\\mathbf{b}_j[\/latex]\uff1a\u8d1d\u585e\u5c14\u63a7\u5236\u70b9[latex]B_j^n(t)[\/latex]\uff1a\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f<\/p>\n\n\n\n\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n\u8be5\u516c\u5f0f\u4e0d\u4ec5\u80fd\u7528\u5728\u4e8c\u7ef4\u5e73\u9762\uff0c\u4e5f\u53ef\u7528\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u3002<\/p>\n\n\n\n\u6027\u8d28<\/h3>\n\n\n\n\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u5fc5\u5b9a\u7ecf\u8fc7[latex]b_0[\/latex]\u548c[latex]b_n[\/latex]<\/p>\n\n\n\n\u5176\u5f00\u59cb\u548c\u7ed3\u5c3e\u5904\u4e0e\u521d\u672b\u7aef\u7ebf\u6bb5\u76f8\u5207<\/p>\n\n\n\n\u63a7\u5236\u70b9\u7ecf\u8fc7\u4eff\u5c04\u53d8\u6362\u540e\uff0c\u4ecd\u80fd\u5f97\u5230\u6b63\u786e\u8d1d\u585e\u5c14\u66f2\u7ebf<\/p>\n\n\n\n\u66f2\u7ebf\u5728\u63a7\u5236\u70b9\u7684\u51f8\u5305\u5185<\/p>\n\n\n\n\u5206\u6bb5\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n\n\n\n\u5f53\u63a7\u5236\u70b9\u53d8\u591a\u65f6\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u96be\u4ee5\u63a7\u5236\uff0c\u5fae\u5c0f\u5730\u6539\u53d8\u4e00\u4e2a\u63a7\u5236\u70b9\u90fd\u4f1a\u5f71\u54cd\u5230\u6574\u4e2a\u66f2\u7ebf\u3002\u6240\u4ee5\u6bcf\u56db\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5206\u522b\u8ba1\u7b97\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002\u56db\u4e2a\u63a7\u5236\u70b9\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u63a7\u5236\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u4f4d\u7f6e\uff0c\u4e2d\u95f4\u4e24\u4e2a\u63a7\u5236\u70b9\u63a7\u5236\u66f2\u7ebf\u7684\u5f62\u72b6\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u5728\u6bcf\u7ec4\u8fde\u63a5\u7684\u4f4d\u7f6e\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u4e0d\u5e73\u6ed1\u3002<\/p>\n\n\n\n\u53d1\u73b0\u5982\u679c\u5728\u8fde\u63a5\u5904\u7684\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u7b49\uff0c\u66f2\u7ebf\u5c06\u5728\u8be5\u5904\u53d8\u5f97\u5e73\u6ed1\uff0c\u5373\u8be5\u5904\u7684\u5bfc\u6570\u4e5f\u8fde\u7eed\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nC0\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u8fde\u7eed\uff0c\u5373\u4e24\u70b9\u76f8\u8fde [latex]a_n=b_0[\/latex]C1\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e00\u9636\u5bfc\u8fde\u7eed [latex]a_n=b_0=\\frac{1}{2}(a_{n-1} + 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\u7136\u540e\u518d\u5c06[latex]b_0^1 b_1^1[\/latex]\u8fde\u8d77\u6765\uff0c\u5e76\u5728[latex]b_0^1 b_1^1[\/latex]\u4e0a\u627e\u5230\u4e00\u70b9[latex]b_0^2[\/latex]\uff0c\u4f7f\u5f97[latex]b_0^1 b_0^2:b_0^2 b_1^1=t:(1-t)[\/latex]<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5f97\u5230\u7684[latex]b_0^2[\/latex]\u5c31\u662f\u6240\u6c42\u66f2\u7ebf\u4e0a\u7684\u4e00\u70b9\u3002\u5c06\u6240\u6709t\u53d6\u503c\u6240\u5f97\u5230\u7684\u70b9\u8fde\u8d77\u6765\uff0c\u4fbf\u662f\u6240\u6c42\u66f2\u7ebf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u4e2a\u66f2\u7ebf\u662f\u7531\u4e09\u4e2a\u70b9\u6240\u51b3\u5b9a\u7684\uff0c\u6240\u4ee5\u53eb\u505a\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/p>\n\n\n\n\u4e5f\u53ef\u4ee5\u7531\u591a\u4e2a\u70b9\u6765\u51b3\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u6bd4\u5982\u4e09\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u4ee3\u6570\u516c\u5f0f<\/h3>\n\n\n\nde Casteljau\u7b97\u6cd5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cfb\u6570\u91d1\u5b57\u5854\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\nn\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n[latex]\\mathbf{b}^n[\/latex]\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u9636\u6570n\uff08n\u6b21\u5411\u91cf\u591a\u9879\u5f0f\uff09[latex]\\mathbf{b}_j[\/latex]\uff1a\u8d1d\u585e\u5c14\u63a7\u5236\u70b9[latex]B_j^n(t)[\/latex]\uff1a\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f<\/p>\n\n\n\n\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n\u8be5\u516c\u5f0f\u4e0d\u4ec5\u80fd\u7528\u5728\u4e8c\u7ef4\u5e73\u9762\uff0c\u4e5f\u53ef\u7528\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u3002<\/p>\n\n\n\n\u6027\u8d28<\/h3>\n\n\n\n\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u5fc5\u5b9a\u7ecf\u8fc7[latex]b_0[\/latex]\u548c[latex]b_n[\/latex]<\/p>\n\n\n\n\u5176\u5f00\u59cb\u548c\u7ed3\u5c3e\u5904\u4e0e\u521d\u672b\u7aef\u7ebf\u6bb5\u76f8\u5207<\/p>\n\n\n\n\u63a7\u5236\u70b9\u7ecf\u8fc7\u4eff\u5c04\u53d8\u6362\u540e\uff0c\u4ecd\u80fd\u5f97\u5230\u6b63\u786e\u8d1d\u585e\u5c14\u66f2\u7ebf<\/p>\n\n\n\n\u66f2\u7ebf\u5728\u63a7\u5236\u70b9\u7684\u51f8\u5305\u5185<\/p>\n\n\n\n\u5206\u6bb5\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n\n\n\n\u5f53\u63a7\u5236\u70b9\u53d8\u591a\u65f6\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u96be\u4ee5\u63a7\u5236\uff0c\u5fae\u5c0f\u5730\u6539\u53d8\u4e00\u4e2a\u63a7\u5236\u70b9\u90fd\u4f1a\u5f71\u54cd\u5230\u6574\u4e2a\u66f2\u7ebf\u3002\u6240\u4ee5\u6bcf\u56db\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5206\u522b\u8ba1\u7b97\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002\u56db\u4e2a\u63a7\u5236\u70b9\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u63a7\u5236\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u4f4d\u7f6e\uff0c\u4e2d\u95f4\u4e24\u4e2a\u63a7\u5236\u70b9\u63a7\u5236\u66f2\u7ebf\u7684\u5f62\u72b6\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u5728\u6bcf\u7ec4\u8fde\u63a5\u7684\u4f4d\u7f6e\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u4e0d\u5e73\u6ed1\u3002<\/p>\n\n\n\n\u53d1\u73b0\u5982\u679c\u5728\u8fde\u63a5\u5904\u7684\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u7b49\uff0c\u66f2\u7ebf\u5c06\u5728\u8be5\u5904\u53d8\u5f97\u5e73\u6ed1\uff0c\u5373\u8be5\u5904\u7684\u5bfc\u6570\u4e5f\u8fde\u7eed\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nC0\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u8fde\u7eed\uff0c\u5373\u4e24\u70b9\u76f8\u8fde [latex]a_n=b_0[\/latex]C1\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e00\u9636\u5bfc\u8fde\u7eed [latex]a_n=b_0=\\frac{1}{2}(a_{n-1} + 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\u5f97\u5230\u7684[latex]b_0^2[\/latex]\u5c31\u662f\u6240\u6c42\u66f2\u7ebf\u4e0a\u7684\u4e00\u70b9\u3002\u5c06\u6240\u6709t\u53d6\u503c\u6240\u5f97\u5230\u7684\u70b9\u8fde\u8d77\u6765\uff0c\u4fbf\u662f\u6240\u6c42\u66f2\u7ebf\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u4e2a\u66f2\u7ebf\u662f\u7531\u4e09\u4e2a\u70b9\u6240\u51b3\u5b9a\u7684\uff0c\u6240\u4ee5\u53eb\u505a\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/p>\n\n\n\n\u4e5f\u53ef\u4ee5\u7531\u591a\u4e2a\u70b9\u6765\u51b3\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u6bd4\u5982\u4e09\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u4ee3\u6570\u516c\u5f0f<\/h3>\n\n\n\nde Casteljau\u7b97\u6cd5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cfb\u6570\u91d1\u5b57\u5854\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\nn\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n[latex]\\mathbf{b}^n[\/latex]\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u9636\u6570n\uff08n\u6b21\u5411\u91cf\u591a\u9879\u5f0f\uff09[latex]\\mathbf{b}_j[\/latex]\uff1a\u8d1d\u585e\u5c14\u63a7\u5236\u70b9[latex]B_j^n(t)[\/latex]\uff1a\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f<\/p>\n\n\n\n\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n\u8be5\u516c\u5f0f\u4e0d\u4ec5\u80fd\u7528\u5728\u4e8c\u7ef4\u5e73\u9762\uff0c\u4e5f\u53ef\u7528\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u3002<\/p>\n\n\n\n\u6027\u8d28<\/h3>\n\n\n\n\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u5fc5\u5b9a\u7ecf\u8fc7[latex]b_0[\/latex]\u548c[latex]b_n[\/latex]<\/p>\n\n\n\n\u5176\u5f00\u59cb\u548c\u7ed3\u5c3e\u5904\u4e0e\u521d\u672b\u7aef\u7ebf\u6bb5\u76f8\u5207<\/p>\n\n\n\n\u63a7\u5236\u70b9\u7ecf\u8fc7\u4eff\u5c04\u53d8\u6362\u540e\uff0c\u4ecd\u80fd\u5f97\u5230\u6b63\u786e\u8d1d\u585e\u5c14\u66f2\u7ebf<\/p>\n\n\n\n\u66f2\u7ebf\u5728\u63a7\u5236\u70b9\u7684\u51f8\u5305\u5185<\/p>\n\n\n\n\u5206\u6bb5\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n\n\n\n\u5f53\u63a7\u5236\u70b9\u53d8\u591a\u65f6\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u96be\u4ee5\u63a7\u5236\uff0c\u5fae\u5c0f\u5730\u6539\u53d8\u4e00\u4e2a\u63a7\u5236\u70b9\u90fd\u4f1a\u5f71\u54cd\u5230\u6574\u4e2a\u66f2\u7ebf\u3002\u6240\u4ee5\u6bcf\u56db\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5206\u522b\u8ba1\u7b97\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002\u56db\u4e2a\u63a7\u5236\u70b9\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u63a7\u5236\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u4f4d\u7f6e\uff0c\u4e2d\u95f4\u4e24\u4e2a\u63a7\u5236\u70b9\u63a7\u5236\u66f2\u7ebf\u7684\u5f62\u72b6\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u5728\u6bcf\u7ec4\u8fde\u63a5\u7684\u4f4d\u7f6e\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u4e0d\u5e73\u6ed1\u3002<\/p>\n\n\n\n\u53d1\u73b0\u5982\u679c\u5728\u8fde\u63a5\u5904\u7684\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u7b49\uff0c\u66f2\u7ebf\u5c06\u5728\u8be5\u5904\u53d8\u5f97\u5e73\u6ed1\uff0c\u5373\u8be5\u5904\u7684\u5bfc\u6570\u4e5f\u8fde\u7eed\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nC0\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u8fde\u7eed\uff0c\u5373\u4e24\u70b9\u76f8\u8fde [latex]a_n=b_0[\/latex]C1\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e00\u9636\u5bfc\u8fde\u7eed [latex]a_n=b_0=\\frac{1}{2}(a_{n-1} + b_1)[\/latex]C2\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e8c\u9636\u5bfc\u8fde\u7eed\u4ee5\u6b64\u7c7b\u63a8<\/p>\n\n\n\n\u66f2\u9762<\/h2>\n\n\n\n\u5c06\u8d1d\u585e\u5c14\u66f2\u7ebf\u6269\u5c55\u5230\u66f2\u9762\uff0c\u752816\u4e2a\u63a7\u5236\u70b9\uff0c\u53734*4\u4e2a\u63a7\u5236\u70b9\u6765\u751f\u6210\u4e00\u4e2a\u66f2\u9762\u3002\u7c7b\u4f3c\u53cc\u7ebf\u6027\u63d2\u503c\uff0c\u6bcf4\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5148\u8ba1\u7b97\u51fat\u65f6\u523b4\u6761\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u70b9\uff0c\u518d\u5c06\u8fd94\u4e2a\u70b9\u4f5c\u4e3a\u63a7\u5236\u70b9\uff0c\u518d\u753b\u51fa\u4e00\u6761\u66f2\u7ebf\u3002 \u5c06\u4e0d\u540ct\u53d6\u503c\u5f97\u5230\u7684\u6240\u6709\u66f2\u7ebf\u8fde\u8d77\u6765\uff0c\u5c31\u80fd\u5f97\u5230\u66f2\u9762\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"\u8d1d\u585e\u5c14\u66f2\u7ebf \u8d1d\u585e\u5c14\u66f2\u7ebf\u662f\u7531\u591a\u4e2a\u70b9\u786e\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u5176\u4e2d\uff0c\u66f2\u7ebf\u4e00\u5b9a\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u70b9\u3002 de Casteljau\u7b97\u6cd5 \u5047\u8bbe\u6709\u4e09\u4e2a\u70b9[ …<\/p>","protected":false},"author":1,"featured_media":1089,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-1063","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=1063"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions"}],"predecessor-version":[{"id":1751,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions\/1751"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1089"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u8fd9\u4e2a\u66f2\u7ebf\u662f\u7531\u4e09\u4e2a\u70b9\u6240\u51b3\u5b9a\u7684\uff0c\u6240\u4ee5\u53eb\u505a\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/p>\n\n\n\n
\u4e5f\u53ef\u4ee5\u7531\u591a\u4e2a\u70b9\u6765\u51b3\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u6bd4\u5982\u4e09\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u4ee3\u6570\u516c\u5f0f<\/h3>\n\n\n\nde Casteljau\u7b97\u6cd5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cfb\u6570\u91d1\u5b57\u5854\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\nn\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n[latex]\\mathbf{b}^n[\/latex]\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u9636\u6570n\uff08n\u6b21\u5411\u91cf\u591a\u9879\u5f0f\uff09[latex]\\mathbf{b}_j[\/latex]\uff1a\u8d1d\u585e\u5c14\u63a7\u5236\u70b9[latex]B_j^n(t)[\/latex]\uff1a\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f<\/p>\n\n\n\n\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n\u8be5\u516c\u5f0f\u4e0d\u4ec5\u80fd\u7528\u5728\u4e8c\u7ef4\u5e73\u9762\uff0c\u4e5f\u53ef\u7528\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u3002<\/p>\n\n\n\n\u6027\u8d28<\/h3>\n\n\n\n\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u5fc5\u5b9a\u7ecf\u8fc7[latex]b_0[\/latex]\u548c[latex]b_n[\/latex]<\/p>\n\n\n\n\u5176\u5f00\u59cb\u548c\u7ed3\u5c3e\u5904\u4e0e\u521d\u672b\u7aef\u7ebf\u6bb5\u76f8\u5207<\/p>\n\n\n\n\u63a7\u5236\u70b9\u7ecf\u8fc7\u4eff\u5c04\u53d8\u6362\u540e\uff0c\u4ecd\u80fd\u5f97\u5230\u6b63\u786e\u8d1d\u585e\u5c14\u66f2\u7ebf<\/p>\n\n\n\n\u66f2\u7ebf\u5728\u63a7\u5236\u70b9\u7684\u51f8\u5305\u5185<\/p>\n\n\n\n\u5206\u6bb5\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n\n\n\n\u5f53\u63a7\u5236\u70b9\u53d8\u591a\u65f6\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u96be\u4ee5\u63a7\u5236\uff0c\u5fae\u5c0f\u5730\u6539\u53d8\u4e00\u4e2a\u63a7\u5236\u70b9\u90fd\u4f1a\u5f71\u54cd\u5230\u6574\u4e2a\u66f2\u7ebf\u3002\u6240\u4ee5\u6bcf\u56db\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5206\u522b\u8ba1\u7b97\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002\u56db\u4e2a\u63a7\u5236\u70b9\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u63a7\u5236\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u4f4d\u7f6e\uff0c\u4e2d\u95f4\u4e24\u4e2a\u63a7\u5236\u70b9\u63a7\u5236\u66f2\u7ebf\u7684\u5f62\u72b6\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u5728\u6bcf\u7ec4\u8fde\u63a5\u7684\u4f4d\u7f6e\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u4e0d\u5e73\u6ed1\u3002<\/p>\n\n\n\n\u53d1\u73b0\u5982\u679c\u5728\u8fde\u63a5\u5904\u7684\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u7b49\uff0c\u66f2\u7ebf\u5c06\u5728\u8be5\u5904\u53d8\u5f97\u5e73\u6ed1\uff0c\u5373\u8be5\u5904\u7684\u5bfc\u6570\u4e5f\u8fde\u7eed\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nC0\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u8fde\u7eed\uff0c\u5373\u4e24\u70b9\u76f8\u8fde [latex]a_n=b_0[\/latex]C1\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e00\u9636\u5bfc\u8fde\u7eed [latex]a_n=b_0=\\frac{1}{2}(a_{n-1} + b_1)[\/latex]C2\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e8c\u9636\u5bfc\u8fde\u7eed\u4ee5\u6b64\u7c7b\u63a8<\/p>\n\n\n\n\u66f2\u9762<\/h2>\n\n\n\n\u5c06\u8d1d\u585e\u5c14\u66f2\u7ebf\u6269\u5c55\u5230\u66f2\u9762\uff0c\u752816\u4e2a\u63a7\u5236\u70b9\uff0c\u53734*4\u4e2a\u63a7\u5236\u70b9\u6765\u751f\u6210\u4e00\u4e2a\u66f2\u9762\u3002\u7c7b\u4f3c\u53cc\u7ebf\u6027\u63d2\u503c\uff0c\u6bcf4\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5148\u8ba1\u7b97\u51fat\u65f6\u523b4\u6761\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u70b9\uff0c\u518d\u5c06\u8fd94\u4e2a\u70b9\u4f5c\u4e3a\u63a7\u5236\u70b9\uff0c\u518d\u753b\u51fa\u4e00\u6761\u66f2\u7ebf\u3002 \u5c06\u4e0d\u540ct\u53d6\u503c\u5f97\u5230\u7684\u6240\u6709\u66f2\u7ebf\u8fde\u8d77\u6765\uff0c\u5c31\u80fd\u5f97\u5230\u66f2\u9762\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"\u8d1d\u585e\u5c14\u66f2\u7ebf \u8d1d\u585e\u5c14\u66f2\u7ebf\u662f\u7531\u591a\u4e2a\u70b9\u786e\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u5176\u4e2d\uff0c\u66f2\u7ebf\u4e00\u5b9a\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u70b9\u3002 de Casteljau\u7b97\u6cd5 \u5047\u8bbe\u6709\u4e09\u4e2a\u70b9[ …<\/p>","protected":false},"author":1,"featured_media":1089,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-1063","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=1063"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions"}],"predecessor-version":[{"id":1751,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions\/1751"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1089"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
de Casteljau\u7b97\u6cd5\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7cfb\u6570\u91d1\u5b57\u5854\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\nn\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n[latex]\\mathbf{b}^n[\/latex]\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u9636\u6570n\uff08n\u6b21\u5411\u91cf\u591a\u9879\u5f0f\uff09[latex]\\mathbf{b}_j[\/latex]\uff1a\u8d1d\u585e\u5c14\u63a7\u5236\u70b9[latex]B_j^n(t)[\/latex]\uff1a\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f<\/p>\n\n\n\n\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n\u8be5\u516c\u5f0f\u4e0d\u4ec5\u80fd\u7528\u5728\u4e8c\u7ef4\u5e73\u9762\uff0c\u4e5f\u53ef\u7528\u4e8e\u4e09\u7ef4\u7a7a\u95f4\u3002<\/p>\n\n\n\n\u6027\u8d28<\/h3>\n\n\n\n\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u5fc5\u5b9a\u7ecf\u8fc7[latex]b_0[\/latex]\u548c[latex]b_n[\/latex]<\/p>\n\n\n\n\u5176\u5f00\u59cb\u548c\u7ed3\u5c3e\u5904\u4e0e\u521d\u672b\u7aef\u7ebf\u6bb5\u76f8\u5207<\/p>\n\n\n\n\u63a7\u5236\u70b9\u7ecf\u8fc7\u4eff\u5c04\u53d8\u6362\u540e\uff0c\u4ecd\u80fd\u5f97\u5230\u6b63\u786e\u8d1d\u585e\u5c14\u66f2\u7ebf<\/p>\n\n\n\n\u66f2\u7ebf\u5728\u63a7\u5236\u70b9\u7684\u51f8\u5305\u5185<\/p>\n\n\n\n\u5206\u6bb5\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n\n\n\n\u5f53\u63a7\u5236\u70b9\u53d8\u591a\u65f6\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u96be\u4ee5\u63a7\u5236\uff0c\u5fae\u5c0f\u5730\u6539\u53d8\u4e00\u4e2a\u63a7\u5236\u70b9\u90fd\u4f1a\u5f71\u54cd\u5230\u6574\u4e2a\u66f2\u7ebf\u3002\u6240\u4ee5\u6bcf\u56db\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5206\u522b\u8ba1\u7b97\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002\u56db\u4e2a\u63a7\u5236\u70b9\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u63a7\u5236\u66f2\u7ebf\u7684\u5f00\u59cb\u548c\u7ed3\u5c3e\u7684\u4f4d\u7f6e\uff0c\u4e2d\u95f4\u4e24\u4e2a\u63a7\u5236\u70b9\u63a7\u5236\u66f2\u7ebf\u7684\u5f62\u72b6\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u8fd9\u65f6\u4f1a\u51fa\u73b0\u95ee\u9898\uff0c\u5728\u6bcf\u7ec4\u8fde\u63a5\u7684\u4f4d\u7f6e\uff0c\u66f2\u7ebf\u4f1a\u53d8\u5f97\u4e0d\u5e73\u6ed1\u3002<\/p>\n\n\n\n\u53d1\u73b0\u5982\u679c\u5728\u8fde\u63a5\u5904\u7684\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\uff0c\u65b9\u5411\u76f8\u7b49\uff0c\u66f2\u7ebf\u5c06\u5728\u8be5\u5904\u53d8\u5f97\u5e73\u6ed1\uff0c\u5373\u8be5\u5904\u7684\u5bfc\u6570\u4e5f\u8fde\u7eed\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nC0\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u8fde\u7eed\uff0c\u5373\u4e24\u70b9\u76f8\u8fde [latex]a_n=b_0[\/latex]C1\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e00\u9636\u5bfc\u8fde\u7eed [latex]a_n=b_0=\\frac{1}{2}(a_{n-1} + b_1)[\/latex]C2\u8fde\u7eed\uff1a\u5728\u8be5\u5904\u7684\u4e8c\u9636\u5bfc\u8fde\u7eed\u4ee5\u6b64\u7c7b\u63a8<\/p>\n\n\n\n\u66f2\u9762<\/h2>\n\n\n\n\u5c06\u8d1d\u585e\u5c14\u66f2\u7ebf\u6269\u5c55\u5230\u66f2\u9762\uff0c\u752816\u4e2a\u63a7\u5236\u70b9\uff0c\u53734*4\u4e2a\u63a7\u5236\u70b9\u6765\u751f\u6210\u4e00\u4e2a\u66f2\u9762\u3002\u7c7b\u4f3c\u53cc\u7ebf\u6027\u63d2\u503c\uff0c\u6bcf4\u4e2a\u63a7\u5236\u70b9\u4e3a\u4e00\u7ec4\uff0c\u5148\u8ba1\u7b97\u51fat\u65f6\u523b4\u6761\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u70b9\uff0c\u518d\u5c06\u8fd94\u4e2a\u70b9\u4f5c\u4e3a\u63a7\u5236\u70b9\uff0c\u518d\u753b\u51fa\u4e00\u6761\u66f2\u7ebf\u3002 \u5c06\u4e0d\u540ct\u53d6\u503c\u5f97\u5230\u7684\u6240\u6709\u66f2\u7ebf\u8fde\u8d77\u6765\uff0c\u5c31\u80fd\u5f97\u5230\u66f2\u9762\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"\u8d1d\u585e\u5c14\u66f2\u7ebf \u8d1d\u585e\u5c14\u66f2\u7ebf\u662f\u7531\u591a\u4e2a\u70b9\u786e\u5b9a\u4e00\u6761\u66f2\u7ebf\uff0c\u5176\u4e2d\uff0c\u66f2\u7ebf\u4e00\u5b9a\u7ecf\u8fc7\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u70b9\u3002 de Casteljau\u7b97\u6cd5 \u5047\u8bbe\u6709\u4e09\u4e2a\u70b9[ …<\/p>","protected":false},"author":1,"featured_media":1089,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[18,14,30,3],"tags":[17,15,16,12,22],"class_list":["post-1063","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-games","category-games101","category-30","category-3","tag-games","tag-games101","tag-16","tag-12","tag-22"],"_links":{"self":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/comments?post=1063"}],"version-history":[{"count":1,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions"}],"predecessor-version":[{"id":1751,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/posts\/1063\/revisions\/1751"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media\/1089"}],"wp:attachment":[{"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/media?parent=1063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/categories?post=1063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.forillusion.com\/index.php\/wp-json\/wp\/v2\/tags?post=1063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\u6bd4\u5982\u4e8c\u6b21\u8d1d\u585e\u5c14\u66f2\u7ebf\uff1a<\/p>\n\n\n\n
[latex]b_0^1(t)=(1-t) b_0+t b_1[\/latex][latex]b_1^1(t)=(1-t) b_1+t b_2[\/latex][latex]b_0^2(t)=(1-t) b_0^1+t b_1^1[\/latex][latex]b_0^2(t)=(1-t)^2 b_0+2 t(1-t) b_1+t^2 b_2[\/latex]<\/p>\n\n\n\n
\u89c2\u5bdf\u4e0a\u5f0f\u53ef\u77e5\uff0cb\u524d\u7684\u7cfb\u6570\u662f\u5bf9[latex](t+1-t)^n[\/latex]\u7684\u5c55\u5f00<\/p>\n\n\n\n
n\u9636\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u4f2f\u6069\u65af\u5766\u5f62\u5f0f\uff1a[latex]\\mathbf{b}^n(t)=\\mathbf{b}0^n(t)=\\sum_{j=0}^n \\mathbf{b}_j B_j^n(t)[\/latex]<\/p>\n\n\n\n
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\u4f2f\u6069\u65af\u5766\u591a\u9879\u5f0f\uff1a[latex]B_i^n(t)=\\left(\\begin{array}{c} n \\ i \\end{array}\\right) t^i(1-t)^{n-i}[\/latex]<\/p>\n\n\n\n
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<\/p>\n","protected":false},"excerpt":{"rendered":"
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