{"id":519,"date":"2017-12-10T22:01:17","date_gmt":"2017-12-10T14:01:17","guid":{"rendered":"http:\/\/www.whudj.cn\/?p=519"},"modified":"2019-06-05T17:19:05","modified_gmt":"2019-06-05T09:19:05","slug":"b-spline%e5%9b%9b%e4%bf%ae%e5%9e%8b-%e7%a7%bb%e5%8a%a8%e6%8e%a7%e5%88%b6%e7%82%b9","status":"publish","type":"post","link":"http:\/\/www.whudj.cn\/?p=519","title":{"rendered":"B-Spline(\u4e94):\u4fee\u578b-\u79fb\u52a8\u63a7\u5236\u70b9"},"content":{"rendered":"

\u5728\u57fa\u51fd\u6570\u7684\u6027\u8d28\u4e2d\u6211\u4eec\u5df2\u7ecf\u5b66\u4e60\u8fc7\uff0cB\u6837\u6761\u57fa\u51fd\u6570\\(N_{i,p}\\)\u7684\u4f5c\u7528\u8303\u56f4\u662f\u5c40\u90e8\u7684\uff0c\u56e0\u6b64\u4e0eBezier\u66f2\u7ebf\u4e0d\u540c\uff0c\u79fb\u52a8\u63a7\u5236\u70b9\\(N_{i,p}\\)\u5bf9B\u6837\u6761\u7684\u5f71\u54cd\u662f\u5c40\u90e8\u7684\u3002\u800c\u4e14\uff0c\u901a\u8fc7\u57fa\u51fd\u6570\u201c\u5f3a\u51f8\u5305\u6027\u201d\u7684\u7279\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u82e5\u5e72\u6837\u6761\u66f2\u7ebf\u4fee\u578b\u7684\u6280\u5de7\u3002<\/p>\n

\u79fb\u52a8\u63a7\u5236\u70b9<\/strong><\/p>\n

B\u6837\u6761\u66f2\u7ebf\u7684\u77e9\u9635\u5f62\u5f0f\u5982\u4e0b\uff1a$$C(u) = \\begin{bmatrix}N_0&N_1& \\cdots &N_n\\end{bmatrix}\\begin{bmatrix}P_0\\\\P_1\\\\ \\cdots \\\\ P_n\\end{bmatrix}$$\u5982\u679c\u5c06\\(P_i\\)\u79fb\u52a8\u5230\\(P_i+\\vec v\\),\u65b0\u66f2\u7ebf\\(D(u)\\)\u7684\u5b9a\u4e49\u662f\uff1a$$D(u) = \\begin{bmatrix}N_0& \\cdots &N_i& \\cdots &N_n\\end{bmatrix}\\begin{bmatrix}P_0\\\\\\cdots \\\\P_i+\\vec v\\\\ \\cdots \\\\ P_n\\end{bmatrix} = C(u) + N_i\\vec v$$\u5373\u65b0\u66f2\u7ebf\u4e3a\u539f\u66f2\u7ebf\u6574\u4f53\u79fb\u52a8\\(N_i\\vec v\\)\u3002<\/p>\n

\u56e0\u4e3a\u57fa\u51fd\u6570\\(N_i\\)\u4ec5\u5728\u533a\u95f4\\([u_i,u_{i+p+1})\\)\u4e0a\u975e0\uff0c\u6240\u4ee5\u63a7\u5236\u70b9\\(P_i\\)\u7684\u79fb\u52a8\u4ec5\u5bf9\u8fd9\u6bb5\u533a\u95f4\u5185\u7684\u66f2\u7ebf\u8d77\u4f5c\u7528\u3002\u800c\u4e14\uff0c\u56e0\u4e3a\\(0<N_i \\le 1\\)\uff0c\u6240\u4ee5\u53ef\u77e5\u66f2\u7ebf\u7684\u79fb\u52a8\u4e0e\\(\\vec v\\)\u540c\u5411\uff0c\u5e76\u4e14\u8ddd\u79bb\u4e0d\u8d85\u8fc7\\(|v|\\)\u3002<\/p>\n

\u4fee\u578b\u6280\u5de7<\/strong><\/p>\n

\u57fa\u51fd\u6570\u7684\u201c\u5f3a\u51f8\u5305\u6027\u201d\u6307\u7684\u662f\u66f2\u7ebf\u4e0a\\(u_i,u_{i+1}\\)\u6bb5\u4e00\u5b9a\u5728\u7531\u63a7\u5236\u70b9\\(P_{i-p},…,P_i\\)\u6784\u6210\u7684\u51f8\u5305\u4e4b\u4e2d\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u63a7\u5236\u51f8\u5305\u7684\u5f62\u72b6\u5f71\u54cd\u66f2\u7ebf\u7684\u5f62\u72b6\u3002\u4e0b\u9762\u7684\u6280\u5de7\uff0c\u5927\u5bb6\u90fd\u53ef\u4ee5\u4e0b\u8f7d Nurbs demo<\/a> \u81ea\u884c\u5b9e\u8df5\u3002<\/p>\n

1\uff09\u4ee4\u00a0\\(P_{i-p},…,P_i\\)\u5171\u7ebf\uff0c\u4f7f\u5f97\u66f2\u7ebf\\(u_i,u_{i+1}\\)\u6bb5\u6210\u4e3a\u76f4\u7ebf\u3002\u56e0\u4e3a\u51f8\u5305\u53d8\u6210\u76f4\u7ebf\uff0c\u51f8\u5305\u5185\u7684\u66f2\u7ebf\u81ea\u7136\u88ab\u201c\u538b\u6241\u201d\u4e3a\u76f4\u7ebf\u3002<\/p>\n

\"\"<\/p>\n

\u5982\u4e0a\u56fe\uff0c\u901a\u8fc7\u4f7f\\(P_3,…,P_6\\)\u5171\u7ebf\uff0c\u53ef\u4ee5\u4f7f\u5f97\u66f2\u7ebf\u6bb5\\([u_6,u_7)\\)\u4e0e\u63a7\u5236\u70b9\u5171\u7ebf\u3002<\/p>\n

2\uff09\u4ee4\\(P_{i-p+1},…,P_{i}\\)\u5171p\u4e2a\u70b9\u91cd\u5408\uff0c\u66f2\u7ebf\u6bb5\u4f7f\u5f97\u66f2\u7ebf\\(u_i,u_{i+1}\\)\u6bb5\u6210\u4e3a\u76f4\u7ebf\uff0c\u5e76\u4e14\u66f2\u7ebf\u901a\u8fc7\u63a7\u5236\u70b9\\(P_i\\)\u3002\u5982\u4e0b\u56fe\u3002\"\"\"\"<\/p>\n

 <\/p>\n

\u9996\u5148\u63a7\u5236\u70b9\u6784\u6210\u76f4\u7ebf\uff0c\u66f2\u7ebf\u53d8\u6210\u76f4\u7ebf\u3002\u5f53\\(u=u_7\\)\u65f6\uff0c\\(N_3=0\\),\\(N_4+N_5+N_6=1\\)\uff0c\u800c\u4e14\u540ep\u4e2a\u63a7\u5236\u70b9\u91cd\u5408\uff0c\u4f7f\u5f97\\(C(u_7)=P_6\\)\u3002<\/p>\n

3\uff09 \u4ee4\\(P_{i-p+1},…,P_{i}\\)\u5171p\u4e2a\u70b9\u91cd\u5408\uff0c\u4e14\\(P_{i-p},P_i,P_{i+1}\\)\u5171\u7ebf,\u66f2\u7ebf\u4e0e\u4e09\u70b9\u6240\u6784\u6210\u7684\u76f4\u7ebf\u76f8\u5207\u3002\u8fd9\u4e00\u6761\u662f\u5bf9\u7b2c\u4e8c\u6761\u7684\u6269\u5c55\u3002\"\"<\/p>\n

\u5982\u56fe\uff0c\\(P_2,P_3=P_4=P_5,P_6\\)\u5171\u7ebf\uff0c\u66f2\u7ebf\u4e0e\u63a7\u5236\u591a\u8fb9\u5f62\\(P_2,P_6\\)\u76f8\u5207\u3002<\/p>\n

\n

\u672c\u8282\u53c2\u8003 Introduction to Computing with Geometry<\/a> 6.3.4\u8282\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u5728\u57fa\u51fd\u6570\u7684\u6027\u8d28\u4e2d\u6211\u4eec\u5df2\u7ecf\u5b66\u4e60\u8fc7\uff0cB\u6837\u6761\u57fa\u51fd\u6570\\(N_{i,p}\\)\u7684\u4f5c\u7528\u8303\u56f4\u662f\u5c40 … 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\/519"}],"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=519"}],"version-history":[{"count":9,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/519\/revisions"}],"predecessor-version":[{"id":1273,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/519\/revisions\/1273"}],"wp:attachment":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=519"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=519"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}