{"id":450,"date":"2017-12-03T19:11:49","date_gmt":"2017-12-03T11:11:49","guid":{"rendered":"http:\/\/www.whudj.cn\/?p=450"},"modified":"2017-12-04T21:19:58","modified_gmt":"2017-12-04T13:19:58","slug":"nurbs%e4%b8%80-%e5%8a%a8%e6%9c%ba%e3%80%81%e5%ae%9a%e4%b9%89%e4%bb%a5%e5%8f%8a%e5%8e%86%e5%8f%b2%e6%bc%ab%e8%b0%88","status":"publish","type":"post","link":"http:\/\/www.whudj.cn\/?p=450","title":{"rendered":"NURBS(\u4e00): 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Paul de Faget de Casteljau\u57281963\u5e74\u53d1\u660e\u4e86de Casteljau\uff08\u5fb7\u5361\u65af\u7279\u91cc\u5965\uff09\u7b97\u6cd5\uff0c\u901a\u8fc7\u8fd9\u5957\u7b97\u6cd5\u53ef\u4ee5\u8ba1\u7b97\u51fa\u201c\u66f2\u7ebf\u201d\u4e0a\u7684\u70b9\u3002\u4ed6\u987f\u609f\u4e86\u4e0e\u5176\u5b9a\u4e49\u4e00\u6761\u4ee5\u957f\u5ea6\u4f5c\u4e3a\u53c2\u6570\u7684\u66f2\u7ebf\uff0c\u4e0d\u5982\u5b9a\u4e49\u4e00\u7cfb\u5217\u63a7\u5236\u70b9\uff0c\u901a\u8fc7\u6539\u53d8\u63a7\u5236\u70b9\u7684\u5f62\u72b6\u5f71\u54cd\u66f2\u7ebf\u5f62\u72b6\u3002\u5728\u5f53\u65f6\uff0cde Casteljau\u7684\u505a\u6cd5\u65e0\u7591\u662f\u6700\u5927\u7684\u521b\u65b0\uff0c\u8d77\u521d\u4e5f\u906d\u5230\u4e86\u516c\u53f8\u5185\u90e8\u7684\u8d28\u7591\uff0c\u4f46\u662f\u8fd9\u4e2a\u5e74\u8f7b\u7684\u6570\u5b66\u5bb6\u6700\u7ec8\u8bf4\u670d\u516c\u53f8\u91c7\u7eb3\u4ed6\u7684\u7b97\u6cd5\uff0c\u5e76\u4e14\u6700\u7ec8\u83b7\u5f97\u6210\u529f\u3002\u96ea\u94c1\u9f99\u4e25\u683c\u8981\u6c42\u5bf9de Casteljau\u7b97\u6cd5\u4fdd\u5bc6\uff0c\u76f4\u52308\u5e74\u4e4b\u540ede Casteljau\u7684\u6210\u679c\u624d\u5f97\u4ee5\u53d1\u8868\u3002<\/p>\n<p>\u5c3d\u7ba1\u96ea\u94c1\u9f99\u8fdb\u884c\u4e86\u4e25\u5bc6\u7684\u4fdd\u5bc6\u5de5\u4f5c\uff0c\u5176\u7ade\u4e89\u5bf9\u624b\u96f7\u8bfa\u516c\u53f8\u8fd8\u662f\u4e86\u89e3\u5230\u4e86de Casteljau\u7684\u5de5\u4f5c\uff0c\u5e76\u4e14\u5bf9\u4ed6\u7684\u5de5\u4f5c\u8fdb\u884c\u4e86\u6df1\u5165\u7684\u7814\u7a76\uff0c\u5c3d\u7ba1\u4e0d\u662fde Casteljau\u7b97\u6cd5\u672c\u8eab\u30021966\u5e74\uff0c\u96f7\u8bfa\u516c\u53f8\u7684bezier\u548c\u4ed6\u7684\u56e2\u961f\u72ec\u7acb\u7684\u91cd\u73b0\u4e86de Casteljau\u7684\u7814\u7a76\u6210\u679c\uff0c\u5e76\u4e14\u5c06\u201c\u66f2\u7ebf\u201d\u6b63\u5f0f\u547d\u540d\u4e3a\u201cBezier\u201d\u66f2\u7ebf\u3002\u4e0e\u96ea\u94c1\u9f99\u4e0d\u540c\uff0c\u96f7\u8bfa\u5141\u8bb8\u8d1d\u585e\u5c14\u53d1\u8868\u4ed6\u7684\u7814\u7a76\u6210\u679c\u3002\u6240\u4ee5\u73b0\u5728\u5927\u5bb6\u4e00\u822c\u90fd\u4e86\u89e3\u8d1d\u585e\u5c14\uff0c\u800cde Casteljau\u5728\u5927\u4f17\u4e2d\u5c31\u6ca1\u6709\u90a3\u4e48\u9ad8\u7684\u77e5\u540d\u5ea6\u4e86\u3002<\/p>\n<p>\u6709\u610f\u601d\u7684\u662f\uff0c\u8d1d\u585e\u5c14\u7684\u5de5\u4f5c\u6700\u521d\u4e5f\u6536\u5230\u4e86\u7ba1\u7406\u5c42\u7684\u5632\u8bbd\u3002\u201c\u5982\u679c\u8bf4\u4f60\u7684\u65b9\u6cd5\u90a3\u4e48\u597d\uff0c\u7f8e\u56fd\u4eba\u80af\u5b9a\u65e9\u5c31\u53d1\u660e\u4e86\uff01\u201d\u542c\u8d77\u6765\u662f\u4e0d\u662f\u4f3c\u66fe\u76f8\u8bc6\uff1f\u53ef\u89c1\u5f53\u65f6\u7684\u6cd5\u56fd\u6c7d\u8f66\u5236\u9020\u4e1a\u8fd8\u662f\u975e\u5e38\u201c\u4f20\u7edf\u201d\u7684\u3002\u5f53\u7136\uff0c\u7f8e\u56fd\u4eba\u4e5f\u6ca1\u6709\u95f2\u7740\uff0cGM\u7684\u5b66\u8005Carl de Boor\u53d1\u660e\u4e86de Boor\u7b97\u6cd5\uff0c\u662f\u4e00\u79cd\u8ba1\u7b97B\u6837\u6761\u4e0a\u70b9\u7684\u65b9\u6cd5\u3002\u5c3d\u7ba1B\u6837\u6761\u4f5c\u4e3a\u4e00\u79cd\u6570\u5b66\u6a21\u578b\u572820\u4e16\u7eaa40\u5e74\u4ee3\u5c31\u5df2\u7ecf\u5b58\u5728\uff0c\u4f46\u662f\u56e0\u4e3ade Boor\u7b97\u6cd5\u4f18\u8d8a\u7684\u6570\u503c\u7a33\u5b9a\u6027\uff0cB\u6837\u6761\u624d\u53d1\u6325\u4e86\u5b83\u5de8\u5927\u7684\u5e94\u7528\u6f5c\u529b\u3002<\/p>\n<p>\u6ce2\u97f3\u516c\u53f8\u7684\u63a2\u7d22\u3002\u6ce2\u97f3\u516c\u53f8\u662fCAGD\u7684\u5148\u9a71\u300250\u5e74\u4ee3\u5c31\u63a8\u51fa\u4e86\u81ea\u5df1\u7684\u8bbe\u8ba1\u8f6f\u4ef6\uff0c\u4f46\u662f\u76f4\u523010\u5e74\u540e\uff0c\u7269\u7406\u7684\u6728\u8d28\u6837\u6761\u4ecd\u7136\u88ab\u5f88\u591a\u6ce2\u97f3\u5de5\u7a0b\u5e08\u5728\u5de5\u4f5c\u4e2d\u4f7f\u7528\u3002\u800c\u4e14\u4e0d\u540c\u7684\u90e8\u95e8\u91c7\u7528\u4e0d\u540c\u7684\u6a21\u578b\uff0cbezier\u66f2\u7ebf\uff0cB\u6837\u6761\u66f2\u7ebf\u7b49\u540c\u65f6\u5b58\u5728\uff0c\u6ce2\u97f3\u8feb\u5207\u9700\u8981\u5236\u5b9a\u4e00\u79cd\u7edf\u4e00\u7684\u6570\u5b66\u6a21\u578b\u7edf\u4e00\u516c\u53f8\u4e0a\u4e0b\u3002\u4e8e\u662f\u6210\u4e86\u4e00\u4e2a\u59d4\u5458\u4f1a\u3002\u8fd9\u4e2a\u59d4\u5458\u4f1a\u6700\u7ec8\u8bbe\u8ba1\u4e86\u4e00\u79cd\u6570\u5b66\u6a21\u578b\uff0c\u79f0\u4e4b\u4e3a\u975e\u5747\u5300\u6709\u7406B\u6837\u6761\uff08NURBS\uff09\u3002\u7edf\u4e00\u4e86\u6ce2\u97f3\u6240\u6709\u7684\u9700\u6c42\u3002\u5e76\u4e14\u5feb\u901f\u6210\u4e3aCAD\u6570\u636e\u4ea4\u6362\u7684\u5de5\u4e1a\u6807\u51c6\u3002<\/p>\n<p>\u867d\u7136\u5728\u822a\u7a7a\uff0c\u6c7d\u8f66\uff0c\u822a\u6d77\u4e0a\u5f97\u4ee5\u5e94\u7528\uff0c\u4f46\u662fNURBS\u5728\u8868\u8fbe\u590d\u6742\u81ea\u7136\u5f62\u72b6\u65b9\u9762\u4f1a\u906d\u9047\u62d3\u6251\u95ee\u9898\uff0cNURBS\u5f88\u96be\u8868\u8fbe\u590d\u6742\u7684\u62d3\u6251\u30021994\u5e74\uff0cPixar \u516c\u53f8\u51fa\u7248\u4e86\u8457\u540d\u7684\u300a\u73a9\u5177\u603b\u52a8\u5458\u300b\u5176\u4e2d\u7684\u5404\u79cd\u4eba\u7269\u4e0e\u9053\u5177\u90fd\u662f\u7531\u5f88\u591aNURBS\u66f2\u9762\u62fc\u63a5\u800c\u6210\u7684\u3002\u4f46\u662f\u8fd9\u79cd\u5904\u7406\u7279\u522b\u7684\u8d39\u65f6\u8d39\u529b\uff0c\u800c\u4e14\u5bb9\u6613\u53d1\u751f\u9519\u8bef\u3002\u56e0\u800c\u523097\u5e74\u300a\u68cb\u9022\u5bf9\u624b\u300b\u53d1\u5e03\u65f6\uff0cPixar\u5207\u6362\u5230\u4e86\u8868\u9762\u7ec6\u5206\uff08subdivision surfaces\uff09\u6280\u672f\u3002<\/p>\n<div id=\"attachment_458\" style=\"width: 398px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-458\" class=\"size-full wp-image-458\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2017\/12\/th.jpg\" alt=\"\" width=\"388\" height=\"160\" \/><p id=\"caption-attachment-458\" class=\"wp-caption-text\">subdivision surfaces<\/p><\/div>\n<p>\u4eceNURBS \u8f6c\u6362\u5230\u66f2\u9762\u7ec6\u5206\uff0c\u662f\u8bbe\u8ba1\u4e0e\u5b9e\u73b0\u7684\u5206\u79bb\u3002\u8bbe\u8ba1\u5e08\u4ecd\u7136\u5e0c\u671b\u4f7f\u7528NURBS\u826f\u597d\u7684\u63a7\u5236\u7279\u6027\uff0c\u4f46\u662f\u52a8\u753b\u6e32\u67d3\u4eba\u5458\u66f4\u5e0c\u671b\u7b80\u5355\u3001\u5bb9\u6613\u8ba1\u7b97\u7684\u6a21\u578b\u3002\u7eb5\u89c2NURBS\u7684\u53d1\u5c55\uff0c\u65e0\u975e\u662f\u6570\u5b66\u6a21\u578b\u4e0d\u65ad\u4e00\u822c\u5316\u7684\u8fc7\u7a0b\uff0c\u4ece\u5f00\u59cb\u7684bezier,\u5230B\u6837\u6761\uff0c\u518d\u5230\u65e0\u7406B\u6837\u6761\uff0c\u518d\u5230NURBS\uff0c\u6570\u5b66\u6a21\u578b\u7684\u6cdb\u5316\u80fd\u529b\u8d8a\u6765\u8d8a\u5f3a\u5927\u3002\u53d1\u5c55\u5230\u73b0\u5728\uff0cCAD\u9886\u57df\u6700\u91cd\u8981\u7684\u4efb\u52a1\u4e4b\u4e00\u5c31\u662f\u5efa\u7acb\u7ec6\u5206\u8868\u9762(subdivision surfaces)\u4e4b\u95f4\u7684\u6865\u6881\u3002<\/p>\n<div id=\"attachment_459\" style=\"width: 595px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-459\" class=\"wp-image-459 size-full\" src=\"http:\/\/www.whudj.cn\/wp-content\/uploads\/2017\/12\/14-Development-of-Computation-Spline-V4-585x304.png\" alt=\"\" width=\"585\" height=\"304\" \/><p id=\"caption-attachment-459\" class=\"wp-caption-text\">nurbs\u53d1\u5c55<\/p><\/div>\n<p>\u6700\u65b0\u7684\u8fdb\u5c55\u662fT-Splines\uff0c\u7531Autodesk\u5f15\u5165,T-Splines \u627f\u8bfa\u5c06\u7ec6\u5206\u8868\u9762\u7684\u9010\u6b65\u7ec6\u5316\u7684\u63a5\u53e3\u3001\u590d\u6742\u7684\u62d3\u6251\u5f62\u72b6\u4e0eNURBS\u66f2\u9762\u7684\u7cbe\u786e\u6027\u4e0e\u63a7\u5236\u529b\u8fdb\u884c\u826f\u597d\u7684\u878d\u5408\uff0c\u8ba9\u7528\u6237\u5177\u6709\u66f4\u9ad8\u7684\u7075\u6d3b\u6027\uff0c\u800c\u4e0d\u9700\u8981\u8003\u8651\u590d\u6742\u7684\u6280\u672f\u7ec6\u8282\u3002<\/p>\n<p>\u5230\u8fd9\u91cc\uff0cNURBS\u7684\u53d1\u5c55\u5386\u53f2\u57fa\u672c\u4e0a\u8bf4\u5b8c\u4e86\u3002\u53ef\u4ee5\u770b\u5230\uff0cnurbs\u4ece\u8fd1\u4ee3\u53d1\u5c55\u5230\u4eca\u5929\uff0c\u4f7f\u547d\u59cb\u7ec8\u90fd\u662f\u63d0\u4f9b\u4e00\u79cd\u76f4\u89c2\u7684\u6570\u5b66\u6a21\u578b\u548c\u64cd\u4f5c\u65b9\u5f0f\uff0c\u89e3\u51b3\u4eba\u4eec\u5728\u751f\u4ea7\u5b9e\u8df5\u4e2d\u7684\u95ee\u9898\u3002\u4f34\u968f\u7740\u8ba1\u7b97\u80fd\u529b\u7684\u65e5\u76ca\u589e\u957f\uff0cAR\/VR ,3D\u6253\u5370\u7b49\u6280\u672f\u7684\u4e0d\u65ad\u589e\u5f3a\uff0c\u5f00\u6e90\u8f6f\u4ef6\u89c4\u6a21\u7684\u4e0d\u65ad\u6269\u5927\uff0cNURBS\u6280\u672f\u5c06\u4f1a\u4e0d\u65ad\u5ef6\u4f38\u5230\u5404\u4e2a\u9886\u57df\u3002<\/p>\n<hr \/>\n<p>\u672c\u6587\u53c2\u8003\uff1a<\/p>\n<ol>\n<li><a href=\"http:\/\/pages.mtu.edu\/~shene\/COURSES\/cs3621\/NOTES\/\">Introduction to Computing with Geometry<\/a> \u7b2c\u516d\u7ae0\u7b2c\u4e00\u8282<\/li>\n<li><a href=\"https:\/\/www.rhino3d.com\/nurbs\">\u4ec0\u4e48\u662fNURBS?<\/a><\/li>\n<li><a href=\"http:\/\/web.cs.wpi.edu\/~matt\/courses\/cs563\/talks\/nurbs.html\">About Nonuniform Rational B-Splines &#8211; NURBS<\/a><\/li>\n<li><a href=\"http:\/\/www.alatown.com\/spline\/\">A Brief History of the Computational Curve<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u4e86\u89e3\u5b8c\u4e00\u79cd\u7279\u6b8a\u7684nurbs\u66f2\u7ebf\uff1a\u8d1d\u585e\u5c14\u66f2\u7ebf\u540e,\u4ece\u672c\u8282\u5f00\u59cb\uff0c\u6211\u5c06\u9010\u6b65\u4ecb\u7ecd\u975e\u5747\u5300\u6709\u7406 &hellip; <a href=\"http:\/\/www.whudj.cn\/?p=450\">Continue reading <span class=\"meta-nav\">&rarr;<\/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\/450"}],"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=450"}],"version-history":[{"count":7,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/450\/revisions"}],"predecessor-version":[{"id":463,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=\/wp\/v2\/posts\/450\/revisions\/463"}],"wp:attachment":[{"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=450"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=450"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.whudj.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=450"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}