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Computer","datePublished":"2023-06-07","dateModified":"2023-06-07","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d0\/Bezier_curve.svg\/250px-Bezier_curve.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d0\/Bezier_curve.svg\/250px-Bezier_curve.svg.png","height":"156","width":"250"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/12064","wordCount":12018,"articleBody":" 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1\u3064\u306e\u66f2\u7dda\u3067\u8907\u96d1\u306a\u5f62\u72b6\u3092\u63d0\u793a\u3059\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u65b0\u3057\u3044\u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u3092\u8ffd\u52a0\u3067\u304d\u308b\u3053\u3068\u306f\u4e8b\u5b9f\u3067\u3059\u304c\u3001\u3053\u308c\u306f\u30011\u3064\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u5909\u4f4d\u304c\u66f2\u7dda\u5168\u4f53\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u305f\u3081\u3001\u5f62\u72b6\u5236\u5fa1\u304c\u975e\u5e38\u306b\u56f0\u96e3\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u3055\u3089\u306b\u3001\u7a0b\u5ea6\u304c\u9ad8\u3044\u307b\u3069\u3001\u5236\u5fa1\u30dd\u30a4\u30f3\u30c8\u306e\u4f4d\u7f6e\u304c\u898b\u3048\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\uff08\u9bae\u3084\u304b\u306b\u3001\u9577\u8ddd\u96e2\u306b\u308f\u305f\u3063\u3066\u79fb\u52d5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u76ee\u306b\u898b\u3048\u308b\u52b9\u679c\u304c\u3042\u308a\u307e\u3059\uff09\u3002\u3053\u306e\u305f\u3081\u3001B\u3067\u6e80\u305f\u3055\u308c\u305f\u66f2\u7dda\u304c\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30ed\u30fc\u30ab\u30eb\u30b7\u30a7\u30a4\u30d7\u30b3\u30f3\u30c8\u30ed\u30fc\u30eb\u306e\u307f\u3092\u63d0\u4f9b\u3057\u30011\u3064\u306e\u5236\u5fa1\u30dd\u30a4\u30f3\u30c8\u306e\u5909\u4f4d\u306b\u3088\u308a\u5bc6\u63a5\u306a\u74b0\u5883\u304c\u5909\u5316\u3057\u307e\u3059\u3002 B\u3067\u6e80\u305f\u3055\u308c\u305f\u66f2\u7dda\u306f\u3001\u591a\u9805\u5f0f\u307e\u305f\u306f\u6e2c\u5b9a\u53ef\u80fd\u306a\uff08\u6bd4\u8f03\u7684\u4f4e\u3044\uff09\u66f2\u7dda\u306e\u65ad\u7247\u3067\u69cb\u6210\u3055\u308c\u308b\u66f2\u7dda\u3067\u3042\u308a\u3001\u305d\u306e\u3088\u3046\u306a\u66f2\u7dda\u3092\u8a18\u8ff0\u3059\u308b\u6570\u5b66\u7684\u65b9\u7a0b\u5f0f\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u30d5\u30e9\u30b0\u30e1\u30f3\u30c8\u306e\u63a5\u7d9a\u30dd\u30a4\u30f3\u30c8\u3067\u66f2\u7dda\u304c\u6ed1\u3089\u304b\u306b\u306a\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002 Nurbs\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u3068B\u3067\u6e80\u305f\u3055\u308c\u305f\u8868\u9762\u306f\u3001\u7279\u5225\u306a\u4eba\u6c17\u3092\u535a\u3057\u307e\u3057\u305f\u3002 Table of Contents       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Multi -Curvey [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] 3\u5ea6\u76ee\u306eMulti -Multi Krzywe [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d9\u30b8\u30a8\u306e\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] B\u3067\u6e80\u305f\u3055\u308c\u305f\u66f2\u7dda [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] Multi -Curvey [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30c7\u30fc\u30bf\u306f\u3067\u3059 \u5236\u5fa1\u30dd\u30a4\u30f3\u30c8  p 0 \u3001 … \u3001 p n {displaystyle p_ {0}\u3001dots\u3001p_ {n}} \u6570 n + \u521d\u3081\u3002 {displaystyle n+1\u3002}  \u30d9\u30b8\u30a8\u66f2\u7dda\u306e\u5f62\u72b6\u306f\u3001\u30d5\u30a3\u30fc\u30eb\u30c9\u304c\u63a1\u7528\u3055\u308c\u305f\u591a\u9805\u5f0f\u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u3066\u3044\u307e\u3059 [ 0 \u3001 \u521d\u3081 ] \u3002 {displaystyle [0.1]\u3002} \u591a\u9805\u5f0f\u306e\u7a0b\u5ea6\u306f\u3001\u30b3\u30f3\u30c8\u30ed\u30fc\u30eb\u30dd\u30a4\u30f3\u30c8\u306e\u6570\u306b\u76f4\u63a5\u4f9d\u5b58\u3057\u307e\u3059 – \u305d\u308c\u306f n {displaystyle n} \uff08\u30b3\u30f3\u30c8\u30ed\u30fc\u30eb\u30dd\u30a4\u30f3\u30c8\u6570\u3092\u5f15\u3044\u305f\u3082\u306e\uff09\u3002\u30de\u30eb\u30c1\u30b9\u30c8\u306f\u901a\u5e38\u200b\u200b\u3001\u30d0\u30fc\u30f3\u30b9\u30bf\u30a4\u30f3\u591a\u9805\u5f0f\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u306b\u63d0\u793a\u3055\u308c\u307e\u3059 [\u521d\u3081] \uff08\u30de\u30fc\u30af\u3055\u308c\u3066\u3044\u307e\u3059 b \u79c1 n \uff08 t \uff09\uff09 \u3001 {displaystyle b_ {i}^{n}\uff08t\uff09\u3001} \u82f1\u6587\u5b66\u306b\u643a\u308f\u308b b \u79c1 \u3001 j \uff08 t \uff09\uff09 {displaystyle b_ {i\u3001j}\uff08t\uff09} \uff09\u3002\u30d0\u30fc\u30f3\u30b9\u30bf\u30a4\u30f3\u30d9\u30fc\u30b9\u306e\u591a\u9805\u5f0f\u306f\u3001\u5236\u5fa1\u30dd\u30a4\u30f3\u30c8\u304c\u5f53\u7136\u3001\u305d\u306e\u3088\u3046\u306a\u591a\u9805\u5f0f\u306e\u4fc2\u6570\u3067\u3042\u308b\u3068\u3044\u3046\u610f\u5473\u3067\u4fbf\u5229\u3067\u3059 – \u8ffd\u52a0\u306e\u5909\u63db\u3092\u884c\u3046\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u66f2\u7dda\u4e0a\u306e\u4efb\u610f\u306e\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u4f9d\u5b58\u95a2\u4fc2\u306b\u3088\u3063\u3066\u8aac\u660e\u3055\u308c\u307e\u3059\u3002 p \uff08 t \uff09\uff09 = \u2211 i=0np ib in\uff08 t \uff09\uff09 dla\u00a0t \u2208 [ 0 \u3001 \u521d\u3081 ] \u3001 {displaystyle p\uff08t\uff09= sum _ {i = 0}^{n} p_ {i} b_ {i}^{n}\uff08t\uff09quad {textrm {dla}} tin [0,1]\u3001} \u305f\u3068\u3048\u3070\u30012\u6b21\u5143\u66f2\u7dda\u306f\u3001\u4e00\u5bfe\u306e\u591a\u9805\u5f0f\u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u307e\u3059\u3002 \uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 \u2211i=0nxiBin(t),\u2211i=0nyiBin(t)\uff09\uff09 \u3002 {displaystyle\uff08x\u3001y\uff09= left\uff08sum _ {i = 0}^{n} x_ {i} b_ {i}^{n}\uff08t\uff09\u3001sum _ {i = 0}^{n} y_ {i} b_ {i}^{n}\uff08t\uff09right\uff09\u3002} \u70b9 p \uff08 t \uff09\uff09 {displaystyle P\uff08t\uff09} De Casteljau\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4f7f\u7528\u3082\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002  \u305d\u308c\u3092\u4f5c\u6210\u3059\u308b2\u6b21\u5143\u30d9\u30b8\u30a84\u5ea6\u304a\u3088\u3073\u591a\u9805\u5f0fX\uff08T\uff09\u304a\u3088\u3073Y\uff08T\uff09\u306e\u4f8b\u3002\u30b3\u30f3\u30c8\u30ed\u30fc\u30eb\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u30d0\u30fc\u30f3\u30b9\u30bf\u30a4\u30f3\u30d9\u30fc\u30b9\u306e\u591a\u9805\u5f0f\u306e\u9752\u3067\u7070\u8272\u306e\u30c1\u30e3\u30fc\u30c8\u3067\u30de\u30fc\u30af\u3055\u308c\u3066\u3044\u307e\u3059\u3002 B\u00e9zier\u306e\u30de\u30eb\u30c1\u30b3\u30a2\u66f2\u7dda\u306e\u7279\u6027\uff1a \u66f2\u7dda\u306f\u3001\u6975\u7aef\u306a\u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u3092\u30a4\u30f3\u30bf\u30fc\u30dd\u30fc\u30eb\u3057\u307e\u3059\uff08\u3064\u307e\u308a\u3001 p \uff08 0 \uff09\uff09 = p 0{displaystyle p\uff080\uff09= p_ {0}} \u79c1 p \uff08 \u521d\u3081 \uff09\uff09 = p n{displaystyle P\uff081\uff09= p_ {n}} \uff09\u3001\u305d\u3057\u3066\u4ed6\u306e\u4eba\u3092\u8fd1\u3065\u3051\u307e\u3059\u3002 \u66f2\u7dda\u306f\u6240\u6709\u3055\u308c\u3066\u3044\u307e\u3059 \u51f8\u30b7\u30a7\u30eb \u3001\u3059\u306a\u308f\u3061 t \u2208 [ 0 \u3001 \u521d\u3081 ] {displaystyletin [0,1]} \u70b9 p \uff08 t \uff09\uff09 {displaystyle P\uff08t\uff09} \u5236\u5fa1\u70b9\u306e\u51f8\u30a8\u30f3\u30d9\u30ed\u30fc\u30d7\u306b\u3042\u308a\u307e\u3059 p 0\u3001 … \u3001 p n{displaystyle p_ {0}\u3001dots\u3001p_ {n}} [3] \u3002 \u66f2\u7dda\u306e\u69cb\u9020\u306f\u3001\u30a2\u30d4\u30cb\u30ab\u30eb\u5909\u63db\u3068\u6bd4\u8f03\u3057\u3066\u5909\u5316\u3057\u307e\u305b\u3093\u3002\u3064\u307e\u308a\u3001\u5909\u63db\u3055\u308c\u305f\u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u304b\u3089\u6c7a\u5b9a\u3055\u308c\u308b\u66f2\u7dda\u306f\u3001\u3053\u306e\u5909\u63db\u5f8c\u306e\u66f2\u7dda\u3068\u540c\u3058\u3067\u3059\u3002 \u5358\u4e00\u306e\u66f2\u7dda\u304c\u3042\u308a\u307e\u3059 \u7121\u9650\u306b\u591a\u3044 \u8868\u73fe – \u8aac\u660e\u3055\u308c\u3066\u3044\u308b\u66f2\u7dda\u306e\u5834\u5408 n {displaystyle n} \u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u6570\u5b57\u306e\u3053\u306e\u3088\u3046\u306a\u4e00\u9023\u306e\u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u306b\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059 n + k {displaystyle n+k}  \uff08 k = \u521d\u3081 \u3001 … \uff09\uff09 \u3001 {displaystyle\uff08k = 1\u3001dots\uff09\u3001} \u307e\u3063\u305f\u304f\u540c\u3058\u66f2\u7dda\u3092\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u8ffd\u52a0\u306e\u30dd\u30a4\u30f3\u30c8\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306e\u3053\u306e\u624b\u9806\u306f\u547c\u3073\u51fa\u3055\u308c\u307e\u3059 \u5b66\u4f4d\u3092\u4e0a\u3052\u308b \uff08 \u5ea6\u306e\u9ad8\u3055 \uff09\u3002\u305f\u3060\u3057\u3001\u5b9f\u969b\u306b\u306f\u3001\u66f2\u7dda\u306f\u53ef\u80fd\u306a\u9650\u308a\u4f4e\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u304c\u3001\u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u306e\u6570\u3092\u5897\u3084\u3059\u3068\u3001\u3055\u307e\u3056\u307e\u306a\u66f2\u7dda\u9593\u3067\u5909\u63db\u3055\u308c\u307e\u3059\u3002 B\u00e9zier\u306e\u591a\u9805\u5f0f\u66f2\u7dda\u306e\u6b20\u70b9\u306f\u3001\u305d\u308c\u3089\u3092\u4f7f\u7528\u3057\u3066\u5186\u9310\u66f2\u7dda\u3001\u5730\u533a\u3001\u6955\u5186\u306a\u3069\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u6b20\u9665\u306b\u306f\u3001\u6e2c\u5b9a\u53ef\u80fd\u306aB\u00e9zier\u66f2\u7dda\u304c\u596a\u308f\u308c\u3066\u3044\u307e\u3059\u3002 3\u5ea6\u76ee\u306eMulti -Multi Krzywe [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  3\u5ea6\u76ee\u306e\u30d9\u30b8\u30a8\u66f2\u7dda \u98db\u884c\u6a5f\u306b\u6a2a\u305f\u308f\u3063\u3066\u3044\u308b3\u5ea6\u76ee\u306e\u66f2\u7dda\u304c\u6700\u3082\u983b\u7e41\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 3\u5ea6\u76ee\u306e\u66f2\u7dda\u3092\u5b9a\u7fa9\u3059\u308b\u3068\u30014\u30dd\u30a4\u30f3\u30c8\u304c\u6c7a\u5b9a\u3055\u308c\u307e\u3059 a \u3001 {displaystyle a\u3001}  b \u3001 {displaystyle b\u3001}  c {displaystyle c} \u79c1 d {displaystyle d} \uff08\u305d\u308c\u306b\u5fdc\u3058\u3066\u56f3\u3067 p 0 \u3001 p \u521d\u3081 \u3001 p 2 \u3001 p 3 {displaystyle p_ {0}\u3001p_ {1}\u3001p_ {2}\u3001p_ {3}} \uff09\u305d\u306e\u5834\u6240\u304c\u66f2\u7dda\u306e\u7d4c\u904e\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002\u66f2\u7dda\u306f\u30dd\u30a4\u30f3\u30c8\u304b\u3089\u59cb\u307e\u308a\u307e\u3059 a {displaystyle a} \u30dd\u30a4\u30f3\u30c8\u306b\u5411\u3051\u3089\u308c\u3066\u3044\u307e\u3059 b \u3002 {displaystyle B.} \u305d\u308c\u304b\u3089\u5f7c\u306f\u30dd\u30a4\u30f3\u30c8\u306b\u5411\u304b\u3063\u3066\u3044\u307e\u3059 d {displaystyle d} \u30dd\u30a4\u30f3\u30c8\u306e\u30dd\u30a4\u30f3\u30c8\u304b\u3089\u5230\u9054\u3057\u307e\u3059 c \u3002 {displaystyle C.} \u30a8\u30d4\u30bd\u30fc\u30c9 AB\u00af {displaystyle {overline {ab}}} \u30dd\u30a4\u30f3\u30c8\u306e\u66f2\u7dda\u306b\u63a5\u3059\u308b a \u3001 {displaystyle a\u3001} \u30a8\u30d4\u30bd\u30fc\u30c9\u4e2d CD\u00af {displaystyle {overline {cd}}} \u30dd\u30a4\u30f3\u30c8\u3067\u306f\u63a5\u7dda\u3067\u3059 d {displaystyle d}  3\u5ea6\u76ee\u306e\u30d9\u30b8\u30a8\u66f2\u7dda\u306f\u3001\u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002 p \uff08 t \uff09\uff09 = a \uff08 \u521d\u3081  –  t \uff09\uff09 3+ 3 b t \uff08 \u521d\u3081  –  t \uff09\uff09 2+ 3 c t 2\uff08 \u521d\u3081  –  t \uff09\uff09 + d t 3{displaystyle p\uff08t\uff09= a\uff081-t\uff09^{3}+3bt\uff081-t\uff09^{2}+3ct^{2}\uff081-t\uff09+dt^{3} quad {}} \u305f\u3081\u306b 0 \u2a7d t \u2a7d \u521d\u3081 \u3001 {displaystyle 0leqslant tleqslant 1\u3001} \u3042\u308c\u306f\uff1a p x\uff08 t \uff09\uff09 = a x\uff08 \u521d\u3081  –  t \uff09\uff09 3+ 3 b xt \uff08 \u521d\u3081  –  t \uff09\uff09 2+ 3 c xt 2\uff08 \u521d\u3081  –  t \uff09\uff09 + d xt 3\u3001 {displaystyle p_ {x}\uff08t\uff09= a_ {x}\uff081-t\uff09^{3}+3b_ {x} t\uff081-t\uff09^{2}+3c_ {x} t^{2}\uff081-t\uff09+d_ {x} t^{3}\u3001}\u3001} p y\uff08 t \uff09\uff09 = a y\uff08 \u521d\u3081  –  t \uff09\uff09 3+ 3 b yt \uff08 \u521d\u3081  –  t \uff09\uff09 2+ 3 c yt 2\uff08 \u521d\u3081  –  t \uff09\uff09 + d yt 3\u3002 {displaystyle p_ {y}\uff08t\uff09= a_ {y}\uff081-t\uff09^{3}+3b_ {y} t\uff081-t\uff09^{2}+3c_ {y} t^{2}\uff081-t\uff09+d_ {y} t^{3}\u3002}\u3002 \u4ee3\u66ff\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u9332\u97f3\uff1a p \uff08 t \uff09\uff09 = [ A,B,C,D] de [ \u221213\u2212313\u2212630\u221233001000] de [ t3t2t1] \u3002 {displaystyle P\uff08t\uff09= left [a\u3001b\u3001c\u3001dright] cdot left [{begin} -1\uff063\uff06-3\uff061 \\ 3\uff06-6\uff063\uff060 \\ -3\uff063\uff060\uff060 \\ 1\uff060\uff060\uff060\uff060END {matrix}}\u53f3] {matrix}}\u53f3]\u3002} \u66f2\u7dda\u306f\u30dd\u30a4\u30f3\u30c8\u304b\u3089\u59cb\u307e\u308a\u307e\u3059 a {displaystyle a}  \uff08 t = 0 \uff09\uff09 {displaystyle\uff08t = 0\uff09} \u305d\u3057\u3066\u3001\u30dd\u30a4\u30f3\u30c8\u3067\u306e\u7d42\u308f\u308a d {displaystyle d}  \uff08 t = \u521d\u3081 \uff09\uff09 \u3002 {displaystyle\uff08t = 1\uff09\u3002}  3\u5ea6\u76ee\u306e\u30d9\u30b8\u30a8\u66f2\u7dda\u306f\u3001\u6b21\u306e\u65b9\u7a0b\u5f0f\u30b7\u30b9\u30c6\u30e0\u3067\u3082\u8aac\u660e\u3067\u304d\u307e\u3059\u3002 a = \uff08 \u30d0\u30c4 0 \u3001 \u3068 0 \uff09\uff09 \u3001 b = \uff08 \u30d0\u30c4 \u521d\u3081 \u3001 \u3068 \u521d\u3081 \uff09\uff09 \u3001 c = \uff08 \u30d0\u30c4 2 \u3001 \u3068 2 \uff09\uff09 \u3001 d = \uff08 \u30d0\u30c4 3 \u3001 \u3068 3 \uff09\uff09 \uff1a {Displaystyle a = (x_ {0}, y_ {0}), b = (x_ {1}, y_ {1}), c = (x_ {2}, y_ {2}), d = (x_ {3}, y_ {3}) {:}}}}}}}}}}}}}}}}}}}}}}}}}}  \u30d0\u30c4 (t)= a xt 3+ b xt 2+ c xt + \u30d0\u30c4 0\u3001 {displaystyle x _ {\uff08t\uff09} = a_ {x} t^{3}+b_ {x} t^{2}+c_ {x} t+x_ {0}\u3001} x1=x0+cx3,{displaystyle x_ {1} = x_ {0}+{frac {c_ {x}} {3}}\u3001} x2=x1+cx+bx3,{displaystyle x_ {2} = x_ {1}+{frac {c_ {x}+b_ {x}} {3}}\u3001} x3=x0+cx+bx+ax,{displaystyle x_ {3} = x_ {0}+c_ {x}+b_ {x}+a_ {x}\u3001} \u3068 (t)= a yt 3+ b yt 2+ c yt + \u3068 0\u3001 {displaystyle y _ {\uff08t\uff09} = a_ {y} t^{3}+b_ {y} t^{2}+c_ {y} t+y_ {0}\u3001} y1=y0+cy3,{displaystyle y_ {1} = y_ {0}+{craud {c_ {y}} {3}}\u3001} y2=y1+cy+by3,{displaystyle y_ {2} = y_ {1}+{craud {c_ {y}+b_ {y}} {3}}\u3001} y3=y0+cy+by+ay.{displaystyle y_ {3} = y_ {0}+c_ {y}+b_ {y}+a_ {y}\u3002} \u3053\u306e\u65b9\u6cd5\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u8a2d\u8a08\u306f\u3001\u65b9\u5411\u5909\u6570\u3092\u53d6\u5f97\u3059\u308b\u305f\u3081\u306b\u9006\u8ee2\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff08\u5404\u30d9\u30b8\u30a8\u66f2\u7dda\u3067\u306f\u4e00\u5b9a\u3067\u3059\uff09\uff1a c x= 3 \uff08 \u30d0\u30c4 1 –  \u30d0\u30c4 0\uff09\uff09 \u3001 {displaystyle c_ {x} = 3\uff08x_ {1} -x_ {0}\uff09\u3001} b x= 3 \uff08 \u30d0\u30c4 2 –  \u30d0\u30c4 1\uff09\uff09  –  c x\u3001 {displaystyle b_ {x} = 3\uff08x_ {2} -x_ {1}\uff09 –  c_ {x}\u3001} a x= \u30d0\u30c4 3 –  \u30d0\u30c4 0 –  c x –  b x\u3001 {displaystyle a_ {x} = x_ {3} -x_ {0} -c_ {x} -b_ {x}\u3001} c y= 3 \uff08 \u3068 1 –  \u3068 0\uff09\uff09 \u3001 {displaystyle c_ {y} = 3\uff08y_ {1} -y_ {0}\uff09\u3001} b y= 3 \uff08 \u3068 2 –  \u3068 1\uff09\uff09  –  c y\u3001 {displaystyle b_ {y} = 3\uff08y_ {2} -y_ {1}\uff09 –  c_ {y}\u3001} a y= \u3068 3 –  \u3068 0 –  c y –  b y\u3002 {displaystyle a_ {y} = y_ {3} -y_ {0} -c_ {y} -b_ {y}\u3002} \u30d9\u30b8\u30a8\u306e\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u5225\u306e\u8a18\u4e8b\uff1a\u30d9\u30b8\u30a8\u306e\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u3002  \u30d9\u30b8\u30a8\u306e\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u306f\u3001\u5e73\u9762\u3078\u306e\u5747\u4e00\u306a\u5ea7\u6a19\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u30d9\u30b8\u30a8\u306e\u30de\u30eb\u30c1\u30b3\u30a2\u66f2\u7dda\u306e\u4e2d\u592e\u6295\u5f71\u3067\u3059 \u306e = \u521d\u3081\u3002 {distrastaStyle w = 1.} \u540c\u3058\u3053\u3068\u304c\u4e0e\u3048\u3089\u308c\u307e\u3059 n + \u521d\u3081 {displaystyle n+1} \u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u3002 \u30b9\u30da\u30fc\u30b9\u304c\u5747\u4e00\u3067\u3042\u308b\u5834\u5408 k + \u521d\u3081 {displaystyle k+1} -inmia\u3001\u305d\u306e\u5f8c\u3001\u66f2\u7dda\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u975e\u5e38\u306b\u591a\u304f\u306e\u591a\u9805\u5f0f\u304c\u5fc5\u8981\u3067\u3059\u3002\u591a\u9805\u5f0f\u66f2\u7dda\u306e\u4efb\u610f\u306e\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059 p \uff08 t \uff09\uff09 = \uff08 \u30d0\u30c4 \uff08 t \uff09\uff09 \u3001 \u3068 \uff08 t \uff09\uff09 \u3001 … \u3001 \u306e \uff08 t \uff09\uff09 \uff09\uff09 \u3002 {displaystyle P\uff08t\uff09=\uff08x\uff08t\uff09\u3001y\uff08t\uff09\u3001dots\u3001w\uff08t\uff09\uff09\u3002} \u30c7\u30ab\u30eb\u30c8\u5ea7\u6a19\u306b\u5207\u308a\u66ff\u3048\u305f\u5f8c\uff08\u30df\u30c9\u30eb\u30ad\u30c3\u30af p \uff08 t \uff09\uff09 {displaystyle P\uff08t\uff09} \u98db\u884c\u6a5f\u306b \u306e = \u521d\u3081 {\u5c55\u793aw = 1} \uff09\uff09 k {displaystyle k} \u6e2c\u5b9a\u53ef\u80fd\u306a\u8868\u73fe\u3001\u304a\u3088\u3073\u3053\u306e\u5e73\u9762\u4e0a\u306e\u30dd\u30a4\u30f3\u30c8\u306b\u30e2\u30c7\u30eb\u304c\u4e0e\u3048\u3089\u308c\u307e\u3059 p \uff08 t \uff09\uff09 = \uff08 X(t)W(t)\u3001 Y(t)W(t)\u3001 … \uff09\uff09 \u3002 {displaystyle P\uff08t\uff09= left\uff08{frac {x\uff08t\uff09} {w\uff08t\uff09}}}\u3001{frac {y\uff08t\uff09} {w\uff08t\uff09}}\u3001dots\u53f3\uff09\u3002}}  \u3082\u3057\u3082 \u306e \uff08 t \uff09\uff09 = const {displaystyle w\uff08t\uff09= {textrm {const}}} \u305d\u308c\u306f\u591a\u9805\u5f0f\u3067\u3042\u308b\u66f2\u7dda\u3067\u3059 – \u975e\u516c\u5f0f\u306b\u8a00\u3048\u3070\u3001\u591a\u9805\u5f0f\u66f2\u7dda\u306f\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002 \u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u306e\u4efb\u610f\u306e\u30dd\u30a4\u30f3\u30c8\u306b\u306f\u3001\u30d1\u30bf\u30fc\u30f3\u304c\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 p \uff08 t \uff09\uff09 = \u2211i=0nwipiBin(t)\u2211i=0nwiBin(t)t \u2208 [ 0 \u3001 \u521d\u3081 ] \u3001 {displaystyle p(t)={frac {sum _{i=0}^{n}w_{i}p_{i}B_{i}^{n}(t)}{sum _{i=0}^{n}w_{i}B_{i}^{n}(t)}}qquad tin [0,1],} \u3069\u3053 \u306e \u79c1 {displaystylew_ {i}} \u3053\u308c\u306f\u5ea7\u6a19\u3067\u3059\u304c\u3001\u3088\u308a\u591a\u304f\u306e\u5834\u5408\u3001\u5236\u5fa1\u70b9\u306e\u5236\u5fa1\u3068\u547c\u3070\u308c\u307e\u3059\u3002 \u66f2\u7dda\u4e0a\u306e\u30dd\u30a4\u30f3\u30c8\u3092\u6307\u5b9a\u3059\u308b\u306b\u306f\u3001De Casteljau\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u307e\u305f\u306f\u6e2c\u5b9a\u53ef\u80fd\u307e\u305f\u306f\u591a\u9805\u5f0f\u66f2\u7dda\u306e\u305f\u3081\u306b\u30d0\u30ea\u30a2\u30f3\u30c8\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 B\u00e9zier\u306e\u591a\u9805\u5f0f\u66f2\u7dda\u306e\u5229\u70b9\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u3053\u308c\u3089\u306f\u3059\u3079\u3066\u306e\u5186\u9310\u66f2\u7dda\u3092\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001CAD\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u91cd\u8981\u3067\u3059\u3002 \u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u306e\u8996\u70b9\u6295\u5f71\u306f\u5e38\u306b\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u3067\u3059\u304c\u3001\u591a\u9805\u5f0f\u66f2\u7dda\u306e\u8996\u70b9\u6295\u5f71\u306f\u591a\u9805\u5f0f\u66f2\u7dda\u3067\u3042\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u3067\u91cd\u8981\u3067\u3059\u3002 \u30b9\u30b1\u30fc\u30eb \u306e i{displaystylew_ {i}} \u305d\u308c\u3089\u306f\u3001\u66f2\u7dda\u306e\u5f62\u72b6\u3092\u3088\u308a\u3088\u304f\u5236\u5fa1\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002 B\u3067\u6e80\u305f\u3055\u308c\u305f\u66f2\u7dda [ \u7de8\u96c6 | \u30b3\u30fc\u30c9\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u5225\u306e\u8a18\u4e8b\uff1aB-Shot Curve\u3002 b\u30b9\u30bf\u30c3\u30af\u66f2\u7dda\u306f\u3001\u901a\u5e38\u306f\u4f4e\u3044\u591a\u9805\u5f0f\u307e\u305f\u306f\u6e2c\u5b9a\u53ef\u80fd\u306a\u30d9\u30b8\u30a8\u66f2\u7dda\u306e\u65ad\u7247\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059 \uff08 n \uff09\uff09 \u3002 {displaystyle\uff08n\uff09\u3002} B\u3067\u8986\u308f\u308c\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc t {displaystylet} \u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u306b\u3082\u5c5e\u3057\u307e\u3059 [ 0 \u3001 \u521d\u3081 ] \u3002 {displaystyle [0.1]\u3002} \u3053\u306e\u30b3\u30f3\u30d1\u30fc\u30c8\u30e1\u30f3\u30c8\u306f\u30b5\u30dd\u30fc\u30c8\u306b\u5206\u5272\u3055\u308c\u3066\u304a\u308a\u3001\u5883\u754c\u7dda\u3092\u6307\u5b9a\u3059\u308b\u6570\u5b57\u306f\u30ce\u30fc\u30c9\u3068\u547c\u3070\u308c\u307e\u3059\u3002 \u7d50\u3073\u76ee \uff09\u3002\u5f8c\u7d9a\u306e\u30ce\u30fc\u30c9\u306f\u5747\u7b49\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u7a7a\u306e\u30b5\u30dd\u30fc\u30c8\u3092\u4f5c\u6210\u3057\u307e\u3059 – \u3053\u308c\u306f\u9593\u9055\u3044\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u30ce\u30fc\u30c9\u304c\u3042\u308b\u5834\u5408 m + \u521d\u3081 {displaystyle m+1}  \uff08 \u306e 0 \u3001 … \u3001 \u306e m \uff09\uff09 \u3001 {displaystyle\uff08u_ {0}\u3001dots\u3001u_ {m}\uff09\u3001} \u305d\u3057\u3066\u3001\u591a\u9805\u5f0f\u306e\u7a0b\u5ea6\u306f\u7b49\u3057\u3044 n \u3001 {displaystyle n\u3001} \u3053\u308c\u306f\u3001\u66f2\u7dda\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u3067\u3059 m  –  n {displaystyle m-n} \u30c1\u30a7\u30c3\u30af\u30dd\u30a4\u30f3\u30c8\u3001\u304a\u3088\u3073\u5168\u4f53\u3092\u69cb\u6210\u3059\u308b\u66f2\u7dda\u306e\u6570\u306f m  –  2 n \u3002 {displaystyle m-2n\u3002} \u63a5\u7740\u66f2\u7dda\u306f\u7bc4\u56f2\u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059 [ \u306e n \u3001 \u306e m  –  n ] \u3001 {displaystyle [u_ {n}\u3001u_ {m-n}]\u3001} \u30aa\u30f3\u3067\u306f\u3042\u308a\u307e\u305b\u3093 [ 0 \u3001 \u521d\u3081 ] \u3002 {displaystyle [0.1]\u3002}  B-Zlajana\u66f2\u7dda\u306e\u4efb\u610f\u306e\u30dd\u30a4\u30f3\u30c8\u306f\u3001Mansfield-de boora-cox\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u8d77\u56e0\u3059\u308b\u7279\u5b9a\u306e\u30d1\u30bf\u30fc\u30f3\u3067\u3059\u3002 p \uff08 t \uff09\uff09 = \u2211 i=0m\u2212n\u22121p in in\uff08 t \uff09\uff09 dla\u00a0t \u2208 [ \u306e n\u3001 \u306e m\u2212n] \u3001 {displaystyle p\uff08t\uff09= sum _ {i = 0}^{m-n-1} p_ {i} n_ {i}^{n}\uff08t\uff09quad {textrm {dla}} tin [u_ {n}\u3001u_ {m n}]\u3001}} \u3069\u3053 n \u79c1 n {displaystyle n_ {i}^{n}} \u306b \u30ca\u30f3\u30c8B\u30b9\u30ea\u30fc\u30d7\u6a5f\u80fd \u7a0b\u5ea6 n \u3002 {displaystyle n\u3002}  B\u3067\u6e80\u305f\u3055\u308c\u305f\u66f2\u7dda\u306b\u306f\u3001\u591a\u9805\u5f0f\u304a\u3088\u3073\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u306b\u95a2\u9023\u3059\u308b\u4ee5\u4e0b\u306e\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\u3002 \u30ed\u30fc\u30ab\u30eb\u30b7\u30a7\u30a4\u30d7\u30b3\u30f3\u30c8\u30ed\u30fc\u30eb  –  1\u3064\u306e\u5236\u5fa1\u70b9\u306e\u52d5\u304d\u306f\u3001\u305b\u3044\u305c\u3044\u3053\u306e\u70b9\u306e\u5c0f\u3055\u306a\u74b0\u5883\u306b\u5f71\u97ff\u3057\u307e\u3059 n {displaystyle n} \u96a3\u63a5\u3059\u308b\u66f2\u7dda\u3002 \u30ce\u30fc\u30c9\u3092\u914d\u7f6e\u3059\u308b\u53ef\u80fd\u6027\u306f\u3001\u66f2\u7dda\u306e\u5f62\u72b6\u3092\u3088\u308a\u826f\u304f\u3088\u308a\u5f37\u529b\u306b\u5236\u5fa1\u3067\u304d\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30ce\u30fc\u30c9\u304c\u4e00\u81f4\u3059\u308b\u5834\u5408\u3001\u3064\u307e\u308a\u7a7a\u306e\u30b5\u30dd\u30fc\u30c8\u304c\u3042\u308b\u5834\u5408\u3001\u300c\u30b7\u30e3\u30fc\u30d7\u300d\uff08\u6ed1\u3089\u304b\u3067\u306f\u306a\u3044\uff09\u63a5\u7d9a\u304c\u53d6\u5f97\u3055\u308c\u307e\u3059\u3002 \u65b0\u3057\u3044\u30ce\u30fc\u30c9\u3092\u7c21\u5358\u306b\u633f\u5165\u3067\u304d\u307e\u3059\u3002 \u30ce\u30c3\u30c8\u633f\u5165 \uff09\u3001\u30e2\u30c7\u30ea\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9\u306e\u304a\u304b\u3052\u3067\u7c21\u5358\u3067\u3059\u3002 Tubility B\u6e80\u305f\u3055\u308c\u305f\u66f2\u7dda\uff08NURB\uff09\u306f\u3001\u901a\u5e38\u306e\u6e2c\u5b9a\u53ef\u80fd\u306a\u66f2\u7dda\u3068\u4e0a\u8a18\u306e\u4e0a\u8a18\u306e\u5229\u70b9\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3001\u7279\u5225\u306a\u91cd\u8981\u6027\u3068\u4eba\u6c17\u3092\u7372\u5f97\u3057\u307e\u3057\u305f\u3002 \u30b8\u30a7\u30fc\u30e0\u30bad J.D.  \u30d5\u30a9\u30fc\u30ea\u30fc  \u30b8\u30a7\u30fc\u30e0\u30bad J.D. \u79c1\u306f\u30a4\u30cb \u3001 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u306e\u7d39\u4ecb \u3001 1\u6708 J.  Zabrodzki \uff08\u7ffb\u8a33\uff09\u3001\u30ef\u30eb\u30b7\u30e3\u30ef\uff1awydawnictwo naukowo-techniczne\u30011995\u3001isbn 83-204-1840-2  \u3002 \u30de\u30a4\u30b1\u30eb M.  \u30e4\u30f3\u30b3\u30d5\u30b9\u30ad\u30fc  \u30de\u30a4\u30b1\u30eb M. \u3001 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u8981\u7d20 \u3001\u30ef\u30eb\u30b7\u30e3\u30ef\uff1awydawnictwo naukowo-techniczne\u30011990\u3001isbn 83-204-1326-5  \u3002 Przemys\u0142aw P.  \u30ad\u30b7\u30a2\u30c3\u30af  Przemys\u0142aw P. \u3001 \u786c\u5316\u3068\u8868\u9762\u30e2\u30c7\u30ea\u30f3\u30b0\u306e\u57fa\u672c\uff1a\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u3067\u306e\u4f7f\u7528 \u3001\u30ef\u30eb\u30b7\u30e3\u30ef\uff1awydawnictwo naukowo-techniczne\u30012000\u3001isbn 83-204-2464-X  \u3002      (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/12064#breadcrumbitem","name":"B\u00e9zieraKrzywa-\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178"}}]}]