{"id":118828,"date":"2025-10-08T07:35:23","date_gmt":"2025-10-07T22:35:23","guid":{"rendered":"https:\/\/adtechmanagement.com\/minnadepr-column\/?p=118828"},"modified":"2025-10-08T07:35:23","modified_gmt":"2025-10-07T22:35:23","slug":"normal-vector-meaning","status":"publish","type":"post","link":"https:\/\/adtechmanagement.com\/minnadepr-column\/2025\/10\/08\/normal-vector-meaning\/","title":{"rendered":"\u6cd5\u7dda\u3068\u306f\uff1f\u610f\u5473\u30fb\u6570\u5b66\u30fb\u7269\u7406\u3067\u306e\u4f7f\u3044\u65b9\u3068\u5fdc\u7528\u3092\u308f\u304b\u308a\u3084\u3059\u304f\u89e3\u8aac"},"content":{"rendered":"<p>\u6cd5\u7dda\uff08\u307b\u3046\u305b\u3093\uff09\u306f\u3001\u6570\u5b66\u3084\u7269\u7406\u3001\u5de5\u5b66\u306e\u5206\u91ce\u3067\u975e\u5e38\u306b\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3059\u3002\u65e5\u5e38\u751f\u6d3b\u3067\u306f\u3042\u307e\u308a\u8033\u306b\u3057\u306a\u3044\u8a00\u8449\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u7269\u4f53\u306e\u8868\u9762\u3084\u66f2\u9762\u306e\u7279\u5fb4\u3092\u7406\u89e3\u3059\u308b\u4e0a\u3067\u6b20\u304b\u305b\u307e\u305b\u3093\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u6cd5\u7dda\u306e\u57fa\u672c\u7684\u306a\u610f\u5473\u304b\u3089\u6570\u5b66\u7684\u5b9a\u7fa9\u3001\u7269\u7406\u3084\u5de5\u5b66\u3067\u306e\u5fdc\u7528\u3001\u8a08\u7b97\u65b9\u6cd5\u3084\u6ce8\u610f\u70b9\u307e\u3067\u5e45\u5e83\u304f\u89e3\u8aac\u3057\u307e\u3059\u3002\u6cd5\u7dda\u306e\u7406\u89e3\u3092\u6df1\u3081\u308b\u3053\u3068\u3067\u3001\u7acb\u4f53\u3084\u66f2\u9762\u306e\u6027\u8cea\u3092\u6b63\u78ba\u306b\u6349\u3048\u308b\u624b\u52a9\u3051\u3068\u306a\u308b\u3067\u3057\u3087\u3046\u3002<\/p>\n<h2>1. \u6cd5\u7dda\u3068\u306f\uff1f\u57fa\u672c\u7684\u306a\u610f\u5473\u3068\u5b9a\u7fa9<\/h2>\n<h3>1.1 \u6cd5\u7dda\u306e\u4e00\u822c\u7684\u306a\u610f\u5473<\/h3>\n<p> \u6cd5\u7dda\u3068\u306f\u3001\u3042\u308b\u66f2\u9762\u3084\u5e73\u9762\u306e\u63a5\u70b9\u306b\u304a\u3044\u3066\u3001\u305d\u306e\u9762\u306b\u5bfe\u3057\u3066\u5782\u76f4\uff08\u76f4\u89d2\uff09\u306b\u4ea4\u308f\u308b\u76f4\u7dda\u3084\u30d9\u30af\u30c8\u30eb\u306e\u3053\u3068\u3092\u6307\u3057\u307e\u3059\u3002\u82f1\u8a9e\u3067\u306f\u300cnormal line\u300d\u3084\u300cnormal vector\u300d\u3068\u547c\u3070\u308c\u307e\u3059\u3002 \u300c\u6cd5\u300d\u3068\u306f\u300c\u898f\u5247\u30fb\u57fa\u6e96\u300d\u3092\u610f\u5473\u3057\u3001\u300c\u7dda\u300d\u306f\u6587\u5b57\u901a\u308a\u7dda\u306e\u3053\u3068\u306a\u306e\u3067\u3001\u300c\u57fa\u6e96\u3068\u306a\u308b\u7dda\u300d\u3068\u3044\u3046\u30a4\u30e1\u30fc\u30b8\u3067\u7406\u89e3\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h3>1.2 \u6cd5\u7dda\u3068\u63a5\u7dda\u306e\u9055\u3044<\/h3>\n<p> \u540c\u3058\u66f2\u9762\u3084\u66f2\u7dda\u4e0a\u306e\u63a5\u70b9\u306b\u304a\u3044\u3066\u3001\u63a5\u7dda\u306f\u305d\u306e\u9762\u3084\u7dda\u306b\u63a5\u3059\u308b\u65b9\u5411\u306e\u7dda\u3067\u3059\u304c\u3001\u6cd5\u7dda\u306f\u305d\u308c\u306b\u5782\u76f4\u306a\u65b9\u5411\u3092\u6307\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u63a5\u7dda\u3068\u6cd5\u7dda\u306f\u76f4\u4ea4\u3059\u308b\u95a2\u4fc2\u306b\u3042\u308a\u307e\u3059\u3002<\/p>\n<h2>2. \u6570\u5b66\u306b\u304a\u3051\u308b\u6cd5\u7dda\u306e\u5b9a\u7fa9\u3068\u8a08\u7b97<\/h2>\n<h3>2.1 \u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb<\/h3>\n<p> \u5e73\u9762\u306e\u6cd5\u7dda\u306f\u3001\u305d\u306e\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u306e\u3053\u3068\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u304c \\( Ax + By + Cz + D = 0 \\) \u3068\u8868\u3055\u308c\u308b\u3068\u304d\u3001\u30d9\u30af\u30c8\u30eb \\( (A, B, C) \\) \u304c\u305d\u306e\u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h3>2.2 \u66f2\u7dda\u306e\u6cd5\u7dda\uff082\u6b21\u5143\u306e\u5834\u5408\uff09<\/h3>\n<p> \u5e73\u9762\u4e0a\u306e\u66f2\u7dda\u306e\u5834\u5408\u3001\u3042\u308b\u70b9\u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u50be\u304d\u3092 \\( m \\) \u3068\u3059\u308b\u3068\u3001\u305d\u306e\u70b9\u306e\u6cd5\u7dda\u306e\u50be\u304d\u306f \\( -\\frac{1}{m} \\) \u3068\u306a\u308a\u307e\u3059\u3002 \u3053\u306e\u6027\u8cea\u3092\u4f7f\u3063\u3066\u3001\u66f2\u7dda\u306e\u4efb\u610f\u306e\u70b9\u3067\u6cd5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002 <\/p>\n<h3>2.3 \u66f2\u9762\u306e\u6cd5\u7dda\uff083\u6b21\u5143\u306e\u5834\u5408\uff09<\/h3>\n<p> 3\u6b21\u5143\u306e\u66f2\u9762\u3067\u306f\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306f\u66f2\u9762\u306e\u63a5\u5e73\u9762\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u66f2\u9762 \\( \\mathbf{r}(u,v) \\) \u306e\u5834\u5408\u3001 \\[ \\mathbf{n} = \\frac{\\partial \\mathbf{r}}{\\partial u} \\times \\frac{\\partial \\mathbf{r}}{\\partial v} \\] \u3068\u3044\u3046\u5916\u7a4d\u3067\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n<h2>3. \u7269\u7406\u5b66\u3084\u5de5\u5b66\u306b\u304a\u3051\u308b\u6cd5\u7dda\u306e\u5f79\u5272<\/h2>\n<h3>3.1 \u529b\u5b66\u306b\u304a\u3051\u308b\u6cd5\u7dda\u529b<\/h3>\n<p> \u7269\u7406\u5b66\u3067\u306f\u3001\u63a5\u89e6\u9762\u306b\u5782\u76f4\u306a\u529b\u3092\u300c\u6cd5\u7dda\u529b\u300d\u3068\u547c\u3073\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u7269\u4f53\u304c\u5e73\u9762\u306b\u7f6e\u304b\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u7269\u4f53\u306e\u91cd\u529b\u306b\u5bfe\u3057\u3066\u5e73\u9762\u304c\u62bc\u3057\u8fd4\u3059\u529b\u304c\u6cd5\u7dda\u529b\u3067\u3059\u3002 \u6cd5\u7dda\u529b\u306f\u63a5\u89e6\u70b9\u3067\u306e\u529b\u306e\u65b9\u5411\u3092\u793a\u3057\u3001\u6469\u64e6\u529b\u306e\u8a08\u7b97\u306b\u3082\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002 <\/p>\n<h3>3.2 \u5149\u5b66\u306b\u304a\u3051\u308b\u6cd5\u7dda\u306e\u610f\u5473<\/h3>\n<p> \u5149\u306e\u53cd\u5c04\u3084\u5c48\u6298\u3092\u8003\u3048\u308b\u969b\u306b\u3001\u5149\u7dda\u304c\u7269\u4f53\u8868\u9762\u306b\u5f53\u305f\u308b\u70b9\u3067\u306e\u6cd5\u7dda\u304c\u57fa\u6e96\u3068\u306a\u308a\u307e\u3059\u3002\u53cd\u5c04\u89d2\u3084\u5165\u5c04\u89d2\u306f\u3053\u306e\u6cd5\u7dda\u306b\u5bfe\u3059\u308b\u89d2\u5ea6\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 \u305d\u306e\u305f\u3081\u3001\u6b63\u78ba\u306a\u6cd5\u7dda\u306e\u628a\u63e1\u306f\u5149\u5b66\u8a2d\u8a08\u306b\u304a\u3044\u3066\u91cd\u8981\u3067\u3059\u3002 <\/p>\n<h3>3.3 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u3067\u306e\u5229\u7528<\/h3>\n<p> 3D\u30e2\u30c7\u30ea\u30f3\u30b0\u3084\u30ec\u30f3\u30c0\u30ea\u30f3\u30b0\u3067\u306f\u3001\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u3063\u3066\u5149\u306e\u5f53\u305f\u308a\u65b9\u3092\u8a08\u7b97\u3057\u3001\u9670\u5f71\u3092\u8868\u73fe\u3057\u307e\u3059\u3002\u6cd5\u7dda\u304c\u6b63\u78ba\u3067\u306a\u3044\u3068\u3001\u30ea\u30a2\u30eb\u306a\u898b\u305f\u76ee\u304c\u640d\u306a\u308f\u308c\u307e\u3059\u3002<\/p>\n<h2>4. \u6cd5\u7dda\u306e\u8a08\u7b97\u65b9\u6cd5\u306e\u5177\u4f53\u4f8b<\/h2>\n<h3>4.1 \u5e73\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u6c42\u3081\u65b9<\/h3>\n<p> \u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u306e\u4fc2\u6570 \\( (A, B, C) \\) \u304c\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u3068\u306a\u308a\u307e\u3059\u3002 \u4f8b\u3048\u3070\u3001\u5e73\u9762 \\( 2x - 3y + 4z - 5 = 0 \\) \u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306f \\( (2, -3, 4) \\) \u3067\u3059\u3002 <\/p>\n<h3>4.2 2\u6b21\u5143\u66f2\u7dda\u306e\u6cd5\u7dda\u306e\u6c42\u3081\u65b9<\/h3>\n<p> \u95a2\u6570 \\( y = f(x) \\) \u306e\u63a5\u7dda\u306e\u50be\u304d\u304c \\( f'(x) \\) \u306e\u3068\u304d\u3001\u6cd5\u7dda\u306e\u50be\u304d\u306f \\( -\\frac{1}{f'(x)} \\) \u3068\u306a\u308a\u307e\u3059\u3002 \u70b9 \\( (x_0, y_0) \\) \u306b\u304a\u3051\u308b\u6cd5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f \\[ y - y_0 = -\\frac{1}{f'(x_0)}(x - x_0) \\] \u3067\u8868\u3055\u308c\u307e\u3059\u3002 <\/p>\n<h3>4.3 3\u6b21\u5143\u66f2\u9762\u306e\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u6c42\u3081\u65b9<\/h3>\n<p> \u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af\u66f2\u9762 \\( \\mathbf{r}(u,v) = (x(u,v), y(u,v), z(u,v)) \\) \u306b\u5bfe\u3057\u3001 \\[ \\mathbf{r}_u = \\frac{\\partial \\mathbf{r}}{\\partial u}, \\quad \\mathbf{r}_v = \\frac{\\partial \\mathbf{r}}{\\partial v} \\] \u3092\u8a08\u7b97\u3057\u3001\u3053\u308c\u3089\u306e\u5916\u7a4d \\[ \\mathbf{n} = \\mathbf{r}_u \\times \\mathbf{r}_v \\] \u304c\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308a\u307e\u3059\u3002 \u4f8b\u3068\u3057\u3066\u7403\u9762\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u8868\u793a\u304b\u3089\u6cd5\u7dda\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<h2>5. \u6cd5\u7dda\u306e\u5411\u304d\u3068\u5358\u4f4d\u30d9\u30af\u30c8\u30eb<\/h2>\n<h3>5.1 \u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u5411\u304d\u306e\u610f\u5473<\/h3>\n<p> \u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306f2\u3064\u306e\u65b9\u5411\u304c\u8003\u3048\u3089\u308c\u308b\u305f\u3081\u3001\u5411\u304d\u3092\u3069\u3061\u3089\u306b\u3059\u308b\u304b\u304c\u554f\u984c\u3068\u306a\u308a\u307e\u3059\u3002\u7269\u7406\u3084CG\u3067\u306f\u300c\u5916\u5411\u304d\u6cd5\u7dda\u300d\u300c\u5185\u5411\u304d\u6cd5\u7dda\u300d\u3068\u3057\u3066\u4f7f\u3044\u5206\u3051\u307e\u3059\u3002 \u5916\u5411\u304d\u6cd5\u7dda\u306f\u7269\u4f53\u306e\u5916\u5074\u3092\u5411\u304d\u3001\u5185\u5411\u304d\u6cd5\u7dda\u306f\u5185\u5074\u3092\u5411\u304d\u307e\u3059\u3002 <\/p>\n<h3>5.2 \u5358\u4f4d\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u5fc5\u8981\u6027<\/h3>\n<p> \u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306f\u5927\u304d\u3055\u304c\u4efb\u610f\u306a\u306e\u3067\u3001\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\uff08\u9577\u30551\u306e\u30d9\u30af\u30c8\u30eb\uff09\u306b\u6b63\u898f\u5316\u3057\u3066\u7528\u3044\u308b\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002\u8a08\u7b97\u3084\u8868\u73fe\u304c\u7c21\u6f54\u306b\u306a\u308b\u305f\u3081\u3067\u3059\u3002<\/p>\n<h2>6. \u6cd5\u7dda\u306e\u5fdc\u7528\u4f8b\u3068\u5b9f\u751f\u6d3b\u3067\u306e\u95a2\u308f\u308a<\/h2>\n<h3>6.1 \u5efa\u7bc9\u30fb\u571f\u6728\u306b\u304a\u3051\u308b\u6cd5\u7dda\u306e\u5f79\u5272<\/h3>\n<p> \u5efa\u7bc9\u8a2d\u8a08\u3084\u69cb\u9020\u89e3\u6790\u3067\u306f\u3001\u58c1\u3084\u6881\u306e\u8868\u9762\u306e\u6cd5\u7dda\u65b9\u5411\u304c\u529b\u306e\u4f1d\u9054\u3084\u8010\u4e45\u6027\u8a55\u4fa1\u306b\u7528\u3044\u3089\u308c\u307e\u3059\u3002\u6cd5\u7dda\u306e\u6982\u5ff5\u306f\u5b89\u5b9a\u6027\u89e3\u6790\u306b\u4e0d\u53ef\u6b20\u3067\u3059\u3002<br \/>\n<h\uff13>6.2 \u81ea\u52d5\u8eca\u3084\u822a\u7a7a\u6a5f\u306e\u7a7a\u529b\u8a2d\u8a08<\/h\uff13><br \/>\n\u7a7a\u6c17\u306e\u6d41\u308c\u306b\u5bfe\u3059\u308b\u8eca\u4f53\u3084\u7ffc\u306e\u6cd5\u7dda\u65b9\u5411\u306f\u3001\u62b5\u6297\u3084\u63da\u529b\u306e\u8a08\u7b97\u306b\u76f4\u7d50\u3057\u307e\u3059\u3002\u6cd5\u7dda\u306e\u5411\u304d\u3068\u5927\u304d\u3055\u3092\u6b63\u78ba\u306b\u6e2c\u5b9a\u3057\u89e3\u6790\u3059\u308b\u3053\u3068\u304c\u6027\u80fd\u5411\u4e0a\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<br \/>\n<h\uff13>6.3 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