{"id":2924,"date":"2019-11-15T12:00:42","date_gmt":"2019-11-15T03:00:42","guid":{"rendered":"https:\/\/virtualcast.jp\/blog\/?p=2924"},"modified":"2024-10-22T19:22:15","modified_gmt":"2024-10-22T10:22:15","slug":"quaternion","status":"publish","type":"post","link":"https:\/\/blog.virtualcast.jp\/blog\/2019\/11\/quaternion\/","title":{"rendered":"Quaternion \u3092\u5b8c\u5168\u306b\u7406\u89e3\u3057\u305f"},"content":{"rendered":"<p>\u3053\u3093\u306b\u3061\u306f\u3001\u958b\u767a\u8005\u306e t-kuhn \u3067\u3059\u3002Unity Engine \u306b\u643a\u308f\u308b\u4ed5\u4e8b\u3092\u3059\u308b\u3068\u5fc5\u305a Quaternion \u306b\u906d\u9047\u3057\u307e\u3059\u3002\u4f55\u3060\u304b\u4e0d\u601d\u8b70\u306a\u540d\u524d\u3067\u6570\u5b66\u6982\u5ff5\u306f\u3068\u3063\u3064\u304d\u306b\u304f\u3044\u304b\u3089\u300c\u3068\u308a\u3042\u3048\u305a\u56de\u8ee2\u3092\u8868\u3059\u30e2\u30ce\u300d\u3068\u8133\u5185\u4fdd\u5b58\u3057\u3066\u6b21\u306b\u9032\u3080\u958b\u767a\u8005\u3082\u591a\u3044\u3067\u3057\u3087\u3046\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f Quaternion * Quaternion \u3068 Quaternion * Vector3 \u304c\u3069\u306e\u3088\u3046\u306a\u5834\u9762\u3067\u4f7f\u308f\u308c\u308b\u304b\u3001\u307e\u305f\u7c21\u5358\u306a\u4f8b\u3092\u3082\u3068\u306b\u8a08\u7b97\u81ea\u4f53\u306f\u3069\u3046\u306a\u3063\u3066\u3044\u308b\u304b\u306b\u3064\u3044\u3066\u66f8\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<pre><code class=\"language-csharp\">\/\/ Unity Engine \u306e Quaternion \u306e\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\u30fc\n\/\/ Quaternion \u306f4\u3064\u306e\u8981\u7d20\uff08x, y, z, w\uff09\u304b\u3089\u3067\u304d\u3066\u3044\u307e\u3059\u3002\npublic Quaternion(float x, float y, float z, float w)\n{\n    this.x = x;\n    this.y = y;\n    this.z = z;\n    this.w = w;\n}<\/code><\/pre>\n<p>\u3042\u308b\u65e5\u3001Quaternion \u30af\u30e9\u30b9\u304c <code>*<\/code> \u306e operator overload \u3092\u5b9a\u7fa9\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u8208\u5473\u3092\u60f9\u304b\u308c\u305f\u3002\u3053\u306e operator overload \u304c\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u304b\u3089 C# \u3067 Quaternion * Quaternion \u3068 Vector3 * Quaternion \u306e\u30b3\u30fc\u30c9\u304c\u66f8\u3051\u308b\u3088\u3046\u306b\u306a\u308b\u3002\u3053\u308c\u304b\u3089\u305d\u308c\u305e\u308c\u306e\u52d5\u4f5c\u3092\u78ba\u8a8d\u3057\u3066\u304b\u3089\u5b9f\u969b\u306e\u8a08\u7b97\u3092\u8ffd\u3063\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h3>Quaternion * Quaternion<\/h3>\n<p>\u307e\u305a\u306f2\u3064\u306e Quaternion q1 \u3068 q2 \u306e\u639b\u3051\u7b97\u306b\u3064\u3044\u3066\u8003\u3048\u3088\u3046\u3002\u4ea4\u63db\u6cd5\u5247\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u304b\u3089<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_1-0.png\" alt=\"\" \/><\/p>\n<p>\u3068\u66f8\u3051\u308b\u3002\u6210\u308a\u7acb\u305f\u306a\u3044\u304b\u3089\u57fa\u672c\u7684\u306b\u306f\uff08\u4f8b\u5916\u306f\u3042\u308b\uff09 q1 * q2 \u3068 q2 * q1 \u3092\u8a08\u7b97\u3057\u305f\u7d50\u679c\u304c\u7570\u306a\u308b\u306f\u305a\u3067\u3059\u3002\u78ba\u8a8d\u3057\u3088\u3046\u3002<\/p>\n<h4>q1 * q2<\/h4>\n<p>\u307e\u305a q1 * q2 \u3067\u3059\u3002<\/p>\n<pre><code class=\"language-csharp\">\/\/ q1 * q2\n\/\/ rotate around y-axis first and then tilt up around the rotated z-axis.\nvar q1 = Quaternion.Euler(0f, Time.time * 50f, 0f);\nvar q2 = Quaternion.Euler(0f, 0f, -45f);\nvar q = q1 * q2;\n_grayVector.transform.rotation = q;<\/code><\/pre>\n<p>\u3053\u306e\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3057\u305f\u3089 <code>_grayVector<\/code> \u306f\u3069\u306e\u3088\u3046\u306b\u52d5\u304f\u3067\u3057\u3087\u3046\u304b\uff1f\u305d\u308c\u3092\u77e5\u308b\u305f\u3081\u306b\u306f\u307e\u305a <code>_grayVector<\/code> \u306e\u56de\u8ee2\u3055\u308c\u3066\u3044\u306a\u3044\u3068\u304d\u306e\u69d8\u5b50\u3092\u78ba\u8a8d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/unrotated-gray-vector-0-1.png\" alt=\"\" \/><\/p>\n<p>\u3053\u306e\u56f3\u306e <code>_grayVector<\/code> \u304c <code>_grayVector.transform.rotation = Quaternion.Identity<\/code> \u306e\u3068\u304d\u306e <code>_grayVector<\/code> \u3067\u3059\u3002\u8d64\u3001\u7dd1\u3001\u9752\u306e\u77e2\u5370\u304c\u9577\u3055 1 \u306e\u4e16\u754c\u5ea7\u6a19\u3060\u3068\u3059\u308b\u3068 <code>_greyVector<\/code> \u306e\u7d42\u70b9\u306f\u3061\u3087\u3046\u3069 <code>(-1f, 0f, 0f)<\/code> \u3092\u6307\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\u3002<\/p>\n<p>\u3055\u3066\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3057\u3088\u3046\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/q1_times_q2.gif\" alt=\"\" \/><\/p>\n<p>\u307e\u305a\u3053\u3053\u3067\u5206\u304b\u308b\u306e\u306f <code>grayVector<\/code> \u306e\u539f\u70b9\u304c\u4e16\u754c\u5ea7\u6a19\u306e\u539f\u70b9\u3068\u540c\u3058\u4f4d\u7f6e\u306b\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u3067\u3059\u3002\u539f\u70b9\u304c\u3082\u3057\u77e2\u5370\u30e1\u30c3\u30b7\u30e5\u306e\u4e2d\u5fc3\u306b\u306a\u3063\u3066\u3044\u305f\u3089\u3053\u306e\u3088\u3046\u306a\u56de\u308a\u65b9\u306f\u3057\u306a\u3044\u3067\u3059\u3002<\/p>\n<p>q1 \u3068 q2 \u306e\u4e2d\u8eab\u3092\u898b\u3088\u3046\uff1a<\/p>\n<ul>\n<li>q1 \uff1a\u6642\u9593\u304c\u7d4c\u3064\u3068\u3068\u3082\u306b y-axis \u3092\u56de\u8ee2\u8ef8\u306b\u56de\u308b<\/li>\n<li>q2 \uff1az-axis \u3092\u56de\u8ee2\u8ef8\u306b -45\u00b0 \u56de\u308b<\/li>\n<\/ul>\n<p>\u5f8c\u3001 q1 * q2 \u306a\u306e\u3067\u6700\u7d42\u7684\u306a\u56de\u8ee2 q \u306f q1 \u304c\u9069\u7528\u3055\u308c\u305f\u5f8c\u306b q2 \u3092\u9069\u7528\u3057\u305f\u3068\u304d\u306e\u7d50\u679c\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u3053\u3067\u975e\u5e38\u306b\u91cd\u8981\u306a\u306e\u306f <strong>q1 \u3092\u9069\u7528\u3057\u305f\u5f8c\u306e\u305d\u308c\u305e\u308c\u56de\u8ee2\u8ef8\u306f q1 \u306e\u56de\u8ee2\u5206\u3060\u3051\u4e00\u7dd2\u306b\u56de\u308b<\/strong> \u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u4e00\u7dd2\u306b\u56de\u8ee2\u3059\u308b\u304b\u3089 q2 \u306e \u56de\u8ee2\u8ef8\u3067\u3042\u308b z-axis \u306f\u6bce\u30d5\u30ec\u30fc\u30e0\u5c11\u3057\u305a\u3064 y-axis \u3092\u56de\u8ee2\u8ef8\u306b\u56de\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<h4>q2 * q1<\/h4>\n<p>\u3055\u3066\u3001\u9806\u756a\u3092\u9006\u306b\u3057\u305f\u3068\u304d\u306e\u7d50\u679c\u3092\u8abf\u3079\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306f <code>q = q2 * q1;<\/code> \u306e\u3068\u3053\u308d\uff08\u3053\u3053\u3092\u9006\u306b\u3057\u305f\uff09\u4ee5\u5916\u4e0a\u306e\u30b3\u30fc\u30c9\u3068\u540c\u3058\u3067\u3059\u3002<\/p>\n<pre><code class=\"language-csharp\">\/\/ q2 * q1\n\/\/ tilt up first and then rotate around the now tilted y-axis\nvar q1 = Quaternion.Euler(0f, Time.time * 50f, 0f);\nvar q2 = Quaternion.Euler(0f, 0f, -45f);\n var q = q2 * q1;\n_grayVector.transform.rotation = q;<\/code><\/pre>\n<p>\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3057\u305f\u7d50\u679c\u306f\u3053\u308c\u3067\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/q2_times_q1.gif\" alt=\"\" \/><\/p>\n<p>\u4eca\u5ea6\u306f\u300cz-axis \u3092\u56de\u8ee2\u8ef8\u306b -45\u00b0 \u56de\u308b\u300d\u3092\u9069\u7528\u3057\u3066\u304b\u3089\u300c\u6642\u9593\u304c\u7d4c\u3064\u3068\u3068\u3082\u306b y-axis \u3092\u56de\u8ee2\u8ef8\u306b\u56de\u308b\u300d\u3002\u56de\u8ee2\u3055\u308c\u3066\u3044\u306a\u3044\u72b6\u614b\uff08\u3053\u306e\u72b6\u614b\u3060\u3068\u4e16\u754c\u5ea7\u6a19\u304c\u56de\u8ee2\u8ef8\u3068\u4e00\u81f4\u3059\u308b\uff09\u304b\u3089 z-axis \u3092\u56de\u8ee2\u8ef8\u306b -45\u00b0 \u56de\u308b\u3068 y-axis \u304c\u4e00\u7dd2\u306b\u56de\u3063\u3066\u50be\u3044\u305f\u72b6\u614b\u3067\u6b62\u307e\u308a\u307e\u3059\u3002\u3053\u306e\u50be\u3044\u305f y-axis \u3092\u56de\u8ee2\u8ef8\u306b\u3055\u3089\u306b\u300c\u6642\u9593\u304c\u7d4c\u3064\u3068\u3068\u3082\u306b\u56de\u308b\u300d\u304b\u3089\u4e0a\u56f3\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>Quaternion * Vector<\/h3>\n<p>Quaternion \u306e\u639b\u3051\u7b97\u3067\u69d8\u3005\u306a\u56de\u8ee2\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u6b21\u306f Quaternion * Vector \u306e\u52d5\u4f5c\u78ba\u8a8d\u3067\u3059\u304c\u3001\u3053\u308c\u306f\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u3092\u4efb\u610f\u306e Quaternion \u3067\u56de\u8ee2\u3055\u305b\u308b\u305f\u3081\u306e operator overload \u3067\u623b\u308a\u5024\u306f <code>Vector3<\/code> \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><code>Vector3<\/code> \u306a\u306e\u3067\u4eca\u5ea6\u306f <code>(-1f, 0f, 0f)<\/code> \u306b\u914d\u7f6e\u3055\u308c\u305f\u9ed2\u3044\u7403\u3092\u8003\u3048\u3088\u3046\u3002<code>_grayVector<\/code> \u306e\u7d42\u70b9\u3082\u3061\u3087\u3046\u3069\u3053\u306e\u4f4d\u7f6e\u3092\u6307\u3057\u3066\u3044\u308b\u304b\u3089\u6b8b\u3057\u3066\u304a\u304f\u3053\u3068\u306b\u3057\u305f\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/unrotated-black-ball-0.png\" alt=\"\" \/><\/p>\n<pre><code class=\"language-csharp\">\/\/ Quaternion * Vector3\nvar q = Quaternion.Euler(new Vector3(0f, Time.time * 50f, -45f));\nvar p = new Vector3(-1f, 0f, 0f);\nvar pDash = q * p;\n_grayVector.transform.rotation = q;\n_blackBall.transform.position = pDash;<\/code><\/pre>\n<p>\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/q_times_vector.gif\" alt=\"\" \/><\/p>\n<p>\u7121\u4e8b\u9ed2\u3044\u7403\u3092 <code>q<\/code> \u3067\u56de\u8ee2\u3055\u305b\u308b\u3053\u3068\u306b\u6210\u529f\u3057\u307e\u3057\u305f\u3002<\/p>\n<h3>\u306a\u3093\u3067\u305d\u308c\u3067\u52d5\u304f\u306e\uff1f<\/h3>\n<p>\u3053\u308c\u3067\u3084\u3063\u3068\u524d\u7f6e\u304d\u304c\u7d42\u308f\u308a\u3001\u79c1\u304c\u672c\u5f53\u306b\u66f8\u304d\u305f\u304b\u3063\u305f\u3068\u3053\u308d\u307e\u3067\u6765\u305f\u3002\u300c\u4f55\u3067\u3053\u306e operator overload \u3067\u3053\u3093\u306a\u7d50\u679c\u306b\u306a\u308b\u304b\uff1f\u300d\u306b\u3064\u3044\u3066\u66f8\u304d\u305f\u304b\u3063\u305f\u306e\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u306a\u3093\u3067 Quaternion * Quaternion \u3068\u3044\u3046\u30b3\u30fc\u30c9\u3092\u66f8\u304f\u3068\u305d\u308c\u3089\u306e\u56de\u8ee2\u3092\u7d44\u307f\u5408\u308f\u305b\u305f Quaternion \u304c\u751f\u307e\u308c\u308b\u304b\u3002\u305d\u3057\u3066\u3001\u4f55\u3067 Quaternion * Vector3 \u3068\u3044\u3046\u30b3\u30fc\u30c9\u3092\u66f8\u304f\u3068 Quaternion \u5206\u56de\u8ee2\u3055\u308c\u305f Vector3 \u304c\u5f97\u3089\u308c\u308b\u304b\u3002<\/p>\n<p>\u3064\u307e\u308a\u3001\u30d6\u30e9\u30c3\u30af\u30dc\u30c3\u30af\u30b9\u306b\u306a\u3063\u3066\u3044\u308b\u305d\u308c\u3089\u306e\u8a08\u7b97\u306e\u6b63\u4f53\u306b\u3064\u3044\u3066\u3053\u308c\u304b\u3089\u66f8\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<h4>Quaternion * Quaternion \u306e\u6b63\u4f53<\/h4>\n<pre><code class=\"language-csharp\">\/\/ q1 * q2\n\/\/ rotate around y-axis first and then tilt up around the rotated z-axis.\nvar q1 = Quaternion.Euler(0f, 135f, 0f);\nvar q2 = Quaternion.Euler(0f, 0f, -45f);\nvar q = q1 * q2;\n_grayVector.transform.rotation = q;<\/code><\/pre>\n<p>\u3053\u306e\u30b3\u30fc\u30c9\u3067\u4f55\u304c\u8d77\u304d\u3066\u3044\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3057\u305f\u3089\u4ee5\u4e0b\u306e\u7d50\u679c\u306b\u306a\u308a\u307e\u3059\u304c\u3001\u79c1\u305f\u3061\u304c\u6c42\u3081\u3066\u3044\u308b\u306e\u306f\u305d\u3053\u3067\u306f\u306a\u3044\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/resultingQ-0-1.png\" alt=\"\" \/><br \/>\nUnity \u306b\u5168\u3066\u3092\u8a08\u7b97\u3057\u3066\u3082\u3089\u3046\u3068 Quaternion <code>q<\/code> \u306b\u683c\u7d0d\u3055\u308c\u308b\u5024\u306f\u6b21\u306e\u901a\u308a\u3067\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_2-0-1.png\" alt=\"\" \/><\/p>\n<p>q1 * q2 \u3092\u8a08\u7b97\u3057\u3066\u540c\u3058\u7d50\u679c\u306b\u306a\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308c\u3070\u3044\u3044\u304c\u3001\u307e\u305a\u306f (1.2) \u3092\u5c11\u3057\u66f8\u304d\u63db\u3048\u307e\u3059\u3002Unity Engine \u306f Quaternion \u306e\u305d\u308c\u305e\u308c\u306e\u6210\u5206\u3092\u5b9f\u6570\u3067\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u8a08\u7b97\u7d50\u679c\u304c\u5408\u3063\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u306e\u6bd4\u8f03\u304c\u3057\u3084\u3059\u304f\u306a\u308b\u3088\u3046\u306b\u5b9f\u6570\u3092\u4e09\u89d2\u95a2\u6570\u306b\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002\u3053\u3046\u3044\u3046\u3068\u304d\u306f <a href=\"https:\/\/www.wolframalpha.com\/input\/?i=0.8535534\">Wolfram Alpha<\/a> \u304c\u4fbf\u5229\u3067\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_3-0-corrected.png\" alt=\"\" \/><\/p>\n<p>\u6b21\u306b q1 \u3068 q2 \u306e\u5024\u3092\u898b\u3088\u3046\u3002\u4e0a\u3068\u540c\u3058\u3088\u3046\u306b\u305d\u308c\u305e\u308c\u306e\u8981\u7d20\u3092\u4e09\u89d2\u95a2\u6570\u3067\u8868\u3059\u3068 q1 \u306f<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_4-0-1.png\" alt=\"\" \/><\/p>\n<p>\u3067 q2 \u306f<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_5-0-1.png\" alt=\"\" \/><\/p>\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u4e00\u5ea6 Quaternion \u3092\u6570\u5b66\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u8868\u73fe\u3059\u308b\u304b\u306b\u3064\u3044\u3066\u66f8\u3044\u3066\u304a\u3053\u3046\u3002q1 \u3092\u6b21\u306e\u3088\u3046\u306b\u66f8\u304d\u307e\u3059<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_6-0.png\" alt=\"\" \/><\/p>\n<p>Quaternion \u306f4\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u30b9\u30ab\u30e9\u30fc\u3068\u533a\u5225\u304c\u4ed8\u304f\u3088\u3046\u306b q1 \u306f\u592a\u6587\u5b57\u306b\u306a\u3063\u3066\u3044\u307e\u3059\uff08\u30d9\u30af\u30c8\u30eb\uff1d\u592a\u6587\u5b57\u3068\u3044\u3046\u7d04\u675f\u3067\u3059\uff09\u3002i, j, k \u304c\u3064\u3044\u3066\u3044\u308b\u8981\u7d20\u3092 Quaternion \u306e\u8907\u7d20\u6210\u5206\u3001s1 \u3092 Quaternion \u306e\u30b9\u30ab\u30e9\u30fc\u6210\u5206\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p>q1 \u3092\u30d9\u30af\u30c8\u30eb\u8868\u8a18\u3067\u8868\u3059\u3068<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_7-0.png\" alt=\"\" \/><\/p>\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u30013\u3064\u306e\u8907\u7d20\u6210\u5206\u3092\u4e00\u3064\u306e3\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306b\u307e\u3068\u3081\u3066\u66f8\u304f\u3068<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_8-0.png\" alt=\"\" \/><\/p>\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>Quaternion \u306e\u639b\u3051\u7b97\u306b\u9032\u3080\u524d\u306b Quaternion \u306e\u57fa\u672c\u5f0f\u3092\u8868\u8a18\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002\u3053\u306e\u57fa\u672c\u5f0f\u306f Quaternion \u3092\u8003\u3048\u4ed8\u3044\u305f Sir William Rowan Hamilton \u304c\u767a\u898b\u3057\u305f\u3082\u306e\u3067 Quaternion \u6570\u5b66\u306e\u57fa\u790e\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_9-0.png\" alt=\"\" \/><\/p>\n<p>\u3053\u308c\u3067 Quaternion \u306e\u639b\u3051\u7b97\u306b\u5fc5\u8981\u306a\u3082\u306e\u304c\u63c3\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_10-0.png\" alt=\"\" \/><\/p>\n<p>(1.10) \u306e\u53f3\u8fba\u3092\u5206\u914d\u6cd5\u5247\u306b\u5f93\u3063\u3066\u5c55\u958b\u3057\u3001\u305d\u3057\u3066 (1.9) \u3092\u9069\u7528\u3059\u308b\u3068<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_11-0.png\" alt=\"\" \/><\/p>\n<p>\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 (1.11) \u306e q1 \u3068 q2 \u306b (1.4) \u3068 (1.5) \u3092\u4ee3\u5165\u3059\u308c\u3070\u3053\u308c\u3067 q \u304c\u6c42\u307e\u308b\u304c\u3001\u9805\u304c16\u500b\u3082\u3042\u308b\u304b\u3089\u3001\u5c11\u3057\u6574\u7406\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u6574\u7406\u3059\u308b\u305f\u3081\u306b\u30d9\u30af\u30c8\u30eb\u306e\u5916\u7a4d\u3068\u5185\u7a4d\u304c\u5fc5\u8981\u306b\u306a\u308b\u304b\u3089\u3053\u3053\u306b\u66f8\u3044\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_12-and-1_13-0.png\" alt=\"\" \/><\/p>\n<p>(1.12), (1.13) \u3088\u308a\u3001(1.11) \u306e\u53f3\u8fba\u306e\u9805\u3092\u6b21\u306e\u3088\u3046\u306b\u6574\u7406\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_14-0.png\" alt=\"\" \/><\/p>\n<p>\u3055\u3066\u3001 (1.14) \u306b (1.4), (1.5) \u3092\u4ee3\u5165\u3057\u3066 (1.5) \u3068\u540c\u3058\u7d50\u679c\u304c\u5f97\u3089\u308c\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u3088\u3046\u3002<\/p>\n<p>\u307e\u305a (1.4) \u3092\u30d9\u30af\u30c8\u30eb\u8868\u8a18\u3067\u8868\u3059\u3068<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_15-and-1_16-0.png\" alt=\"\" \/><\/p>\n<p>\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u540c\u69d8\u306b (1.5) \u3088\u308a<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_17-and-1_18-0.png\" alt=\"\" \/><\/p>\n<p>(1.15) ~ (1.18) \u3092 (1.14) \u306b\u4ee3\u5165\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/from-1_19-to-1_21-0-corrected-1.png\" alt=\"\" \/><\/p>\n<p>\u3068 q \u304c\u6c42\u307e\u308a (1.3) \u3068\u6bd4\u8f03\u3059\u308b\u3068 Unity Engine \u3068<strong>\u540c\u3058\u7d50\u679c<\/strong>\u304c\u5f97\u3089\u308c\u305f\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3084\u3063\u305f\u305c\uff01\u4f55\u3082\u6570\u5b66\u7684\u306b\u8a3c\u660e\u3057\u305f\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u7c21\u5358\u306a\u4f8b\u3092\u901a\u3057\u3066 Unity Engine \u304c\u5185\u90e8\u7684\u306b<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_14-0.png\" alt=\"\" \/><\/p>\n<p>\u3068\u540c\u7b49\u306a\u6570\u5f0f\u3067 Quaternion * Quaternion \u3092\u8a08\u7b97\u3057\u3066\u3044\u308b\u3068\u78ba\u4fe1\u304c\u6301\u3066\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u3002\u6700\u5f8c\u306b (1.1) \u3092\u3082\u3046\u4e00\u5ea6\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_1-0.png\" alt=\"\" \/><\/p>\n<p>Quaternion \u306e\u639b\u3051\u7b97\u3067\u306f\u4ea4\u63db\u6cd5\u5247\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u3068\u4e0a\u306b\u66f8\u304d\u307e\u3057\u305f\u304c\u3001 (1.14) \u3092\u898b\u308b\u3068\u300c\u3042\u3041\u3001\u78ba\u304b\u306b\u3001\u3053\u308a\u3083\u4ea4\u63db\u6cd5\u5247\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u306d\u30fc\u300d\u3068\u305d\u306e\u7406\u7531\u304c\u5206\u304b\u308b\u4eba\u3082\u304b\u306a\u308a\u591a\u3044\u306e\u3067\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\uff08\u30d2\u30f3\u30c8\uff1a\u5916\u7a4d\uff09\u3002<\/p>\n<h4>Quaternion * Vector3 \u306e\u6b63\u4f53<\/h4>\n<p>\u5358\u5200\u76f4\u5165\u306b\u66f8\u304d\u307e\u3059\u3068 Unity Engine \u306e Quaternion * Vector3 \u306e\u8a08\u7b97\u306e\u6b63\u4f53\u306f<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_22-0.png\" alt=\"\" \/><\/p>\n<p>\u3067\u3059\u3002\u3053\u3053\u3067\u3001 p \u306f\u56de\u3057\u305f\u3044\u30d9\u30af\u30c8\u30eb\u3067\u3001 p' \u306f\u56de\u3057\u305f\u5f8c\u306b\u5f97\u3089\u308c\u305f\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002 q \u306f\u3082\u3061\u308d\u3093 Quaternion \u3067\u3059\u3002<\/p>\n<p>\u3055\u3066\u3001\u524d\u7ae0\u3068\u540c\u3058\u3075\u3046\u306b Unity Engine \u3068\u81ea\u529b\u3067\u8a08\u7b97\u3057\u305f\u7d50\u679c\u304c\u4e00\u81f4\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066 Unity Engine \u304c\u5185\u90e8\u7684\u306b\u3084\u3063\u3066\u3044\u308b\u8a08\u7b97\u304c (1.22) \u3068\u540c\u7b49\u3067\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/Startpos-0.png\" alt=\"\" \/><\/p>\n<p>\u9ed2\u3044\u7403\u306e\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u3092\u524d\u7ae0\u6c42\u3081\u305f q \u3067\u56de\u8ee2\u3055\u305b\u3088\u3046\u3002\u4e0a\u56f3\u306b\u56de\u8ee2\u3092\u9069\u7528\u3059\u308b\u524d\u306e\u72b6\u614b\u3092\u793a\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/Endpos-0.png\" alt=\"\" \/><\/p>\n<p>\u305d\u3057\u3066\u3053\u308c\u304c\u56de\u8ee2\u3092\u9069\u7528\u3057\u305f\u5f8c\u306e\u72b6\u614b\u3067\u3059\u3002 Unity Engine \u3067\u306f Quaternion \u30af\u30e9\u30b9\u304c\u5b9a\u7fa9\u3057\u3066\u3044\u308b * operator overload \u3092\u5229\u7528\u3057\u3066<\/p>\n<pre><code>var q = Quaternion.Euler(new Vector3(0f, 135f, -45f));\nvar p = new Vector3(-1f, 0f, 0f);\nvar pDash = q * p;<\/code><\/pre>\n<p>\u3068\u66f8\u3051\u307e\u3059\u304c\u3001\u5b9f\u969b\u306e\u8a08\u7b97\u306f q * p \u3067\u306f\u306a\u304f\u3066<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_22-0.png\" alt=\"\" \/><\/p>\n<p>\u3067\u3059\u3002\u56de\u8ee2\u524d\u306e\u30d9\u30af\u30c8\u30eb p \u306f<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_23-0.png\" alt=\"\" \/><\/p>\n<p>\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u3057\u3066\u3001Unity Engine \u3067\u8a08\u7b97\u3057\u305f\u7d50\u679c\u3001\u56de\u8ee2\u5f8c\u306e\u30d9\u30af\u30c8\u30eb p' \u306f<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_24-0-corrected.png\" alt=\"\" \/><\/p>\n<p>\u3067\u3059\u3002\u3055\u3066\u3001 (1.22) \u306b (1.23), (1.21) \u3092\u4ee3\u5165\u3057\u81ea\u529b\u3067\u8a08\u7b97\u3059\u308b\u30bf\u30fc\u30f3\u3067\u3059\u3002<\/p>\n<p>\u307e\u305a\u3001 q \u306e\u9006\u884c\u5217 q^-1 \u3092\u8a08\u7b97\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_25-0-corrected.png\" alt=\"\" \/><\/p>\n<p>(1.22) \u306e\u8a08\u7b97\u3092\u4e8c\u3064\u306b\u5206\u3051\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_26-and-1_27-0.png\" alt=\"\" \/><\/p>\n<p>(1.26) \u3092\u8a08\u7b97\u3057\u3066\u304b\u3089 (1.27) \u3092\u8a08\u7b97\u3059\u308c\u3070 p' \u304c\u6c42\u307e\u308a\u307e\u3059\u3002\u639b\u3051\u7b97\u306e\u3084\u308a\u304b\u305f\u306f Quaternion * Quaternion \u3068\u4e00\u7dd2\u3067\u3059\u304c\u3001 p \u30924\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306b\u62e1\u5f35\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002<\/p>\n<p>\u524d\u7ae0\u3067\u6c42\u307e\u3063\u305f q \u3092\u3082\u3046\u4e00\u5ea6\u66f8\u3044\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_28-0-corrected.png\" alt=\"\" \/><\/p>\n<p>\u6b21\u306b4\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306b\u62e1\u5f35\u3055\u308c\u305f p \u3092\u66f8\u3044\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_29-0.png\" alt=\"\" \/><\/p>\n<p>0\u306e\u8981\u7d20\u304c3\u3064\u3082\u3042\u308b\u306e\u306f\u8a08\u7b97\u304c\u697d\u306b\u306a\u308b\u304b\u3089\u5b09\u3057\u3044\u3067\u3059\u306d\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_30-0-corrected.png\" alt=\"\" \/><\/p>\n<p>\u3053\u308c\u3067 (1.26) \u306e\u8a08\u7b97\u304c\u3067\u304d\u307e\u3057\u305f\u3002 \u6b21\u306b (1.27) \u306e\u8a08\u7b97\u306b\u9032\u307f\u307e\u3059\u3002 (1.26) \u3068\u540c\u69d8\u306b\u3001\u5b9a\u7fa9\u304b\u3089\u3044\u304d\u307e\u3059\u3002<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_31-and-1_32-0-corrected.png\" alt=\"\" \/><\/p>\n<p>\u305d\u3057\u3066\u524d\u3068\u540c\u69d8\u306b\u8a08\u7b97\u3057\u3066\u3044\u304f\u3068<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_33-0-corrected.png\" alt=\"\" \/><\/p>\n<p>\u3068 p' \u304c\u6c42\u307e\u308a\u307e\u3059\u3002 Unity Engine \u304c\u8a08\u7b97\u3057\u305f\u5024 (1.24) \u3068\u6bd4\u8f03\u3059\u308b\u3068\u4e00\u81f4\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308b\uff01\u6700\u5f8c\u306e\u6700\u5f8c\u306b\u3059\u3054\u3044\u91cf\u306b\u306a\u308a\u307e\u3057\u305f\u304c\u3001\u8a08\u7b97\u304c\u5408\u3063\u3066\u3044\u308b\u3088\u3046\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u8a08\u7b97\u3092\u901a\u3057\u3066 Unity Engine \u3067 Quaternion * Vector3 \u3092\u66f8\u304f\u3068\u5185\u90e8\u7684\u306b\u884c\u308f\u308c\u308b\u306e\u304c<\/p>\n<p><img src=\"https:\/\/virtualcast.jp\/blog\/wp-content\/uploads\/2019\/11\/1_22-0.png\" alt=\"\" \/><\/p>\n<p>\u306b\u76f8\u5f53\u3059\u308b\u51e6\u7406\u3067\u3042\u308b\u3053\u3068\u306b\u78ba\u4fe1\u304c\u6301\u3066\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n<h4>\u30ea\u30f3\u30af\u96c6<\/h4>\n<ul>\n<li><a href=\"http:\/\/www2.cs.uregina.ca\/~anima\/408\/Notes\/Quaternions\/Quaternions.htm\">Quaternion \u6570\u5b66\u306b\u3064\u3044\u3066\u306e\u89e3\u8aac<\/a><\/li>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=d4EgbgTm0Bg\">3Blue1Brown\u3055\u3093\u304c Quaternion \u306b\u3064\u3044\u3066\u8aac\u660e\u3059\u308b\u52d5\u753b\u305d\u306e\uff11<\/a><\/li>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=zjMuIxRvygQ\">3Blue1Brown\u3055\u3093\u304c Quaternion \u306b\u3064\u3044\u3066\u8aac\u660e\u3059\u308b\u52d5\u753b\u305d\u306e\uff12<\/a><\/li>\n<li><a href=\"https:\/\/docs.unity3d.com\/Manual\/QuaternionAndEulerRotationsInUnity.html\">Rotation and Orientation in Unity<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3093\u306b\u3061\u306f\u3001\u958b\u767a\u8005\u306e t-kuhn \u3067\u3059\u3002Unity Engine \u306b\u643a\u308f\u308b\u4ed5\u4e8b\u3092\u3059\u308b\u3068\u5fc5\u305a Quaternion \u306b\u906d\u9047\u3057\u307e\u3059\u3002\u4f55\u3060\u304b\u4e0d\u601d\u8b70\u306a\u540d\u524d\u3067\u6570\u5b66\u6982\u5ff5\u306f\u3068\u3063\u3064\u304d\u306b\u304f\u3044\u304b\u3089\u300c\u3068\u308a\u3042\u3048\u305a\u56de\u8ee2\u3092\u8868\u3059\u30e2\u30ce\u300d\u3068\u8133\u5185\u4fdd\u5b58\u3057\u3066...<\/p>\n","protected":false},"author":35,"featured_media":3124,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[105,26],"tags":[23],"_links":{"self":[{"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/posts\/2924"}],"collection":[{"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/users\/35"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/comments?post=2924"}],"version-history":[{"count":135,"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/posts\/2924\/revisions"}],"predecessor-version":[{"id":9298,"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/posts\/2924\/revisions\/9298"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/media\/3124"}],"wp:attachment":[{"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/media?parent=2924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/categories?post=2924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.virtualcast.jp\/blog\/wp-json\/wp\/v2\/tags?post=2924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}