{"id":2311,"date":"2020-07-20T16:41:47","date_gmt":"2020-07-20T08:41:47","guid":{"rendered":"https:\/\/www.clonefactor.com\/wordpress\/?p=2311"},"modified":"2020-07-20T16:41:49","modified_gmt":"2020-07-20T08:41:49","slug":"quaternion-%e6%8e%83%e7%9b%b2","status":"publish","type":"post","link":"https:\/\/www.clonefactor.com\/wordpress\/program\/math\/2311\/","title":{"rendered":"Quaternion \u6383\u76f2"},"content":{"rendered":"\n

\u53d6\u5f97\u55ae\u4e00 Quaternion \u7684\u67d0\u500b\u65b9\u5411(Direction – vector)?<\/h2>\n

\u7531\u65bc Quaternion \u662f\u7ba1\u7406\u8f49\u5411\u7684, \u5c31\u50cf Local \/ World Space \u7a7a\u9593<\/a>\u00a0\u88e1\u6240\u5c55\u793a\u7684
“\u5b83” Quaternion \u81ea\u5df1\u5c31\u662f\u4ee3\u8868\u4e00\u500b\u7269\u4ef6\u7684\u8f49\u5411 (Local space).
\u800c\u5b83\u7684\u8f49\u5411\u662f\u4ed8\u52a0\u5728\u4e16\u754c\u5750\u6a19\u4e0a\u9762\u7684 (World space).
\u5b83\u5c31\u50cf\u662f\u4e00\u500b\u8a18\u9304\u4e86\u67d0\u7269\u4ef6\u7684\u65b9\u4f4d\u7684\u8f49\u63db, \u800c\u5728\u7251\u7a0b\u6642, \u6211\u5011\u53ef\u4ee5\u5229\u7528 Quaternion \u4f86\u8f49\u63db Local \/ world direction
\u7528 Unity3D C#\u7684\u65b9\u5f0f\u4f86\u770b\u7684\u8a71\u5c31\u50cf\u9019\u6a23.<\/p>\n

Quaternion facing = \/* whatever *\/;\nVector3 myForward = facing * Vector3.forward;\nVector3 myRight = facing * Vector3.right;\nVector3 myUpward = facing * Vector3.up;\nVector3 myLeft = -myRight;\nVector3 myBack = -myForward;\nVector3 myBottom = -myUpward;<\/pre>\n
\u9664\u4e86\u4e0a\u9762\u7bc4\u4f8b\u7684 6 \u500b Local space \u7684 vector direction,
\u6211\u5011\u9084\u53ef\u4ee5\u628a\u4efb\u610f\u4e00\u652f\u7684 Vector3 \u4e1f\u9032\u53bb\u53d6\u5f97\u76f8\u5c0d\u61c9\u7684 World space direction.
\u8aaa\u767d\u4e00\u9ede\u7684\u4f8b\u5b50\u5c31\u662f : \u4f60\u73fe\u5728\u53ef\u4ee5\u5229\u7528 Quaternion \u53d6\u5f97\u67d0\u500b\u4eba\u7269\u7684\u5de6\u624b\u5230\u5e95\u662f\u4e0d\u662f\u6307\u8457\u5317\u65b9\u54af.<\/p>\n
\u56db\u5143\u6578\u7684\u8f49\u5411\u758a\u52a0 (\u76f8\u4e58)<\/h2>\n
\u55ae\u4e00\u500b\u8f49\u5411\u53ef\u4ee5\u7528\u7684\u5730\u65b9\u4e0d\u591a, \u4f46\u591a\u5c64\u8f49\u5411\u7684\u65b9\u5411\u904b\u7b97\u61c9\u8a72\u5c31\u975e\u5e38\u591a,
\u4f46\u662f\u56db\u5143\u6578\u7684\u77e9\u9663\u662f\u6c92\u6709 “\u52a0” (+) \u9019\u4e00\u500b\u904b\u7b97\u7b26\u865f\u7684,
\u984c\u5916: \u56e0\u70ba\u628a Quaterion \u7684\u56db\u5143\u6578\u8f49\u63db\u70ba matrix \u7684\u8a71\u770b\u8d77\u4f86\u662f\u9019\u6a23\u7684.<\/p>\n
<\/p>\n
\u5728 Quaterion \u88e1\u982d\u8981\u758a\u52a0\u5176\u4ed6 Quaterion \u7684\u8a71\u5c31\u53ea\u6709”\u4e58” (*)
\u8aaa\u767d\u4e00\u9ede\u751a\u9ebc\u662f\u591a\u5c64\u7d1a\u7684\u8f49\u5411?
\u6211\u5011\u4ee5\u624b\u81c2\u4f86\u505a\u4f8b\u5b50\u4f86\u8aaa\u660e\u4e00\u4e0b.<\/p>\n
“\u4e0a\u81c2” \u7684\u8f49\u52d5\u6703\u5e36\u52d5 “\u524d\u81c2”
\u9019\u88e1\u9762, “\u524d\u81c2” \u7684\u8f49\u5411\u662f\u4f9d\u5f9e “\u4e0a\u81c2” \u7684\u8f49\u5411\u7684.
\u6240\u4ee5 “\u4e0a\u81c2” \u662f\u7236\u5c64\u7d1a\u7684\u8f49\u5411,
“\u4e0b\u81c2” \u662f\u5b50\u5c64\u7d1a\u7684\u8f49\u5411.<\/p>\n
\u5728\u6578\u5b78\u6982\u5ff5\u4e0a\u53ea\u8981\u628a\u5169\u500b Quaterion \u76f8\u4e58\u5c31\u662f\u4ee3\u8868\u5169\u500b\u8f49\u5411\u7684\u7d2f\u52a0.
\u5728 Unity3D C# \u4e2d\u770b\u8d77\u4f86\u662f\u9019\u6a23\u7684.<\/p>\n
Quaternion upperArm = \/* local downward *\/\nQuaternion lowerArm = \/* local upward *\/\n\nQuaternion armRotation = upperArm * lowerArm;<\/pre>\n
\u6211\u5011\u5ffd\u7565\u6389\u8eab\u9ad4, \u5047\u8a2d “\u4e0a\u81c2” \u7684\u4e0b\u65b9\u5c31\u662f\u4e16\u754c\u7684\u4e0b\u65b9, \u800c “\u524d\u81c2” (lower arm) \u662f\u6307\u5411\u81ea\u5df1\u7684\u4e0a\u65b9\u7684\u8a71
\u5c31\u80fd\u770b\u5230\u9019\u6a23\u7684\u666f\u50cf.<\/p>\n
\"\"<\/p>\n
\u5982\u679c\u4e0d\u660e\u767d\u70ba\u4f55\u662f\u6307\u5411\u4e16\u754c\u5750\u6a19”\u524d\u65b9”\u7684\u670b\u53cb\u8981\u518d\u7406\u89e3\u4e00\u4e0b Local \/ World Space \u7a7a\u9593<\/a> \u5594,
\u8981\u5617\u8a66\u628a\u81ea\u5df1\u4ee3\u5165 “\u524d\u81c2” \u7684\u89d2\u5f0f\u4f86\u8003\u616e\u5230\u5e95\u76f8\u5c0d\u7684\u89d2\u5ea6\u662f\u751a\u9ebc.<\/p>\n
\u591a\u5c64\u8f49\u5411\u6d88\u9664\/\u6e1b\u6cd5 (\u8aa4)<\/h3>\n
\u5728\u904b\u7b97\u4e0a, \u5982\u679c\u53ea\u6709\u758a\u52a0\u7684\u8a71\u5fc5\u7136\u5e0c\u671b\u6709\u6e1b\u6cd5\u7f77,\u4f46\u662f\u55b2 \u56db\u5143\u6578\u5c31\u53ea\u6709\u4e58\u6578.
\u6240\u4ee5\u6211\u5011\u600e\u6a23\u4ee5\u4e58\u6578\u4f86 “\u6d88\u9664” \u67d0\u500b\u7279\u5b9a\u7684\u8f49\u5411\u5462?!
\u7b54\u6848\u662f\u628a Quaternion \u9019\u500b\u77e9\u9663\u53cd\u8f49 (Inverse)
\u8a3b: \u4e26\u4e0d\u662f\u628a x,y,z,w \u53cd\u8f49\u554a… \u662f\u628a\u77e9\u9663\u53cd\u8f49.<\/p>\n
\u5047\u8a2d Quaternion A, B
\u6211\u5011\u76f8\u7b97 A – B \u7684\u8a71\u61c9\u8a72\u662f\u5beb\u6210
Quaternion answer = A * Quaternion.Inverse(B);<\/p>\n
\u76f8\u4e58\u9806\u5e8f\u7684\u7279\u6027<\/h3>\n
\u56db\u5143\u6578\u8f49\u5411\u662f\u6709\u9806\u5e8f\u7684 a * b \u8ddf b * a \u7684\u610f\u7fa9\u4e0d\u76f8\u540c,<\/p>\n
\u7c21\u55ae\u4f86\u8aaa Quaternion \u7684\u758a\u52a0\u6b21\u5e8f\u662f\u5f9e\u53f3\u5230\u5de6\u4f86\u770b\u7684.
\u800c\u540c\u4e00\u6642\u9593\u6211\u5011\u5beb\u7b97\u5f0f\/\u7a0b\u5e8f\u591a\u662f\u5f9e\u5de6\u5230\u53f3\u7684\u5beb\u7684\u5f88\u5bb9\u6613\u5c31\u72af\u4e86\u932f\u8aa4.
\u4ee5\u4e0a\u9762\u624b\u81c2\u7684\u8209\u4f8b\u4f86\u8aaa\u660e,
“\u524d\u81c2”\u5148\u8f49\u5411\u4e0a\u65b9, \u7136\u5f8c”\u4e0a\u81c2”\u624d\u8f49\u5230\u4e0b\u65b9.<\/p>\n
\u6211\u5011\u4ee5 C# \u8868\u73fe\u518d\u770b\u4e00\u4e0b\u8f49\u5411\u7684\u95dc\u4fc2<\/p>\n
Quaternion parent; \/\/ \u7236\u5c64\u8f49\u5411
Quaternion child; \/\/ \u5b50\u5c64\u8f49\u5411
Quaternion combine; \/\/ \u6700\u7d42\u8f49\u5411<\/p>\n
1) combine = parent * child;
\u5728\u9019\u88e1\u8aaa\u660e\u7684\u662f \u5148\u8f49\u52d5 child, \u7136\u5f8c\u518d\u8f49\u52d5 parent<\/p>\n
2) child == parent.Inverse() * combine;
\u7531\u525b\u525b\u7684\u7b54\u6848(Combine)\u4e58\u4e0a parent.Inverse()\u5373\u662f\u53d6\u6d88 parent \u7684\u610f\u601d.
\u56e0\u70ba\u5168\u5beb\u61c9\u8a72\u662f child = parent.Inverse() * parent * child;<\/p>\n
3) parent == combine * child.Inverse();
\u540c\u7406\u8981\u7531combine \u89e3\u62c6 parent \u7684\u8f49\u5411\u5c31\u9019\u6a23.
\u56e0\u70ba\u5168\u5beb\u61c9\u8a72\u662f parent = parent * child * child.Inverse();<\/p>\n
Reference :<\/p>\n
https:\/\/en.wikipedia.org\/wiki\/Quaternions_and_spatial_rotation<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u53d6\u5f97\u55ae\u4e00 Quaternion \u7684\u67d0\u500b\u65b9\u5411(Direction – vector)? \u7531 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[78],"tags":[74],"class_list":["post-2311","post","type-post","status-publish","format-standard","hentry","category-math","tag-quaternion"],"_links":{"self":[{"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/posts\/2311","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/comments?post=2311"}],"version-history":[{"count":4,"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/posts\/2311\/revisions"}],"predecessor-version":[{"id":2316,"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/posts\/2311\/revisions\/2316"}],"wp:attachment":[{"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/media?parent=2311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/categories?post=2311"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.clonefactor.com\/wordpress\/wp-json\/wp\/v2\/tags?post=2311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}