Java 两个四元数旋转的点积
声明：本页面是StackOverFlow热门问题的中英对照翻译，遵循CC BY-SA 4.0协议，如果您需要使用它，必须同样遵循CC BY-SA许可，注明原文地址和作者信息，同时你必须将它归于原作者（不是我）：StackOverFlow
原文地址: http://stackoverflow.com/questions/21513637/
Warning: these are provided under cc-by-sa 4.0 license. You are free to use/share it, But you must attribute it to the original authors (not me):
StackOverFlow
dot product of two quaternion rotations
提问by Kent
I understand that the dot (or inner) product of two quaternions is the angle between the rotations (including the axis-rotation). This makes the dot product equal to the angle between two points on the quaternion hypersphere.
I can not, however, find how to actually compute the dot product.
我知道两个四元数的点（或内）积是旋转（包括轴旋转）之间的角度。这使得点积等于四元数超球面上两点之间的角度。
但是，我无法找到如何实际计算点积。
Any help would be appreciated!
任何帮助，将不胜感激！
current code:
当前代码：
public static float dot(Quaternion left, Quaternion right){
float angle;
//compute
return angle;
}
Defined are Quaternion.w, Quaternion.x, Quaternion.y, and Quaternion.z.
定义为 Quaternion.w、Quaternion.x、Quaternion.y 和 Quaternion.z。
Note: It can be assumed that the quaternions are normalised.
注意：可以假设四元数是归一化的。
采纳答案by user3146587
The dot product for quaternions is simply the standard Euclidean dot product in 4D:
四元数的点积只是 4D 中的标准欧几里得点积：
dot = left.x * right.x + left.y * right.y + left.z * right.z + left.w * right.w
Then the angle your are looking for is the arccosof the dot product (note that the dot product is not the angle): acos(dot).
那么你要找的角度就是arccos点积的（注意点积不是角度）：acos(dot)。
However, if you are looking for the relative rotation between two quaternions, say from q1to q2, you should compute the relative quaternion q = q1^-1 * q2and then find the rotation associated withq.
但是，如果您正在寻找两个四元数之间的相对旋转，例如从q1to q2，您应该计算相对四元数q = q1^-1 * q2，然后找到与 关联的旋转q。
回答by minorlogic
Just NOTE: acos(dot) is very not stable from numerical point of view.
请注意：从数字的角度来看，acos(dot) 非常不稳定。
as was said previos, q = q1^-1 * q2 and than angle = 2*atan2(q.vec.length(), q.w)
正如之前所说， q = q1^-1 * q2 而不是 angle = 2*atan2(q.vec.length(), qw)
回答by Murt Moriarty
Should it be 2 x acos(dot) to get the angle between quaternions.
应该是 2 x acos(dot) 来获得四元数之间的角度。
