如何形象地理解四元数？ - 知乎
如何形象地理解四元数？ 关于 quaternion 的资料（包括网络教程与书籍）已经看过很多，但大脑内无法形成对 quaternion 的形象理解。 请问是否要对群论、四维赋范… 显示全部 关注者 …
Combining rotation quaternions - Mathematics Stack Exchange
If I combine 2 rotation quaternions by multiplying them, lets say one represents some rotation around x axis and other represents some rotation around some arbitrary axis. The order of …
How can one intuitively think about quaternions?
Oct 19, 2010 · Here is the intuitive interpretation of this. Given a particular rotation axis $\omega$, if you restrict the 4D quaternion space to the 2D plane containing $ (1,0,0,0)$ and $ …
Real world uses of Quaternions? - Mathematics Stack Exchange
The quaternion algebra shows there as a way of disentangling two Alamouti coded signals transmitted by a pair of antennas. The advantages come from the fact that even if the signal …
四元数和旋转 (Quaternion & rotation)
四元数 (quaternion)可以看作中学时学的复数的扩充，它有三个虚部。 形式如下： ，可以写成 具有如下性质： 设 ， ，则 3.2 共 轭四元数 一个四元数 的共轭 (用 表示)为 一个四元数和它的共 …
What does multiplication of two quaternions give?
Apr 13, 2013 · A nice thing is that multiplication of two normalized quaternions again produces a normalized quaternion. Quaternion inversion (or just conjugate for the normalized case) …
Concise description of why rotation quaternions use half the angle
Aug 5, 2015 · The idea of Hamilton was to find some generalization of this formula for three-dimensional rotations. The quaternions can do such a generalization identifying a $3D$ -vector …
How to convert a quaternion from one coordinate system to another
Jun 24, 2022 · I am trying to find a way of converting a quaternion from an arbitrary coordinate system to a fixed coordinate system that is used in my application. I have two different …
rotations - How do you rotate a vector by a unit quaternion ...
Do one quaternion multiplication and you rotate the circular component just that far around, and the quaternion axis gives you the rest of the location, and the fourth dimension says how far …
difference between 2 quaternions - Mathematics Stack Exchange
Mar 1, 2016 · Your terminology and symbolism are confusing. "Hamilton product" refers to the product of quaternions, and while vectors can be considered quaternions with 0 scalar part, …