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
Feb 3, 2017 · 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. …
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 …
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 $ …
Concise description of why rotation quaternions use half the angle
Aug 5, 2015 · Every quaternion multiplication does a rotation on two different complex planes. When you multiply by a quaternion, the vector part is the axis of 3D rotation. The part you want …
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) …
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 …
Understanding quaternions - Mathematics Stack Exchange
May 27, 2020 · Of course adding two quaternions gives a quaternion, so algebraically this is clear. I don't really think it's clear geometrically, however, and with good reason: this is a very …
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 …
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, …