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 exceptional …
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 $ …
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 2,579 被浏览
Quaternions: why does ijk = -1 and ij=k and -ji=k
about this "A right angle rotation about XX axis followed by an equal amount of rotation about Y corresponds to an overall effective rotation of 90∘90∘ about Z axis. So, ij=kij=k.". the usual three axis …
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轭的积等于 …
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 from one antenna is …
Confusion with getting a unit quaternion from two vectors
Jun 26, 2025 · Quaternions. For me, the quaternions are a 4D algebra $\Bbb H=\Bbb R\oplus\Bbb R^3$ and every quaternion is uniquely expressible as a sum of a scalar and a 3D vector. The product of …
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 coordinate systems, one …
rotations - Getting yaw, pitch or roll parts from a quaternion ...
Jun 21, 2020 · This quaternion means a rotation around an axis. I need to get/extract only one component of this rotation (only yaw, only pitch or only roll, or maybe combined).
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 ahead or …