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 …

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 …

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 …

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 $ …

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 …

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) …

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 …

where log/exp are the quaternion logarithm/exponential. If you can convert between rotation vectors (where the direction is the rotation axis and the magnitude is the angle) and …

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, …

Mar 7, 2020 · Convert the two orientations to versors also known as unit quaternions and rotation quaternions, using one of the methods described in the Rotation matrix Wikipedia article. Let's …