# Questions tagged [quaternions]

For questions about the quaternions: a noncommutative four dimensional division algebra over the real numbers. Also for questions about quaternion algebras.

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### Calculating coordinates using an offset from an entity in 3D space knowing its position and rotation.

I am working on a game mod for FiveM which allows players to see bullet impacts and their angle of impact, and am trying to implement 'attaching' this evidence to objects which are not static. I have ...
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### 120 cell generated from quaternions

The two quaternions $\omega={1\over 2}(-1,1,1,1)$ and $q={1\over 4}(0,2,\sqrt{5}+1,\sqrt{5}-1)$ generate a finite group under multiplication with 120 elements that form the vertices of a 600 cell, ...
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### how to offset a rotation contained in a unit quaternion rotation from the origin of a rigid object.

I'm using Unity3D for a project. The way it handles sorting transformations is with a 3vector-unit quaternion-3vector "sandwich" (the 1st vector for position, the quaternion for rotation, ...
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### Real matrices commuting with quaternion matrices

This is an interesting question from a class I'm taking that I'm not really sure how to approach. It is known that we can define many embeddings of the quaternion algebra $\mathbb{H}$ in the real ...
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### Quaternions for coordinate frame rotation

I am attempting to switch over from Euler matrices to quaternions. Normally I am presented with a desired final orientation vector in the form of a unit direction and the angles of rotation to create ...
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### Find any or all Lipschitz quaternions corresponding to a given quaternion norm

In this answer, in response to the question "How to find $2+7𝑖$ from $53$?", user @Cocopuffs provided a reference to a Jacobsthal sum, which enables obtaining a Gaussian integer, based on a ...
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### About transforming angles from one coordinate system to another

Say I have a gimble's wanted direction (in elevation phi and azimuth theta) in coordinate system xyz. Now I'm rotating the gimbal it by r about the x axis, p about the y axis and q about the z axis to ...
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### Does there exist some isomorphism from $Q_8$ to $\Bbb Z_4 \times\Bbb Z_2$?

I am wondering if some direct decomposition exists for quaternion group. I think that I am mixing some things, but let me explain and ask for clarification, tips from your side to let me understand my ...
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1 vote
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### The commutator subgroup of real quaternion division ring

Let $\mathbb{H}$ be the ring of real quaternions and let $\mathbb{H}^*$ be the set of units in $\mathbb{H}$. Denoted by $[\mathbb{H}^*,\mathbb{H}^*]$ the commutator subgroup of $\mathbb{H}^*$. I want ...
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1 vote
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### Angle between two quaternions

I am struggling to get my head around what I believe should be a simple problem. I am getting a quaternion wxyz from an IMU (inertial measurement unit), I want to check the angle between the ...
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### Atan2 to unit rotation quaternion [closed]

In 3D space, I have an angle theta representing the orientation of the object. This angle is the result of the atan2 function. Using theta, how can I derive the unit quaternion which represents the ...