# Tagged Questions

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

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### How to decompose a unit quaternion into 3 Tait-Bryan quaternions instead of 3 real numbers?

I'm familiar with the formulas for decomposing a unit quaternion $Q$ into chained Tait-Bryan angles $\phi\theta\psi$ (Wikipedia has the formulas for the $zyx$ chain here), but I'm looking to instead ...
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### Relative positioning using quaternions

Say I have quaternion $q_1$, which I have achieved from my IMU module. I want to state that current position is $initial$. Then I want to compute Euler angles relative to this initial position at the ...
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### What algebra do you get if you switch the sign of one pair of anticommuting quaternion products?

What are the properties of an altered quaternion algebra defined by: ii = jj = kk = -1, ij = -ji = -k, ik = -ki = +j, jk = -kj = +i, Is it associated with any manifold?
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### Extract the angle of rotation from a unit quaternion

Sorry for boring you my friends before the spring vacation. I am haunted by a simple problem of how to extract rotation angle from a unit quaternion. Suppose $a$ is a unit quaternion which takes the ...
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### Quaternion for beginner

QUATERNION ROTATIONI have 2 points in 3d space ,point A= <5,3,6> and B=<8,2,3> I want to rotate "point B" by 30 degree from point A. how do I solve this question using quaternion. Plz, ...
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### Quaternions and Rotations [duplicate]

I have 2 points in 3d space ,point A= <5,3,6> and B=<8,2,3> I want to rotate "point B" by 30 degree from point A. how do I solve this question using quaternion. Plz, explain the steps....
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### Calculate ψ knowing object orientation in 3D through forward and up vector

I've got a so called right, up, forward tridimensional reference plane and an object $P$ in it. Its orientation in space is defined by two vectors, forward and up: -forward gives azimuth $θ$ and ...
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### Translation offset when converting Matrix to Dual Quaternion skinning

i have a problem with dual quaternion skinning. if i convert my matrixes to dual quaternions i have a fixed offset from the bones (rotation is correct). if i transform everything with identity, than ...
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### Every Hamiltonian group contains a subgroup isomorphic to $Q_8$

I read somewhere that every Hamiltonian group (a non abelian group with every subgroup normal) contains a subgroup isomorphic to quaternion group. But I cannot find its proof anywhere on net or in ...
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### difference between 2 quaternions

I'm trying to calculate quaternions relative to a given orientation. It is easiest for me to explain my intentions by means of an example: Suppose you have a vector $v1=[0,0,1]$ and I want to rotate ...
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### Proof of quaternion algebra being simple using norm

I was wondering if the following simple (pun unintended) proof of the quaternion algebra $A=\left(\frac{a,b}{F}\right)$ being simple is valid. I saw many more complicated proofs online, eg: Proof ...
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### Check that $u_4\bar{u_3}u_2\bar{u_1}=i$ and $\bar{u_1}u_2\bar{u_3}u_4=1$ so the product of the four reflections is indeed $q \to iq$

This is an exercise from "Naive Lie Theory" and $u_1, u_2, ...,u_4$ are the unit quaternions. I have read the section many times but still don't understand. Can someone explain the material and solve ...
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### Understanding rotations of $\mathbb{R}^4$ and pairs of quaternions, showing a rotation is a product of reflections in hyperplanes

I am working through Stillwell's "Naive Lie Theory" and am completely stumped by the questions in this section. An example of one of the questions is Show that the rotation that sends $1$ to $i$, $i$...
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### Book(s) on Algebras (Quaternions)?

Well, lately I've been looking for a book on quaternions but I've realized that quaternions are a particular case of the named Algebras(I think Geometric Algebra). Since here, I've found all kind of ...
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### Elements of order 2 in the special linear group

I am trying to show that the unique Sylow $2$-subgroup of the special linear group $SL(2,\mathbb{F_{3}})$ is isomorphic to the quaternion group $Q_{8}$. Call the unique Sylow $2$-subgroup $P$, and ...
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I'm implementing a extended Kalman filter using quaternions. I've extended this paper to deal with my custom observations. My state space is analogous to the one in the previous paper : $\mathbf{... 1answer 29 views ### Problem with converting rotation representations (quaternion, axis-angle, etc) I have a computer device - a 3D pointer (Sensable Phantom Omni). It returns cartesian position (X,Y,Z) and orientation quaternion (x,y,z,w). Now I have a 3D visualization software (PyMOL) and I need ... 1answer 24 views ### Quaternion for transforming one frame to other? I am new to quaternions and learning how they can replace rotation matrices. I know that we can use rotation matrices to describe a transformation from one frame to other. Where one may be a rotated ... 1answer 105 views ### Convert quaternions to xyz degrees I knew quaternion for the first time a few days ago and I still don't get the way it works even when reading explanations. All I want to do is to make a subtraction between two quaternions and convert ... 0answers 22 views ### How do I calculate Jacobian of formula containing quaternions and vectors? I am facing a problem in robotics where a robot is localized in 3D-space to build up a map simultaneously (see SLAM, e.g. [1]). One approach is to build up a graph of poses$x_i$and transforms$z_{ij}...
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My task is: "Describe rotation $S \circ R$ by axis and angle, where $R$ is rotation around $(0,1,1)$ by 90 degrees, and $S$ is rotation around $(1,-1,0)$ by 90 degrees." I should use quaternion ...
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### Quaternion - Angle computation using accelerometer and gyroscope

I have been using a 6dof LSM6DS0 IMU unit (with accelerometer and gyroscope). And I am trying to calculate the angle of rotation around all the three axes. I have tried may methods but not getting the ...
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### Extracting the Axis a Quaternion is rotating around from the Quaternion itself Directly

Quaternion has components X, Y, Z, and W. If you created a Quaternion with input being a 3D Vector representing the axis (X,Y,Z) and a floating point number representing the amount to rotate around ...
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### multiplication of quaternions is like complex numbers multiplication?

Suppose $p = z + j w$ where $z = x_0 + i x_1$ and $w = x_2+ix^3$. Let $q = \alpha + j \beta$ where $\alpha = y_1 + i y_2$ and $\beta = y_2 + i y_3$. How can we multiply $p$ and $q$. Is is just like ...
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### calculating the orientation of an object

If you have a rotation matrix (or an attitude/direct cosine matrix, which are all synonyms). This matrix actually transforms vectors from one reference frame to another. But if your goal is to know/...
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### What is the $\sqrt{-1}$ when working in a quaternion space?

I dont think I really need to elaborate, do I? If you know what quaternions are then you know there are several imaginary-value options to choose from, or axes, along which the $\sqrt{-1}$ may exist. ...
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### Rotation matrix between two similar cuboids using their upper sides ( and the planes defined by these sides)

I have two different images and with them an estimation of two planes ( defined in the same system). I would like to get the rotation matrix, quaternion or euler angles of a surface within this planes....