# Tagged Questions

This tag is for questions about *rotations*: a type of rigid motion in a space.

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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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### Translate and Rotate mesh

I have a mesh constituted of some vertices in 3d space, let's call them $(x_1,y_1,z_1),(x_2,y_2,z_2),\cdots,(x_n,y_n,z_n)$. The mesh's central point is $(0,0,0)$. How to find out the new coordinates ...
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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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### How to rotate a 3D object, using only local x-, y-, and z-rotations, so that it always faces a camera at the origin

I have been struggling with a difficult problem involving 3D rotations. I first came across this problem in a computer science context, but I've attempted to generalize it a bit before posting. (I ...
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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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### 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 ...
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### Translate Pitch and Roll Angles of Object to those at different Yaw

I have been trying to find a method to translate the pitch and roll angles of one object to those of another connected object at a different yaw - i.e I have an IMU mounted on a quadcopter frame and a ...
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### Conjugating rotation by another rotation

If $g ∈ \mathrm{SO}(3)$ is the rotation about axis $p$ by angle $α$, and $h$ is a rotation mapping $p$ to another line $q$, then $g$ conjugated by $h$ is the rotation about $q$ by the same angle $α$. ...
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### Alternative to affine space

I've been reading up on affine geometry. An affine space (correct me if I'm wrong) is a set of "points" along with a set of translations on those points such that for any two points $P, Q$ there ...
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### How to calculate RPM from xyz arbitrary rotation?

As the title suggests, how can I calculate RPM of a Rigid Body that is arbitrarily rotating through the world? (It's rotating on all axies.) (sp) I have seen lots of 2d implementations but nothing ...
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### Find the Volume when region is rotated around unknown vertical line

A region is bounded by the $y = 0$, $x = 1$ and $y = arctan(x)$. This region is rotated around a vertical line $x = b$, where $b > 1$. The solid formed has $Volume = 5$. To solve the problem, I ...
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### Calculate position of object rotating around an axis

I have the value θ with range [0, 360] of the object rotating about the y-axis pictured below. Given a certain radius ...
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### Is every linear operator which is $SO(n)$-invariant necessarily isotropic?

Let $M_n$ be the vector space of $n \times n$ real matrices. We say a linear operator $\alpha:M_n \to M_n$ is hemitropic* if: $(*) \, \, \alpha(S^TXS)=S^T\alpha(X)S \, , \, \forall S \in SO(n)$ and ...
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### Solving the Rotation Differential Equation when the reference frame itself is rotating

Consider the three-dimensional general rotation differential equation $\mathbf{\dot{R}}_{b}^{i} = \mathbf{{R}}_{b}^{i} [{\boldsymbol{\omega}_{ib}^{b}}]_\times$ where $i$ is an inertial frame of ...
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### Rotations via Rotors

I am reading this PDF and have a question regarding an example which is given page $9$ with regard to using rotors to perform rotation. I made screenshots for reference: As the text suggest we ...
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### Is there a relationship between Rotors and the Rodrigues' rotation formula

I am trying to understand quaternion in general, and it seems like the path to making sense of how they actually work is to first understand rotors and other techniques related to rotations. By ...
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### How do I rotate a triangle in a graph? [duplicate]

I am trying to rotate this triangle 45degrees counter-clockwise, how do I do that? A = 4,5 (point of rotation (the one that does not move)) B = 4,1 C = ~2.8,1 what is: A', B', C'? I want points ...
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### Rotors/Quaternions: double reflection question

I am trying to learn/understand quaternion. I found this reference (among many others): http://www.geometricalgebra.net/quaternions.html It states (see attached screenshot of that page), that to ...
I am trying to transform a rectangle centered at the origin and dimensions of $(\| P_2 - P_1 \|, 0, \| \mathbf{V_P} \|)$ to a triangle in 3D space with points $P_0$, $P_1$, and $P_2$ where ...