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

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-1
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0answers
15 views

Rotation addition with quaternions

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 ...
0
votes
0answers
10 views

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 ...
1
vote
1answer
32 views

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 ...
0
votes
0answers
11 views

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 ...
2
votes
2answers
20 views

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 ...
2
votes
1answer
12 views

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 ...
0
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0answers
16 views

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 ...
1
vote
1answer
29 views

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 $α$. ...
-1
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0answers
17 views

How does one convert between rotation pseudo-vectors and rotation matrices for any number of dimensions? [closed]

I already know the two and three dimensional cases but I want to know a generic formula. In two dimensions one just has one angle, $\theta$. And the rotation matrix is $\left[\begin{array}{cc} \cos ...
0
votes
2answers
17 views

Find real points of intersection of the equations algebraically [closed]

Can you help me to find pints of intersection of given system of equesions? Can't do it by myself. $xy + x - 2y + 3 = 0$ $x^2 + 4y^2 - 9 = 0$
0
votes
1answer
15 views

How to rotate in quaternions but for 2d version for arbitrary angle?

I am trying to understand the idea behind rotating in quaternions, but first I want to understand the math for 2d rotation. I saw some youtube videos, and I know that for 2D, a point in 2D can be ...
0
votes
1answer
32 views

Find unit vector given Roll, Pitch and Yaw

Is it possible to find the unit vector with: Roll € [-90 (banked to right), 90 (banked to left)], Pitch € [-90 (all the way down), 90 (all the way up)] Yaw € [0, 360 (N)] I calculated it without the ...
1
vote
0answers
6 views

To prove that a generator-candidate is sufficient to find all elements in $SO(3)$

I am attempting to prove that some sequential series of rotation axes $\mathbf{v}_1,\mathbf{v}_2,\ldots,\mathbf{v}_n\in\mathbb{R}^3$ is enough to generate all possible rotations when making a full ...
1
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0answers
28 views

Calculate Rotation and Translation Matrix to align elements of input matrix A to Target matrix B in 2d?

I have a matrix in 2D space; the matrix contains elements which I would like to translate into the center of the matrix. Then, I would like to rotate these elements (I mean the positions of the ...
4
votes
1answer
63 views

Quaternions: Why is the angle $\frac{\theta}{2}$? [duplicate]

The equation for creating a quaternion from an axis-angle representation is $$x'= x \sin\left(\frac \theta 2\right)$$ $$y' = y \sin\left(\frac \theta 2\right)$$ $$z' = z \sin\left(\frac \theta ...
0
votes
0answers
17 views

Davenport's Q-method (Finding an orientation matching a set of point samples)

I have an initial set of 3D positions that form a shape. After letting them move independently, my goal is to find the best rotation of the original configuration to try to match the current state. ...
2
votes
1answer
29 views

rotation to quaternion matrix handeness

I've understand that quaternions do not have handness but rotation matricies derived from unit quaternions does. The following formula is given by wikipedia for quaternion to rotation matrix ...
0
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0answers
24 views

Trying to develop a formula for relative angle relationships in fixed space

Fixed space is defined relative to origin $(0,0,0)$. Fixed space has an origin with angles $(0,0,0)$ as well. A particle $P$ has $(x,y,z)$ coordinates relative to the origin: $P_x$, $P_y$, and ...
0
votes
0answers
23 views

If a sphere is rotated so that $90°$N $0°$E is transformed to $50°$N $6°$E, to which point is $18°$N $77°$E transformed?

If a sphere is rotated so that point $90°$N $0°$E is moved along a great circle to point $50°$N $6°$E, to which point is point $18°$N $77°$E moved? $90°$N $0°$E $\implies 50°$N $6°$E $18°$N $77°$E ...
0
votes
2answers
42 views

Closed-form solution to 3D vector rotation problem

Let $v_1$, $v_2$, $v_3$, $v_4$ be four unit vectors starting at the origin. The vector $v_1$ (in red) is unknown, however the angle $\theta_2$ between $v_2$ and $v_1$ is known. The vector $v_1$ is ...
1
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0answers
22 views

Normalizing disturbed rotation matrix

I was playing with simulations of Euler's equations of rotation in this question. This involves integrating an ordinary differential equation of a rotation matrix, $R$, which is calculated for all of ...
1
vote
1answer
50 views

Reach all possible rotations parametric to time.

I was recently playing with a CAD 3D modelling program. Once you rotate a part using the mouse and let go, it keeps rotating the part using the rotation matrix provided by the mouse input. The ...
1
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0answers
30 views

How to integrate 3D rotations (orientations)?

What is the 3D rotation equivalent of integrating (or a simpler version of the problem, simply evaluating or enumerating) all the values? For example in one dimension we have the possibility of an ...
3
votes
1answer
68 views

How to change between these two coordinate systems?

I have a problem with the coordinate system change between two 3D rotation sensors A and B. The coordinate systems have the same origin and are (mostly) perpendicular. I tested a somewhat pure ...
0
votes
2answers
20 views

Axes Rotation Problem

Given $$x^2 - 4xy + 5(\sqrt5y) + 4y^2 + 1 = 0$$ rotate the axes to eliminate the $xy$-term in the equation, then write the equation is standard form.
0
votes
0answers
12 views

Surface Area for a Curve Rotated Around the Y-Axis

I tried finding the surface area of a function rotated about the y-axis but I don't trust my answer. If I am looking for the surface area of a function y=f(x) rotated about the y-axis. $$S= 2\pi ...
0
votes
1answer
25 views

Calculating the next xy by applying a magnitude on a simple orbital path

I am trying to create a very simple 2D animation where a planet performs a very simple perfect orbit/rotation around a supergiant. The initial placement of the planet is random, with the only ...
0
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0answers
41 views

Meaning of “infinitesimal quantities” for angular velocity

In this question, Steven Stadnicki says that the sum of 3D angular velocities is commutative, even though the sum of 3D orientations isn't, because velocities are "infinitesimal quantities". I'm ...
0
votes
2answers
48 views

Type and mathematics of a spiral

Can anyone provide the name of a type of spiral described in the following, and a link to any description of the math that describes the spiral: It is like an Archimedean spiral but with one ...
0
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0answers
9 views

Understanding an elliptic rotation (linear transformation) with a epidemiological application

Currently working my way through this paper (http://eprints.maths.ox.ac.uk/375/1/157.pdf) and I'm having some trouble understanding this elliptic rotation. It begins by obtaining a difference ...
0
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0answers
84 views

Angular velocity computation

Say I have two different unit quaternion $Q1$ and $Q2$ representing two different orientations in 3D space. How can I compute the angular velocity $\omega$ that would produce a rotation from $Q1$ to ...
0
votes
1answer
34 views

How to extract an equation from transformation matrix multiplication?

I am trying to rotate a point in a 3D space in the 3 axis together around a specific origin point. Unfortunately I can't use matrices in my application,All I can do is just the basic math operations ...
1
vote
1answer
45 views

Obtain plane equation from the rotating angles that generated it

Consider an $(x, y, z)$ system where positive $x$ points to the right, positive $y$ points upwards, and positive $z$ points outside of the screen. I create a new system $(x', y', z')$ by applying two ...
1
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0answers
23 views

rotation of spherical surface in spherical coordinates

I need to plot a spherical surface in computer (like the surface of a lens). I know the normal vector (as an example, say $\ n=(1,2,3) $) of this surface and it originates from the centre of the ...
0
votes
1answer
12 views

rotate a scalar valued spherical function

I want to rotate a function $f(\theta,\phi)$ around an arbitrary angle in 3D space. (Assuming $\phi$ is in the $xy$ plane and goes from $0$ to $2\pi$, and $\theta$ starts from $+z$ and goes from $0$ ...
2
votes
0answers
47 views

Standard Basis of $SU(2)$--where does the 1/2 come from?

The most common matrix representation of $SU(2)$ is given by $$ \begin{pmatrix} a & b\\ b^* & -a^*\\ \end{pmatrix} $$ where $a,b\in\mathbb{C}$. If we denote real components by the subscript ...
-1
votes
3answers
33 views

Radians/second question [closed]

I'm stuck on this circle question that my cousin in high school asked me and basically, I need clarification on what I remember should be fine-> tire has radius of 42.5 cm rotating 3500 ...
0
votes
1answer
25 views

How to find the best rotation matrix between two Gaussian random variables?

My question is really simple, given two paired sets of points $\{x_i\}$ and $\{y_i\}$ defined in an N-dimensional space $\{(x_1,y_1), (x_2,y_2), ..., (x_n,y_n)\} \in {\rm I\!R}^N \times {\rm I\!R}^N ...
2
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0answers
23 views

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 ...
0
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0answers
18 views

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 ...
0
votes
1answer
11 views

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 ...
0
votes
1answer
22 views

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 ...
4
votes
1answer
83 views

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 ...
0
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0answers
27 views

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 ...
0
votes
1answer
58 views

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 ...
1
vote
1answer
32 views

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 ...
1
vote
1answer
55 views

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 ...
2
votes
0answers
24 views

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 ...
0
votes
1answer
38 views

How to tumble a camera about a point

I'm trying to implement camera tumbling as described by this document. I have a camera that defines a view position and orientation. Additionally, there is a center of interest, which is a distance ...
2
votes
1answer
21 views

Rotation of Rectangle Based on a Triangle in 3D Space

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 ...