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

learn more… | top users | synonyms

0
votes
0answers
3 views

Rotating a plane defined by a normal and a distance from the origin around an arbitrary point in 3D space

I have a plane defined by its normal and its distance from the origin. I have a rotation matrix and a point in 3D space around which to do the rotation. What formula will allow me to do the rotation? ...
1
vote
0answers
26 views

Cross product uniqueness

I have following relationship between vectors $A_1'(t)=\psi(t)\times A_1(t) \tag1$ $A_2'(t)=\psi(t)\times A_2(t) \tag2$ $A_3'(t)=\psi(t)\times A_3(t) \tag3$ Given Data " ' " means derivative ...
0
votes
4answers
53 views

Rotating Frame and Angular Velocity

We have an equation $ \frac{dr}{dt}=\Omega \times \bf r \tag 1$ SPECIFICATIONS $\times$ means cross product,$\Omega$ constant angular velocity,${\bf r}$ is the postion vector of an object Given ...
0
votes
2answers
37 views

Inverse of a Rotation matrix

If $R $ is a rotation matrix (determinant 1,orthonormal) can we say that $R^{-1}$ is also a rotation matrix? If yes how do we prove it?
0
votes
0answers
15 views

When do two configurations of points belong to the same Euler Equivalence Class?

When can I say, of two or more configurations of points in a plane, that they belong to the same Euler Equivalence Class? From Euler's rotation theorem, I gather that two configurations of points are ...
7
votes
1answer
105 views

Quaternion integration

If the angular velocity is changing continuously, the following holds true $ q(t)=q(0)\exp\left({\int_{0}^{t}\frac{q_\omega(\tau)}{2}\ d\tau}\right) \tag 1$ Specifications and Data $q(t),q(0)$ ...
0
votes
1answer
15 views

Rotating vector functions

Suppose you have a vector function of space: $\vec{E}(x,y,z)=Ex(x,y,z)\hat{x}+Ey(x,y,z)\hat{y}+Ez(x,y,z)\hat{z}$. Suppose now you want to rotate the whole vector function by using a unitary rotation ...
3
votes
1answer
42 views

Finding quaternion that transforms to particular basis

I want to find a quaternion $x \in{\mathbb{H}} $ that transforms (rotates) the $ i,j,k $ basis to a particular basis. In equations: $$ x i x^{-1} = a_1 $$ $$ x j x^{-1} = a_2 $$ $$ x k x^{-1} = a_3 ...
0
votes
0answers
32 views

Rotate a Vector Towards a Point [closed]

I was wondering, how would rotate a vector so it faces a specific point? This is in a 3d game world (where I want to rotate a character unit to face an enemy character unit). Thanks in advance EDIT: ...
2
votes
3answers
56 views

Calculate the area of the ellipsoid that rotates around the $x$-axis

So we are about to calculate the area of the ellipsoid around the $x$-axis. $$ \frac {x^{2}}{2}+y^{2} = 1 \implies x=\sqrt{2-y^{2}}$$ We are squaring it so the sign shouldn't matter. I was ...
0
votes
2answers
22 views

Rotate and translate a line so that it passes through two given points

I have 2 point and a line segment in 2d space. The line only rotates and translates using its mid point. How do I calculate the translation and rotation required for the line to be touching the 2 ...
0
votes
0answers
36 views

Rigid body rotation

The problem I am trying to solve is that I am trying to rotate a rigid body and align it to the X axis in 3D space. I have chosen two points on the body (p1, p2). First I move the coordinates to align ...
0
votes
2answers
27 views

Finding the matrix of a rotation.

I have to find the corresponding matrix for the following rotation: $R_ \frac{π}{4}$ (1,1) My general matrix formula is: $$\begin{pmatrix}1&0&h\\ 0&1&k\\ 0&0&1 ...
0
votes
0answers
23 views

Calculating rotated relative positions on 2D plane

For a game project, I need to calculate positions of items on a 2D plane relative to the camera. Camera can be rotated, and it's coordinates refer to it's center. In the attached images, ...
1
vote
0answers
7 views

Find path between two attitudes subject to body rate constraints

Here's my problem. I have an initial orientation and angular velocity of a body and a final orientation and velocity occurring at a specified time in the future. I have control over how input ...
0
votes
1answer
35 views

Everyday life examples of hyperbolic rotations

I'm trying to find some intuition in Lorentz transformations. I understand that they are basically rotations by imaginary angle of vector of the form $\{ict,x\}$ (for $1+1$ space-time dimensions), and ...
4
votes
1answer
102 views

How can I rotate a box?

So, to collide two ships together, I currently use: ...
0
votes
0answers
10 views

Convert Euler angles from one group of rotation axes to another

I have Z-X-Z Euler angles which I would like to convert to X-Y-X Euler angles. What would be the formula for that? The exact choice of source and target rotation axis is not important, I just wish to ...
-1
votes
2answers
53 views

How to check if an object is on the line of fire?

In my game all objects are facing right direction by default but they can be rotated and one of my object (let's call it "shooter") needs to know if any object is on its line of fire. If so, it ...
0
votes
0answers
2 views

How can I apply a median filter directly to a time-varying rotation matrix?

I need MatLab script which would take a series of rotation matrices (referring to an actual physical object's orientation) and apply median filter to it to eliminate speckle noise from it. The way ...
0
votes
1answer
20 views

How can I refer a 3D pose (position + orientation) to a different coordinate system?

I'm working on a robotics project where all poses and marker positions/orientations are stored as a matrix: $$ \mathbf{P} =\begin{bmatrix} \mathbf{R} & \mathbf{t}\\ ...
1
vote
2answers
47 views

Derive a quaternion from three axis

My problem originates from some code that I'm writing to parse an obscure file-type in which a geometric entity is defined in it's own 'local space', and a rotation and translation are provided to ...
2
votes
2answers
54 views

Solving for a Rotation Matrix Equation $R_1 R_\mathrm{x} R_2 = R_\mathrm{x}$

I would like to solve for an equation $R_1 R_\mathrm{x} R_2 = R_\mathrm{x}$ where $R_1$, $R_2$, and $R_\mathrm{x}$ are 3x3 rotation matrices, $R_1$ and $R_2$ are known, and $R_\mathrm{x}$ is unknown. ...
2
votes
0answers
64 views

Rotating a cube about an axis through opposite vertices

I have a cube made using CSS transforms that I'm trying to animate rotating about an axis going through 2 opposite vertices. What I have: Initial cube: ...
0
votes
0answers
20 views

How to prove that the Kronecker delta is the unique isotropic tensor of order 2?

Is there a way to prove that the Kronecker delta $\delta_{ij}$ is indeed the only isotropic second order tensor (i.e. invariant under rotation), i.e. so we can write $T_{ij} = \lambda \delta_{ij}$ ...
0
votes
0answers
23 views

How do I compute corners of geodesic rectangle?

I have the center of a rectangle as a latitude and longitude as well as the length of the sides in meters and the orientation in radians. How can I compute the ...
1
vote
0answers
36 views

Show that isotropic function S(A) and A have same eigenvectors

Given $\boldsymbol{A}$ is a positive definite, symmetric second order tensor and $\boldsymbol{Q}\boldsymbol{S}(\boldsymbol{A})\boldsymbol{Q}^T = \boldsymbol{S}(\boldsymbol{QAQ}^T)$ $\forall ...
0
votes
1answer
18 views

Coordinates rotation and function change

In the Cartesian coordinates $(x,y)$, I have a vector function $\bar{f}(x)=\hat{x}A\cos(yk)$, where $A$ and $k$ are constants. I make now a 45 degrees rotation (in the same plane) to the new set of ...
1
vote
1answer
58 views

How to find an angle in range(0, 360) between 2 vectors?

I know that the common approach in order to find an angle is to calculate the dot product between 2 vectors and then calculate arcus cos of it. But in this solution I can get an angle only in the ...
0
votes
1answer
22 views

Rotate $xyz$ by use of pitch and yaw around origin

I have a project for a game which uses pitch/yaw for the direction of a players head. The pitch ranges from $0$ to $180$ and the yaw is $0$ to $360$. Yaw modifies $X$ and $Z$, pitch modifies the $Y$, ...
1
vote
1answer
42 views

How do I rotate a rectangle of latitude and longitude?

I have a rectangle with its corners specified in latitude and longitude. I would like to rotate it about it's centre a certain number of degrees. I was using longitude as an x value and latitude as a ...
2
votes
1answer
25 views

Can I convert between a rotation about an axis and a rotation according to two angles (all in 3D) without solving a system of nonlinear equations?

I am writing a program that needs to be able to switch between a rotation described by 2 angles to a rotation described an axis and one angle. I found one way to do this from this question, which ...
1
vote
1answer
45 views

Rotated arc in $\mathbb{R}$ [closed]

We have got the arc $$A = \{(x,y) \in \mathbb{R} \mid x^2 + y ^2 = R ^2, 0 \leq x \leq R, 0 \leq y \leq R\}$$ and $R$ is positive real number. What is the area of ​​rotational figure obtained if ...
5
votes
1answer
38 views

Abstract question about the rotation in 3D [closed]

I've made the following observersations: Zero-dimmensional entities, points, don't really rotate. One-dimmensional entities, lines, rotate about a stationary point. Two-dimmensional entities, ...
0
votes
0answers
23 views

Stopping angular momentum to obtain a particular angle

While the overall project relates to software development, it boils down to a simple (i think) physics problem. I have a joint (a motor, pretty much.) that needs to move to a specific angle. I can ...
0
votes
1answer
61 views

Basic Eigenvalue Question

The rotation matrix $$T=\left[\begin{array}{c c}\cos\theta&-\sin\theta\\ \sin\theta&\cos\theta\end{array}\right]$$ has no eigenvectors as an operator $T:\mathbb{R}^2\to\mathbb{R}^2$. Here ...
0
votes
1answer
36 views

Rotation matrix of triangle in 3D

How can I find out the rotation matrix of a right angle triangle defined by 3 points in 3D space (assuming the un-rotated triangle faces the x axis)
0
votes
0answers
26 views

Find the angle of rotation about a vector caused by application of a rotation matrix

I have a rotation matrix $R$ and a unit vector $\mathbf{v}$. How can I find the angle of rotation about $\mathbf{v}$ caused by the application of $R$?
1
vote
1answer
58 views

Rotations - linear or quadratic?

In linear algebra rotations are represented by matrices, i.e. linear transformations How do you formally prove that rotation is a linear transformation? But this page is very interesting ...
1
vote
0answers
20 views

Eigenvalues of rotation invariant operators on 2-sphere

Work on $L^2(S^2)$, where $S^2$ is the 2-sphere. Suppose that I have an operator, $T$, that is rotation invariant. That is, $T$ commutes with $R$ for any rotation operator $R$. Suppose furthermore ...
0
votes
1answer
34 views

Rotating a point on a circle

The wheels on a bicycle have $r$-inch radii. After the front wheel picks up a tack, the bike rolls for another $d$ feet and stops. How far above the ground is the tack? I've been thinking about this ...
1
vote
0answers
21 views

Find bounding box dimensions around rotated object

Consider the following rectangle with dimensions 320 by 130. After rotating the rectangle 10 degrees clockwise from the center (x: 160, y: 65), it looks like this. My question is: How do ...
0
votes
1answer
32 views

What's the difference between these rotations?

1) Each point on the coordinate plane is rotated $\theta$ degrees about the origin. 2) Each point $P$ with the coordinates $(x,y)$ is rotated $\frac{\pi}{4}$ radians about the origin. The answer ...
0
votes
0answers
20 views

Rotation of point with infinite child objects. (Chain rotation)

More of a thought experiment here, knowledge for knowledges sake. Let's say you can create infinite points that rotate smoothly and at the same speed as each other through a full revolution - let's ...
0
votes
0answers
42 views

Angular displacement/speed of a rotating sphere from 3d points

I have 3d points on the surface of a unit sphere that describe every minute its rotation. I want to know angular velocity of this sphere. The sphere center is fixed and the axis of rotation can change ...
0
votes
0answers
35 views

Computing the coordinates of a point, offset from a rotated point.

Good day. I have a question which should be easy but I have not been able to figure it out. The coordinates of a point on a unit circle, given an angle, is $$\begin{align} x &= \cos(\alpha) \\ y ...
0
votes
1answer
23 views

Change of Eigenvalues of Ellipsoid Tensor during Rotation

I have an ellipsoid defined by the semiaxes $a,b,c$ and the orthonormal vectors $v_x, v_y, v_z$ describing the directions in which the axes point. The matrix ...
0
votes
0answers
16 views

Finding the smallest possible set of euler angles, without changing the end-rotation

Euler angles aren't unique, so one rotation can be represented through different combinations of pitch, yaw and roll. In my case I have a set of euler angles and I need to find out if there's a ...
2
votes
3answers
42 views

What kind of transformation an upper triangular matrix represents

Every matrix represents a linear transformation, but depending on characteristics of the matrix, the linear transformation it represents can be limited to a specific type. For example, an orthogonal ...
2
votes
0answers
25 views

Random Rotation of Points using Householder matrices

I have $N$ points in $D$ dimensions, were $D$ is big, for sure more than $100$. $N$ is also big. The goal is to produce an algorithm in my code, that will take as input this dataset and will give ...