0
votes
2answers
26 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
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
19 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}\\ ...
2
votes
2answers
51 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. ...
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 $Y$, ...
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 $R$?
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 ...
0
votes
3answers
58 views

Does R' = R*R'*R^(-1) hold?

Given two 3D rotation matrices ($3\times 3$) $R$ and $R'$, does this equivalence hold?: $R' = R*R'*R^{-1}$ My intuition tells me so, but I can't find a formal proof for it. Thanks.
2
votes
1answer
22 views

proof for euler-rodrigues formula - matrix form

I need for a matrix representation. Exactly I want to know how to get the Euler-Rodrigues formula in a matrix form like here. Thanks!
2
votes
1answer
28 views

Eigenvectors of this matrix - what's the relation to rotation operator?

I have found the eigenvalues to be 0, 1 and 2. The corresponding eigenvectors are: $\frac{1}{\sqrt 2} (1 , -1, 0)$ and $(0, 0, 1)$ and $\frac{1}{\sqrt 2}(1, 1, 0)$. I found that when $x^2 + 2xy + ...
2
votes
2answers
202 views

Rotate Existing Vector

Hello and apologies if the title of the question is not very precise. Question: I am reading the document talking about the simulation of photons in tissues using a Monte Carlo simulation. The exact ...
0
votes
2answers
41 views

Rotation counterclockwise

Let $A_{\theta}$ be rotation counterclockwise by $\theta$ as follows: $$A_\theta = \left[ \begin{matrix} \cos(\theta) & -\sin(\theta)\\ \sin(\theta) & \cos(\theta)\end{matrix} \right]$$ ...
0
votes
0answers
28 views

How do I do the math necessary to make these five matrices multiplied together equal the result shown?

I'm currently studying the math involved with rotating vertices around an arbitrary axis in 3D space. For this, I have found the following page to be very helpful: ...
0
votes
1answer
30 views

Find the Axis of rotation of rotation matrix $K$ after solving $(K-I)v=0$

$$K=\ \begin{pmatrix} 0 & 0 & 1\\ -1 & 0 & 0\\ 0 & -1 & 0 \end{pmatrix}$$ Find the axis of rotation for the rotation matrix $K$. This is from my previous thread click here ...
0
votes
2answers
62 views

Find the axis of rotation from the rotation matrix.

This is a problem from the book "Mathematical Methods in the Physical Sciences" Third Edition by author Mary L. Boas. on page 129, Example 5, just in case any of you are familiar with it. So I ...
0
votes
1answer
47 views

How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
0
votes
0answers
20 views

How to nullify one of the axises rotation in a rotation matrix?

Let's say that I've got a matrix with some rotation stored. Now I wan't to somehow make an Y rotation equals 0 (or rather make it equal to the starting moment without rotation). How would I do it? I ...
0
votes
2answers
38 views

How do I calculate the inverse of these matrices?

In learning how to rotate vertices about an arbitrary axis in 3D space, I came across the following matrices, which I need to calculate the inverse of to properly "undo" any rotation caused by them: ...
0
votes
1answer
56 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
0
votes
0answers
28 views

How to move coordinate systems using rotation matrices.

I am having some trouble with this question. I understand that the rotation matrix will be 4x4 and that the first 3 columns will just be $u$, $v$ and $n$ transposed but I dont know what I am ...
0
votes
2answers
327 views

How to rotate a matrix by 45 degrees?

Assume you have a 2D matrix. Ignore the blue squares. The first image represents the initial matrix and the second represents the matrix rotated by 45 degrees. For example, let's consider a ...
1
vote
0answers
43 views

If matrix $M$ represents rotation around the origin, how to represent rotation about another point in terms of $M$?

For homework from school I have to made some tasks. There are no lessons because it is a second change. my question is: Multiplication by matrix $M$ represents rotation around the origin. If we do ...
1
vote
0answers
21 views

Rotating two objects

I have two lines. Both created in this format: Line 1 $$line1 = \left\{ \begin{array}{c} startX, startY \\ endX, endY \end{array} \right\}$$ $$line2 = \left\{ \begin{array}{c} startX, startY \\ endX, ...
0
votes
0answers
75 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
0
votes
2answers
60 views

Rotation of Matrices and their interpretation

Given are now two matrices and I have to discuss what the given functions are doing (geometrically). Maybe you can revise/add the following: given are the matrices $ A = \begin{pmatrix} \cos(a) ...
1
vote
1answer
88 views

Obtaining rotation matrix from Euler angles if all three rotations happen at once. Does order of multiplication matter?

I'm having a problem getting my head around Euler Angles. Specifically if I wish to obtain a rotation matrix for a system where pitch, roll and yaw have all changed at once by various values... how ...
7
votes
4answers
191 views

Geometry of the Cayley Transform

I'm trying to understand the geometry of the Cayley transform. Suppose I have a $3 \times 3$ rotation matrix $R$ (i.e an orthogonal matrix with determinant equal to $1$). Let's ignore the corner case ...
0
votes
1answer
51 views

Describing Cartesian transformations in Cylindrical Polar Coordinates

I have a question about converting functions defined in Cartesian coordinates to a cylindrical polar system. The particular coordinate transformation that I'm reading about is: \begin{equation} ...
1
vote
2answers
147 views

Combine a rotation matrix with transformation matrix in 3D (column-major style)

I'm trying to concatenate a rotation matrix with a 4x4 homogeneous transformation matrix with column-major convention. I want this rotation matrix to perform a rotation about the X axis (or YZ plane) ...
0
votes
2answers
338 views

Transformation Matrix for rotation around a point that is not the origin

I need to find the matrix that rotates an arbitrary point around $\begin{bmatrix}5 \\6\end{bmatrix}$ by 35* anticlockwise. I figure I need to first move the plane to centre it at the origin, perform ...
1
vote
1answer
142 views

How do you find angular velocity given a pair of 3x3 rotation matrices?

Let's say I have two 3x3 rotation matrices R1 and R2, each signifying rotation from the global frame to the local frame. I am also given the time difference t between these two matrices. How would I ...
0
votes
0answers
49 views

Rotation matrix of a frame with respect to the world frame given angular velocity

I am trying to solve a practice problem for my robotics class. Here is the question: A top is rotating around an axis A with $w_1$ rad/sec and the axis itself is rotating around the vertical with ...
1
vote
0answers
174 views

Reverse rotation back to original coordinates (Euler Angles)

so in the program I'm trying to write (still, it's a mathematical question) I have a set of coordinates and angles (Euler angles) which represent the place and orientation of an object in space, ...
0
votes
2answers
123 views

Given the degrees to rotate around axis, how do you come up with rotation matrix?

Given angles (in degrees) to rotate around, $x$-, $y$-, $z$-axis how does one come up with the rotation matrix? For example if you have a point $p$ represented by a vector, how do you rotate it by ...
0
votes
1answer
56 views

Find rotation angle of given image

At first: our aim is to find the total transformation of left house to the right house. What I did it first is translating the house with the center to the origin. I already found out that the ...
0
votes
0answers
81 views

How does orthonormal basis rotating work?

When you insert an orthonormal set into the column vectors of a matrix, you create a rotation matrix. I can't understand how this works, by simply placing the the vectors in there you have a rotation ...
3
votes
3answers
145 views

Why are orthogonal matrices generalizations of rotations and reflections?

I recently took linear algebra course, all the I learned about orthogonal matrix is that matrices is that Q transposed is Q inverse, and therefore it has a nice computational property. Recently, to my ...
0
votes
3answers
52 views

Getting $x,y$ position on an image based on given value

This should be simple but my math skills are really bad ... I have an image of 36 images (6 by 6 matrix). These small images are 36 instances of a direction arrow (like from Google maps GPS), each ...
0
votes
2answers
79 views

Matrix of transform rotation [solved]

Im trying to create matrix which rotates vector. I have $\vec{g}=(g_1,g_2,g_3);\:g_1\in\mathbb{R},g_2\in\mathbb{R},g_3\in\mathbb{R}$ - it represents gravitation. And $\vec{o}=(o_1,o_2,o_3)$ is vector ...
2
votes
1answer
78 views

Getting rotation matrix from a vector

I have a vector pointing in some direction and I'm trying to find a matrix $M$ that rotates the vector $v_1=(1,0,0)$ to $v_2=(x,y,z)$, i.e., $M v_1 = v_2$. What is $M$ if $v_1$ and $v_2$ are known? ...
1
vote
2answers
193 views

I've seen “hyperbolic rotation” - from this: generalization to multisection rotation: is this possible?

This question is more in recreational mathematics area By accident I came across the concept of "hyperbolic rotation" where we use a matrix containing $\cosh$ and $\sinh$ instead of the ...
0
votes
0answers
20 views

Resolving bearings for tilted structure (vector rotations)

I am trying to find a neat solution to resolving bearings for a tilted structure. For example, if I know that a hub is $268.74^{\circ}$ and offset ($X = -3.542 $m, $Y = -1.857$ m, $Z = 2.013$m) with ...
0
votes
0answers
97 views

Pointing a not stabilized camera using imu data and matrix rotation in the euclidean space

this is my scenario: I have a support with a pan/tilt camera and an imu. This support can be moved by changing the pitch, and roll. From the same position of the support, but independent from the ...
0
votes
0answers
168 views

Converting a 3x3 matrix to euler angles in various rotation orders

So let's say I have a 3x3 orientation matrix set up like: a b c d e f g h i which I have generated from euler angles in a left-handed, Y-vertical system. ...
1
vote
2answers
199 views

Rotation matrix in arbitrary dimension to align vector

I was sure it's going to be trivial to do, but then got stuck. Problem - given a vector $u\in\mathbb{R}^d$ in $d$ dimensions, find a rotation matrix $M$, such that (Rotation) $M^T=M^{-1}$, ...
0
votes
3answers
493 views

Rotation of matrices

I am doing rotation of matrices at the moment, I know that if I want to rotate a point, let's say (2,1) 90 degrees clockwise, I have to multiply the matrix [ 2 1 ] * [0 1, -1 0] , but how do I find ...
5
votes
0answers
82 views

Complex Numbers vs. Matrix

I have a line starting at the origin, and i extend it to a point $(a,b)$ in the plane. This thing can be called a vector and be represented as $(a,b), [a\text{ }b]^T$ (column vector) or by ...
0
votes
1answer
192 views

Step in Euler's rotation theorem

I have been examining the matrix proof for Euler's rotation theorem on Wikipedia. I have deduced every step up to proving that $\det (R - I) = 0$ for any rotation matrix R. However, I'm having ...
1
vote
2answers
181 views

Rotate rectangles in a rectangle

Is there a general and easy way to calculate the new x and y coords of the rectangles in the big rectangle if I rotate the parent rectangle about 90deg. I know the x and y coords of each rectangle in ...
0
votes
1answer
68 views

Mapping a plane in $\Bbb R^3$ to $\Bbb R^2$

I have three points that represent a rigid body. The rigid body undergoes a planar transformation in $\Bbb R^3$ due to rotation and translation. I am working with angular velocity with nonzero $\vec ...