The rotations tag has no wiki summary.
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Rotation invariant tensors
It is often claimed that the only tensors invariant under the orthogonal transformations (rotations) are the Kronecker delta $\delta_{ij}$, the Levi-Civita epsilon $\epsilon_{ijk}$ and various ...
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Understanding quaternions and axis angle representations
I have a sensor that gives me a quaternion. I convert the quaternion to an axis-angle representation using http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/. When I ...
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344 views
Convert from fixed axis $XYZ$ rotations to Euler $ZXZ$ rotations
Because I'm a new user, I can't post images or hyperlinks, there is a complete version with images here:
...
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43 views
3D rotation group
It is known that the group $\text{SO}(3)$ of rotation-matrices (matrices $A$ with det(A)=1)
are generated from three parameters. This can be expressed by the fact, that
any rotation matrix is a ...
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60 views
Desired Z axis and Yaw to ZXY Euler Angles?
I'm trying to calculate a desired pair of pitch and roll Euler angles (the XY in ZXY format) given a desired z-axis of the rotated frame (expressed in the world frame) and a specified yaw angle ...
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Help me to vizualise this falling ball on spinning Earth
The earth rotates. The ball falls in an latitude, not equator, let say in Germany. I am trying to understand how to express the ball in terms of the angular velocity on the planet. The constant ...
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178 views
Gimbal lock and zero jacobian determinant
I'm having a hard time visualizing the gimbal lock problem. Suppose $p=(a,b,c)$ is a point where the euler angle $f:\mathbb R^3\to SO_3$ has zero jacobian determinant. Then to say that $p$ is where ...
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4d rotations and quaternions
I have a question about 4d rotation:
I programmed a little 4d game and I used the classical hyper-sphere coordinates, to rotate a vector.
It works, but it has some problems :(
(just for clarity I ...
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246 views
What is the difference between a “change of basis” and a “similarity transformation”?
In crystallography we define a "misorientation", $M_{AB/A}$, as the rotation required to bring crystal A into coincidence with crystal B, as measured with respect to the reference frame of crystal A. ...
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38 views
Problems sampling from a $pdf$ over $SO\left(3\right)$
I have a probability density function over $SO\left(3\right)$, which I am trying to sample from. The $pdf$ is given as a generalized fourier series:
$$ f\left(\omega,\theta,\phi\right)=\sum ...
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23 views
Reverse of rotate a vector around an axis - Finding North with magnometer
I've been reading the wikipedia page on rotation matrices and I know the reverse (or at least a very related) version of this question has been asked many times before on this site. However my ...
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24 views
Optimimal rotation using non-linear conjugate gradient
The problem I'd like to ask is the following : let $M_1$ and $M_2$ two rigid bodies with a quadratic constraint function $f$ attached to its grid points. $M_2$ is always kept static while $M_1$ can be ...
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51 views
Euclidean Transformation
Given 2 squares in the same plane join any corner of one square to a corner of the other square. Continue joining corners going in the same direction(clockwise or anticlockwise). Using only rotation, ...
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Compute the covariance of $R_2 R_1^T$ where $R_2$ and $R_1$ are rotation matrices with Gaussian uncertainty
I have estimates of two 3x3 rotation matrices $R_1$, $R_2$ expressed in terms of their expected values $R_{1\mu}$ and $R_{2\mu}$ and covariances $\Sigma_1$, $\Sigma_2$. The latter are expressed in the ...
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225 views
Sequence of Euler (yaw/pitch/roll) rotations?
I'm an android programmer and I have a problem that it's base is in about Mathematics.So excuse me if it is very easy ,abstract or bad formatted.But I need a simple ...
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180 views
Rotating co-ordinates in 3D
Suppose I have 3 axes, $x$, $y$, and $z$ such that $x$ is horizontal, $y$ is vertical, and $z$ goes in/out of the computer screen where $+$ve values stick out and $-$ve values are sunken in.
Suppose ...
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533 views
Visualizing elemental rotations using Euler angles in Matlab
I'd like to visualize elemental rotations using Z-Y-X convention in Matlab. If you'd like to follow me exactly, I'll be refering to a paper Quadrotor Dynamics and Control by Randal Beard.
The base ...
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Complicated triple integral
I have a Euclidean geometric problem whereby the triple integral over SO(3) I am trying to solve seems to confuse many CAS softwares (including Maxima and Mathematica). The problem is
$$
a = ...
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What's rotation matrix minus its transpose?
In a paper I've been reading ("Non-linear complementary filters on the special orthogonal group", Robert Mahony et al. link: warning PDF) there is an operation:
$P_a(\tilde{R}) = \frac{1}{2} ...
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181 views
Rotate a 2D square by x degrees
Say I have a square represented by the following matrix:
0 0
10 0
10 10
0 10
0 0
Now, what would I multiply this matrix by to rotate the square (or what ...
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121 views
Projection of the area of a bounded plane over other bounded plane
I have two bounded planes $\pi$ and $\rho$ in three dimensional space. Each plane is bounded by a coplanar rectangle. How can I find the orthogonal projection area of $\pi$ over $\rho$?
Thanks in ...
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Quaternion exponential map, rotations and interpolation
A code snippet I need to optimize is performing something peculiar. It seems that it's somehow related to transforming from a frame of reference to another. This is what it does, in mathematical ...
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Transformation into cartesian coordinates
I need some help with specific transformations and rotations.
But first, I need to describe context.
Imagine two points in space situated at $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ respectively. In
a ...
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When to use Oblique and Orthogonal rotation in EFA?
I am quite confused on when to use oblique and orthogonal rotation in EFA. I have read from articles that orthogonal is more preferred than oblique rotation, because it is widely used. But some say ...
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Differentiation of Rotation Matrix
I have some troubles on differentiating a time-varying rotational matrix $R(t) \in SO(3)$. If I use a axis-angle representation with the Rodrigues formula we have:
$R(t) = \exp(\,A(t) \theta(t)\,) = ...
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Fnd rotation and translation matrix with specific normal
I am try to find the rotation and translation matrix between my coordinate system [0,0,0] with the vectors [1,0,0],[0,1,0],[0,0,1] to some point ps=[x,y,z]
I have eqaution of ball : ...
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How to find the transformation of an arbitrary vector R when rotated an angle of phi about another arbitrary vector N?
I have a vector R which i an supposed to rotate it by an angle phi about another vector N, what is the corresponding transformation in three dimensions?
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Proving equivalence intrinsic extrinsic rotations
Rotations can be generated by skew symmetric matrices $[v]^{\times}$ as:
$$
R = e^{\theta[v]^{\times}}
$$
Where $v$ is the normalized axis of rotation and $\theta$ the angle of rotation. Using this ...
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127 views
Pattern for extracting euler angles from a rotation matrix
There must be some kind of pattern when converting from one euler angle sequence to another, for example, if I were to convert from ZXY to ...
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94 views
Rotating a system of points to obtain a point in a given place
Given an arbitrary number of points which lie on the surface of a unit sphere, one of which is arbitrarily <0, 0, 1> (which I will call K) in a rotated system ...
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46 views
Special values for 3D rotations matrices
I wanted to know if there are other "special" angles when using the rotation matrices in 3D. Looking at them I see that if the value of $\theta = 0$ or $\theta = 2\pi$ then the rotation matrices are ...
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Procedural pipe building in 3D - given current pipe and direction of flow next, determine dir of next pipe
I'm trying to create an intuitive pipe-building system, but I can't seem to formulate the algorithm more elegantly than too many conditionals. I wonder if there may be a two-line algorithm for this.
...
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Unknown depth issue: Triangle, Pyramid, Rotation, Translation, Zoom?
Edit: Had to delete the 2nd picture
Another tricky question. What you can see here is my physical pyramid built with 3 leds which form a triangle in 1 plane and another led in the mid center, about ...
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Determining a point in 3D space
So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). ...
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Rotate a triangle to next 'visible' side
I have a triangle along the y/z axis (I can only see the flat side facing me).
How do I rotate it around the x axis so that the next side faces me?
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How to relate $S^1$ (SO(2)) to a stretched version of $S^1$ ($SO(2) \subset SO(3)$)?
I want to decompose the quaternion parameterization of $SO\left(3\right)$ into the subspace of $SO\left(2\right)$ defined by choosing the z-axis as the rotation axis, and find a relationship between ...
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Rotation around x-axis reverses direction when theta is negative
I am currently trying to simulate rotations of a 3d model in a C++ problem, but am a bit perplexed by the behaviour of my program. I had considered posting this in stackoverflow.com, but the problem ...
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What are the other elements that stabilize a body diagonal of a cube besides the group of rotations about that diagonal?
I am trying to understand why the order of the stabilizer group of a body diagonal of a cube is 6 rather than 3. It is clear to me that rotations about that diagonal stabilize the diagonal, by ...
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Change the center of rotation of a square
I have a square rotated relative to his center and I know the angle of rotation.
How to calculate the angle of rotation relative to his upper left corner?
For example I have a square rotated around ...
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259 views
Calculating normal vector to a rotated plane
Forgive me if this isn't well phrased, it's been a while since I've done any maths!
I have a 2d image whose central point is located at the world origin, and it is in the plane $z = 0$.
If I rotate ...
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103 views
translation matrices
If I have a parametric function like this $x=t+2$ and $y=t^2$ the parabola is shifted two units to the right.
How do I translate it back to the origin?
Is this the matrix?
$$\begin{pmatrix} 1 & ...
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415 views
Explicit calculation of 3x3 rotation matrix from combining three angle-unit axis rotations?
I need to remove dependence on a programming library from a computer application I'm working on and instead hand code a geometric operation. Please can you show explicitly (for someone with little ...
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221 views
rotation and converting between coordinate systems
Let's say you have coordinates 'a','b','c','d' in the coordinate system (x,y), and it needs to be transformed to coordinates 'e','f','g','h' in the coordinate system (x',y').
Example
...
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130 views
Converting global coordinates into set of local matrices for ik skeleton creation
I have the 3d global positions of a set of joints as they move over time and the ik skeleton structure which relates them. I am currently writing some code to convert this information in .bvh file. I ...
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Composition of intrinsic rotations yaw, pitch, roll.
I am using the æronautical meanings of yaw, pitch and roll (intrinsic rotations, not extrinsic). Say I know the yaw ($=\theta_z$ radians about the intrinsic $z$ axis of an object), pitch ($=\theta_x$ ...
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Measuring rotation about an axis
I need to measure how much a rotation $q$ has been rotated about a given axis $\hat{a}$. $q$ in my case is a quaternion but it could be any sort of 3d rotation and I know its original orientation.
...
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Smooth random rotations
For a computer simulation, I want to create a randomly tumbling/rotating 3D object.
Unit quaternions describe rotations 'well' without any singularities.
Since rotations are points on a 4D ...
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59 views
Determine which face of die is up in 3D space
I'm developing a game using jmonkeyengine 3, but this question is more about math (rotation) than anything else, so I think I'm asking on the correct site. I'm terrible with math and I've tried to ...
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209 views
Rotate an angle-axis represented rotation?
Okay, I am a programmer, and I am working on some procedural generation, yada yada. I have a cube, which I will refer to as the "object". This cube's rotation is depicted via a grouping of two ...
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Rotating an object around a tilted axis
I have the coordinates of a centre point . I also have an array called the asteroid normal which I assume is the relative rotation of the axis (its 3 numbers between zero and one).
How can I make an ...
