Tagged Questions
9
votes
6answers
7k views
Calculate Rotation Matrix to align Vector A to Vector B in 3d?
I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
6
votes
6answers
622 views
Find the rotation matrix for +15° out of the rotation matrix +60° without using trigonometric functions
Find the rotation matrix for +15° out of the rotation matrix +60° without using trigonometric functions. And as much as I would love to tell you what I did so far. I don't even know where to start ...
5
votes
3answers
316 views
Freedoms of real orthogonal matrices
I was trying to figure out, how many degrees of freedoms a $n\times n$-orthogonal matrix posses.The easiest way to determine that seems to be the fact that the matrix exponential of an antisymmetric ...
5
votes
1answer
418 views
3D Rotation Matrix Uniqueness
Given a 3D rotation matrix R in a basis B. Can we consider R as being unique in B? Is there any other 3d rotation matrix R' representing the same 3D rotation in B? How could I prove that?
Note: I do ...
4
votes
0answers
31 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 ...
3
votes
2answers
452 views
What does $M^{-1}RM$ represent?
I'm a bit confused about the use of $M^{-1}RM$ where $R$ is a transformation matrix.
Actually I was looking at the script here which reads and renders bvh files. But, I could not understand the ...
3
votes
3answers
477 views
How to create 2x2 matrix to rotate vector to right side?
I have vector u=(x,y) and i need to create matrix M: M*u=(1,0).
But that matrix has to rotate vector, instead of keep and ...
3
votes
5answers
201 views
How can I calculate a $4\times 4$ rotation matrix to match a 4d direction vector?
I have two 4d vectors, and need to calculate a $4\times 4$ rotation matrix to point from one to the other.
edit - I'm getting an idea of how to do it conceptually: find the plane in which the vectors ...
3
votes
1answer
362 views
Can axis/angle notation match all possible orientations of a rotation matrix?
The rotation group is isomorphic to the orthogonal group $SO(3)$. So a rotation matrix can represent all the possible rotation transformations on the euclidean space $R3$ obtainable by the operation ...
3
votes
1answer
506 views
Understanding rotation matrices
How does $ {\sqrt 2 \over 2} = \cos (45 \text{ degrees })$?
Is my graph (the one underneath the original) accurate with how I've depicted the representation of the triangle that the trig function ...
3
votes
2answers
308 views
Plane and Matrix Question
I have this questions and it's really tough for me.
Flat on a plane (with normal N through point P) sits a tank at point
Q. The tank's local coordinate system is described by the 3x3 rotation
...
3
votes
1answer
66 views
Angle after two rotations in $\mathbb R ^3$
Question: A rotation through $45^{\circ}$ about the x-axis is followed by a similar one about the z-axis. Show that the rotation corresponding to their combined effect has its axis inclined at equal ...
3
votes
1answer
676 views
Generalized rotation matrix in N dimensional space around N-2 unit vector
There is a 2d rotation matrix around point $(0, 0)$ with angle $\theta$.
$$
\left[ \begin{array}{ccc}
\cos(\theta) & -\sin(\theta) \\
\sin(\theta) & \cos(\theta) \end{array} \right]
$$
Next, ...
3
votes
0answers
408 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:
...
2
votes
3answers
347 views
Reverse rotation matrix
I have to write an algorithm that can given a rotation matrix, find k and fi.
R = rotationMatrix(k, fi)
i am given R and need to fin k and fi, but i don't know how to do this, and the only formula i ...
