Linked Questions

1
vote
1answer
4k views

How to find transformation matrix, specifically a rotation, between two given 3d vectors? [duplicate]

How to find transformation matrix, specifically a rotation, between two given 3d vectors? I've found something about it but with quaternions. I don't know anything about quaternions. So it would be ...
0
votes
0answers
35 views

Rotate vector by angles between a unit vector and the positive x axis [duplicate]

If I know that a vector $\vec{y}$ resulted from shifting another vector by a vector $\vec{d}$, it is easy to get the original vector back as simple as $\vec{x}=\vec{y}-\vec{d}$. Now suppose that $\...
5
votes
6answers
3k 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 ...
2
votes
1answer
6k views

How to find Euler's angles?

I have read about Euler's angles and matrices, including $zxz,zyz$, etc . I am not obliged to use a specific rotation but rather I want to figure out what angles I need to use for alpha,theta, gamma ...
2
votes
3answers
753 views

Decomposing rotation into rotation around certain axis and remaining rotation

Let R be a rotation matrix in three-dimensional euclidean space, R ∈ SO(3). Let v be a unit vector in said space. Is it possible to decompose R into matrices A and B so that following holds? AB = ...
4
votes
2answers
993 views

Rotation of a regular tetrahedron

The tetrahedron can be written with its apex at the north pole of a sphere with the four vertices: \begin{eqnarray} a(0,0,\sqrt{6}/4) \; , \; a(\sqrt{3}/3, 0, -\sqrt{6}/12) \; , \; a(-\sqrt{3}/6, 1/...
1
vote
2answers
2k views

Calculate quaternions from two directional vectors.

I am using RobotStudio to move an end-effector from one coordinate and direction to another coordinate and direction. I understand how to move the robot to all my points, but for the direction T need ...
3
votes
2answers
302 views

Is there a close form solution for parallel transport on 2 sphere along the great circles.

I need to transport a tangent vector on 2-sphere from point $p$ to $q$ along the geodesic, which is defined using great circles in this case. I believe there are iterative solutions to achieve that ...
0
votes
1answer
2k views

Rotating a quaternion around its z-axis to point its x-axis towards a given point

How can i rotate a quaternion around its z-axis in order to make the x-axis point towards a certain (x,y)-point? I have been able to calculate quaternions by rotating a unit vector [0,0,1] onto ...
3
votes
1answer
1k views

find 3 angles to rotate vector to align with second vector

First I would like to say that I have seen posts such as that found here: Calculate Rotation Matrix to align Vector A to Vector B in 3d? As well as formulas such as: https://en.wikipedia.org/wiki/...
1
vote
1answer
1k views

Finding normal of arbitrarily oriented ellipsoid

For an axis-aligned ellipsoid, the equation is $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1. $$ With $a=b$ this will give a spheroid with the $z$ axis as its symmetry axis. A spheroid ...
1
vote
2answers
488 views

Find orthogonal matrix Q

Find $3 \times 3$ orthogonal matrix Q such that: $$Q \left[\begin{array}{r} 3\\ 0 \\ 4\end{array}\right] = \left[\begin{array}{r} 5\\ 0 \\ 0\end{array}\right]$$ How can I find matrix Q if I only ...
2
votes
2answers
327 views

Generating uniformly distributed points within rotated ellipsoid

I want to generate uniformly distributed points within an ellipsoid that has been rotated. I have the vectors for the major, minor and intermediate axes of the rotated ellipsoid. The ellipsoid is ...
1
vote
0answers
514 views

How can I use the Bullet-Physics's ray-cast normal to calculate angles for a object to lay on a surface?

[Give the normal of a surface in XYZ format, how do I calculate rotations (also in XYZ format) needed to set an object parallel to the surface?] I have a collision library that uses the bullet ...
1
vote
0answers
513 views

Rotate basis to align with vector

I have a coordinate system with the Basis $B=(e_x, e_y, e_z)$ and two vectors $r$ and $a$. Now, I want to rotate the basis so that the $e_x$ unit vector points in the direction of the vector $r(x,y,z)$...

15 30 50 per page