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Equation for 2-Axis Rotation to Point to Target Azimuth & Elevation

The first step is to attach a local coordinate frame $O x'y'z'$ to the beam. This coordinate frame and the world coordinate frame share the same origin $O$. The $Ox'$ axis extends along the length of ...
of course's user avatar
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Getting azimuth/elevation angle for a sensor that is not in rotation origin

I will be assuming that the target point (T) is at a much greater distance than the offset of your optical sensor (S) from its effective center of rotation (C). orient the optical sensor such that ...
Sam's user avatar
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Generate random point on the ellipsoid in 3d.

P = [cc,0,0]; P1 = f2-origin'; cP = cross(P, P1); I've identified the mistake I made, which is that when calculating the angle of rotation, I should compute it ...
ZHIHA's user avatar
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Rotation of $3$-dimensional space vectors

As peterwhy noted in his comments, an axis of rotation for the pair $P$ and $P'$ is any line that lies in the perpendicular bisecting plane of the line segment $PP'$. This plane has the equation $ n \...
of course's user avatar
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Rotating vector in 3D space onto xz-plane

Maybe a more simple approach is to compute the angle $\phi$ wrt the z axis then do $\theta = \pi/2 - \phi$
Benet Oriol's user avatar
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Difference between rotation matrices

As a general convention, the columns of a rotation matrix describe the directions of a local coordinate system as seen from the inertial coordinate system. $${\rm R}=\left[\begin{array}{c|c} \hat{u} &...
John Alexiou's user avatar
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Compositions of two rotations

Look at this using affine transformations. The rotation about the origin is $$\small {\rm R}_{1}=\begin{bmatrix}\cos\Theta & \text{-}\sin\Theta\\ \sin\Theta & \cos\Theta\\ & & 1 \end{...
John Alexiou's user avatar
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Rotation of $3$-dimensional space vectors

Assuming $P$ is not parallel to $P'$, the unit-length axis of rotation is $k=\frac{P\times P'}{\lvert P\times P' \rvert}$, where $\times$ denotes the vector cross product. To find the angle of ...
FabrizzioMuzz's user avatar
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Pitch, Yaw, Roll calculation

It is a property of rotation in $3D$ that the axis of rotation lies in the plane that is perpendicular to the straight line segment connecting the initial point and the final point, and that passes ...
of course's user avatar
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What is the math required to do 4d rotations?

By "plane of rotation" it sounds like you want every point in that plane to remain fixed, as the axis of rotation remains fixed for a 3-d rotation. The complement would then be a plane ...
rschwieb's user avatar
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What is the math required to do 4d rotations?

Here is a R function performing such a rotation: ...
Stéphane Laurent's user avatar
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Given latitude and longitude and facing north, how can I calculate the rotation needed to face another latitude and longitude (namely 0,0)?

Since we're talking about angles, the radius of Earth doesn't matter, and we can take it as $1$. The coordinates in $(x,y,z)$ of a point on Earth, assumed a sphere centered at the origin $(0,0,0)$ ...
of course's user avatar
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Calculate Rotation Matrix to align Vector $A$ to Vector $B$ in $3D$?

The other answers have given formulas, but for code I want to highlight that this is super simple in python using scipy's Rotation module, as of the just-released scipy v1.12.0: ...
Scott's user avatar
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