# Questions tagged [rotations]

This tag is for questions about *rotations*: a type of rigid motion in a space.

1,998 questions
1answer
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### How to calculate a point after rotation given two unit vectors?

I have two unit vectors: before and after rotation. Point (0, 0, 1) is moved to (-0.42, 0.19, 0.88) after rotation. If I had a point of (-0.066, 0.635, -0.184) before rotation, how it would be ...
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### How to get an axis of rotation value without the others axis influencing it?

I have written a PID controller that regulate a Roll angle inside a game engine (using euler coordinates), and it works fine when used "upright". But as soon as my object goes inverted or points in ...
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### Translate point after rotation relative to different origin

I have 200x380 input image and coordinates (63,146) where (0,0) is top-left: I rotate about the centre some amount of degrees and expand the "canvas" to avoid cropping resulting in larger output ...
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### Question about definition of rotation on sphere

I just started M.A. and I do not have enough knowledge about aforementioned concepts. I truly want to know everything about this mapping in details. A rotation of the sphere s^2 is a map r= r_(p,α) ...
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### How to use rotational matrices to change orientation of a circle?

Let the following circle be defined by the equation $$\vec{r}(t)= \rho \cos(t) \hat{\mathbf{i}} + \rho \sin(t)\hat{\mathbf{j}}$$ Now suppose the circle is rotated and then translated as follows: ...
1answer
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### what makes quaternion representation of rotations unique? [on hold]

So i'm curious about what actually makes quaternions unique. Quaternions are 4 dimensional and multiplication is non commutative. But what part makes the solution unique? Is it because multiplication ...
0answers
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### Determining an equation from a graph

Background: I am trying to make a script for a 2d game that calculates how fast the player moves based on the the direction they are trying moving. To do this, it uses variables that represent ...
1answer
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### Finding quaternion, representing transformation from one vector to another [closed]

Intro. Previously, I've asked a question on converting rgb triple to quaternion. After that question I've managed to get unit quaternions. Since they were unit ...
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### Euler angle in two given coordinates

I have two coordinates. One is standard and the other is arbitrary. A rotation is represented as ZYX in the standard coordinates. (yes, It is not exactly a Euler angle. I'm sorry about this) and ...