# Tagged Questions

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### Calculating rotated relative positions on 2D plane

For a game project, I need to calculate positions of items on a 2D plane relative to the camera. Camera can be rotated, and it's coordinates refer to it's center. In the attached images, ...
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### Integration of a rotated triangle: determining the slope of a side

I'm working through MIT's OCW single-variable calculus course. The problem is taken from Problem set 7: Question 4B-5.1 Q: Find the volume of an equilateral triangle with side length a which is ...
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### Word problem involving rotation [closed]

If a wheel rotates at 195 degrees every 1.3 seconds. What will the revolutions per minute be?
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### Finding the coordinates of the top and bottom circles of a moving and rotating cylinder in 3D

I have a cylinder that is moving and rotating in a 3D space. I need to calculate the coordinates of the center of the cylinder's top and bottom circles. Here's the information I have : I have at the ...
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### I've seen “hyperbolic rotation” - from this: generalization to multisection rotation: is this possible?

This question is more in recreational mathematics area By accident I came across the concept of "hyperbolic rotation" where we use a matrix containing $\cosh$ and $\sinh$ instead of the ...
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### Resolving bearings for tilted structure (vector rotations)

I am trying to find a neat solution to resolving bearings for a tilted structure. For example, if I know that a hub is $268.74^{\circ}$ and offset ($X = -3.542$m, $Y = -1.857$ m, $Z = 2.013$m) with ...
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### Converting a 3x3 matrix to euler angles in various rotation orders

So let's say I have a 3x3 orientation matrix set up like: a b c d e f g h i which I have generated from euler angles in a left-handed, Y-vertical system. ...
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### Get unrotated position of a rectangle.

I'm struggeling with the following problem. I have a rotated rectangular. The following values are known. The size of the rect, the angle the rect is rotated by and the position of point A. The ...
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### Rotation vs lift distance

I'm working on a homework problem and I think I found an answer, but not positive. Here is the question: A winch with a $6$-inch radius is used to lift a container. The winch is designed so that as ...
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### How to figure out if a point is inside the bounds of a rotated rectangle [duplicate]

I'm trying to figure out an approach (or a formula) to determine if a point (x,y) is inside the bounds of a rotated rectangle. For this test we can assume that the rectangle is centered on the ...
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### Size of new box rotated and the rescaled

I have a box of height h and width w. I rotate it to r degrees. Now I resize it so that it can original box in it. What will be the size of newly box. Original Box: Box after rotating some ...
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### Algorithm for finding orientation of each face on a polyhedron?

I am working on making a dice rolling application and I need to find out how far in each of the three dimensions I must rotate each of the dice to make the correct side face the camera so the user can ...
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### Get $x,y$ coord of a rectangle when rotation is $0$

I have this square div in the page. I need to get the $x,y$ coords (left/top) of the box based on rotation 0 even when the box is rotated at a different angle. Is there a formula to calculate the the ...
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### New x coordinate of a rotated line

I need help finding the equation to find $x$ I work in GIS and I'm working on a script that uses the new x coordinate of a rotated line. I havent work with trigonometry in a long long time so I ...
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### Optimal rotation to align a circle with external points

I have a circle $C$ with radius $r$ and a set of finite points $P=\left \{ p_1,p_2,\ldots,p_n \right \}$ are identified external to the circle $C$. These points may lie on the exterior or the interior ...
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### 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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### matrix representation of a trigonometric rotation

Hey guys!I have a couple of doubts regarding this exercise, for a) I think that the Matrix rotation of P is [(cos t, -sen t) , (-sen t, cos t)] and for Q [(-cos t, -sen t), ( sen t, cos t)] , is ...
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### How to rotate base points of a scalene triangle to represent an isosceles triangle

Given the following graph: Where SP is the start point and EP is the end point of a line - how would I rotate p1 and p2 on axis SP in such a way that they would represent an isosceles triangle e.g. ...
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### Rotating a line segment in 3D to a prescribed orientation

I have a general line segment with endpoints $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ referenced to a 3D Cartesian coordinate frame E. I wish to rotate this coordinate fram E to a new coordinate system F ...
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### Find the coordinates of a point on a circle

I have a circle like so Given a rotation θ and a radius r, how do I find the coordinate (x,y)? Keep in mind, this rotation could be anywhere between 0 and 360 degrees. For example, I have a ...
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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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### How $v=(-\sin\frac{\alpha}{2}\sin\frac{\beta}{2},\cos\frac{\alpha}{2}\sin\frac{\beta}{2},\sin\frac{\alpha}{2}\cos\frac{\beta}{2})$ is derived from…

In the book Quarternion and Rotation Sequences, I can't seem to work out how the final equation (colored in $\color{red}{red}$) is derived from the original equation (colored in $\color{blue}{blue}$). ...
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### Rotating about a point?

This is part of a program. I am trying to take an image at a given pair of coordinates and move it in a circular path around another given pair of coordinates. The program is structured so that the ...
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### Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a bit more complicated than the post title suggests because I was running out of words. I suppose the full title would be: "Finding the distance between the centre of an arbitrarily rotated ...
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### Change in slope accompanying clockwise rotation of a line

Given a line with slope $m$, if the line is rotated $90^{\circ}$ clockwise the slope of the resulting figure is $-m$, how can I determine the slope if the line is rotated $30^{\circ}$ or $60^{\circ}$ ...
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### “Trivial” trigonometry problem

I am really stuck on this problem, and I figured you people could probably help me with it. I have a rectangle with width w and height h with a certain point p inside it. This point is given by the ...
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### 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 ...
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### Line Rotation Problems in Trigonometry

I have 2 lines that i draw like this: ...
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### Counteract preceding rotations

In a situation where I have two axis adjacent back to back (let's say a robotic arm) I can sometimes perform two rotations ($R_1, R_2$) such that the resulting position and direction is unchanged. ...
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### Determine whether or not a point lies within a rotated rectangle

I need some maths help for a 2D game I am programming. In this game I have a rectangle, specified by its centers' X and Y coordinates, and its width and height. I then rotate this rectangle via ...
How should I rotate a point $(x,y)$ to location $(a,b)$ on the co-ordinate by any angle?