0
votes
0answers
25 views

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, ...
0
votes
0answers
41 views

Computing the coordinates of a point, offset from a rotated point.

Good day. I have a question which should be easy but I have not been able to figure it out. The coordinates of a point on a unit circle, given an angle, is $$\begin{align} x &= \cos(\alpha) \\ y ...
0
votes
0answers
31 views

Vector Magnitude during rotation

Probably something I should now already but this is confusing me no end! Lets say we have a force which is directed at 69 degrees inclination (from the X axis) with a magnitude of 500, shown below: ...
0
votes
1answer
25 views

Finding linear and angular speeds

(b) A wheel of radius 5 in. is rotating 45°/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec? So for this one I thought the linear speed (v)= 5(pi/2) because ...
1
vote
2answers
61 views

Rotate $z = 0$ plane in 3D

I have 100 points on $z=0$ plane. I want to rotate those points, such that they lie on any plane $P(a,b,c,d)$, preserving distances. Hence, I need a rotation matrix. For instance, if my points are ...
0
votes
0answers
38 views

How to find optimal perpendicular axis of rotation vector?

I am drawing lines on the screen. Each line has a point (x,y,z) and a direction (u,v,w). I want to draw arrow heads on these ...
-1
votes
1answer
100 views

How to draw arrows by rotating lines in 3d space?

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
0
votes
1answer
48 views

How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
0
votes
2answers
40 views

How do I calculate the inverse of these matrices?

In learning how to rotate vertices about an arbitrary axis in 3D space, I came across the following matrices, which I need to calculate the inverse of to properly "undo" any rotation caused by them: ...
1
vote
0answers
21 views

Rotating two objects

I have two lines. Both created in this format: Line 1 $$line1 = \left\{ \begin{array}{c} startX, startY \\ endX, endY \end{array} \right\}$$ $$line2 = \left\{ \begin{array}{c} startX, startY \\ endX, ...
5
votes
1answer
85 views

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 ...
-1
votes
3answers
147 views

Word problem involving rotation [closed]

If a wheel rotates at 195 degrees every 1.3 seconds. What will the revolutions per minute be?
0
votes
0answers
33 views

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 ...
1
vote
2answers
205 views

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 ...
0
votes
0answers
20 views

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 ...
0
votes
0answers
174 views

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. ...
0
votes
1answer
35 views

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 ...
1
vote
1answer
141 views

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 ...
1
vote
0answers
29 views

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 ...
5
votes
1answer
199 views

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 ...
2
votes
1answer
127 views

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 ...
0
votes
2answers
275 views

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 ...
1
vote
1answer
195 views

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 ...
4
votes
1answer
81 views

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 ...
2
votes
0answers
202 views

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 ...
-1
votes
3answers
189 views

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 ...
1
vote
1answer
127 views

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. ...
1
vote
1answer
209 views

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 ...
3
votes
1answer
4k views

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 ...
0
votes
0answers
135 views

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). ...
1
vote
1answer
69 views

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 $\color{blue}{blue}$). ...
1
vote
1answer
195 views

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 ...
0
votes
1answer
483 views

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 ...
0
votes
1answer
712 views

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 $60^{\circ}$ ...
8
votes
3answers
339 views

“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 ...
3
votes
3answers
675 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 ...
0
votes
1answer
231 views

Line Rotation Problems in Trigonometry

I have 2 lines that i draw like this: ...
0
votes
0answers
77 views

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. ...
0
votes
1answer
966 views

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 ...
1
vote
0answers
2k views

Compute Altitude and Azimuth using either Quaternions or Rotation Matrix or Roll, Pitch and Yaw component

I am struck with a mathematical problem. I want to convert the iPhone device's attitude information which is available in one of the following forms: Quaternion Rotation Matrix Roll, Pitch and Yaw ...
3
votes
3answers
9k views

Rotate a point in circle about an angle

How should I rotate a point $(x,y)$ to location $(a,b)$ on the co-ordinate by any angle?