0
votes
1answer
12 views

Coordinates rotation and function change

In the Cartesian coordinates $(x,y)$, I have a vector function $\bar{f}(x)=\hat{x}A\cos(yk)$, where $A$ and $k$ are constants. I make now a 45 degrees rotation (in the same plane) to the new set of ...
0
votes
1answer
20 views

Estimate Rotation and Translation from two sets of points in different coordinate systems

I got one set of 3d $(x,y,z)$ points $( \# \geq3 )$ located in two diffent coordinatesystems. Is it possible to estimate the rotation and translation between these systems? Something like $$ ...
0
votes
1answer
17 views

What are the coordinates of a point on a rigid body after a rotation in 3D Euclidean space, given the initial coordinates and a center of rotation

Main question Let ($x_p$, $y_p$, $z_p$) be the initial coordinates of a point $P$ on a rigid body in a right-handed 3D Euclidean space. Let ($x_r$, $y_r$, $z_r$) be the coordinates of a center of ...
0
votes
2answers
30 views

Rotation of axes give the same point in space?

I am playing around with rotation of axes formulas and not getting it. I don't understand how this rotates anything when it is just giving you different coordinates for the SAME point in space. How ...
0
votes
1answer
52 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
1
vote
1answer
22 views

Rotation of velocity vectors in Cartesian Coordinates

I want to rotate a $(X,Y,Z)$ coordinate-system around it $Z$-axis. For the coordinates this can be done with the rotation matrix: $$ R_Z(\theta)= \begin{pmatrix} cos \theta & -\sin(\theta) & ...
0
votes
0answers
25 views

How to move coordinate systems using rotation matrices.

I am having some trouble with this question. I understand that the rotation matrix will be 4x4 and that the first 3 columns will just be $u$, $v$ and $n$ transposed but I dont know what I am ...
0
votes
0answers
71 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
0
votes
1answer
17 views

Proving the existence of a ____ number of conditions under a rotation of coordinates.

I'm reading a section on Rotation of Coordinate Systems and this is throwing me off: 'In n-dimensional space, the rotation matrix will have $n^2$ elements, upon which orthogonality relations place ...
1
vote
0answers
167 views

Reverse rotation back to original coordinates (Euler Angles)

so in the program I'm trying to write (still, it's a mathematical question) I have a set of coordinates and angles (Euler angles) which represent the place and orientation of an object in space, ...
0
votes
2answers
178 views

Find Rotation Matrix to rotate axes and move coordinates of point from P0 to P1

I have a point $P_0 = [x_0, y_0, z_0]'$. I want to rotate the axes so that the new coordinates will be $P_1 = [x_1, y_1, z_1]'$. Define the following rotation matrices: $R_x = \left[\matrix{ ...
1
vote
1answer
52 views

Find the Bounding Rectangle of Rotated Rectangle

I have rectangle with co-ordinates(x1,y1) and (x2,y2) and I have to rotate the rectangle an amount of θ about it centre using Rotation Matrix ...
0
votes
2answers
325 views

Rotate 3D coordinate system such that z-axis is parallel to a given vector

Assume I have a Cartesian $xyz$ coordinate system with a point $p=(p_x,p_y,p_z)$. In addition a vector $n=(n_x,n_y,n_z)$ is given. How do I rotate the coordinate system to obtain a new $uvw$ system ...
2
votes
3answers
58 views

What separates rotations from other co-ordinate transformations?

I am confused about some seemingly elementary ideas. From what I have understood, a rotation is just a specific class of co-ordinate transformations. If this is true, what exactly separates a rotation ...
0
votes
0answers
673 views

How do I calculate roll, pitch, yaw from a unit vector?

I am provided a unit vector giving a direction in x, y, z coordinates, and that the roll is defined as about the x axis, pitch around y, yaw around z. I'm trying to determine how to calculate roll, ...
0
votes
0answers
74 views

coordinate transformation and scaling

I have a global coordinate system that I need to transform to a local coordinate system. The new and old coordinate systems are shown below. Using transformation rules, I came with with the ...
1
vote
0answers
28 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 ...
1
vote
1answer
180 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 ...
2
votes
1answer
281 views

How to get Euler angles with respect to initial Euler angle

I have a sensor which gives me Euler angles (roll,pitch,yaw). There is a baseline value of Euler angle (assume it is $5,10,15$) at the beginning.I want to calibrate from this baseline values all ...
0
votes
1answer
154 views

How do I calculate a position in front of a quaternion given the initial position and the quaternion?

Well I want to determine the position in front of, lets say 'an object'. 'An objects' has a position (pX,pY,pZ) and a quaternion rotation (qX,qY,qZ,qW) (where qW seems always to be ...
1
vote
0answers
399 views

Sequence of Euler (yaw/pitch/roll) rotations?

I'm an android programmer and I have a problem that it's base is in about Mathematics.So excuse me if it is very easy ,abstract or bad formatted.But I need a simple ...
1
vote
0answers
486 views

Rotating co-ordinates in 3D

Suppose I have 3 axes, $x$, $y$, and $z$ such that $x$ is horizontal, $y$ is vertical, and $z$ goes in/out of the computer screen where $+$ve values stick out and $-$ve values are sunken in. Suppose ...
4
votes
2answers
351 views

How to solve an overdetermined system of point mappings via rotation and translation

I have a set of points in one coordinate system $P_1, \ldots, P_n$ and their corresponding points in another coordinate system $Q_1, \ldots , Q_n$. All points are in $\mathbb{R}^3$. I'm looking for a ...
3
votes
1answer
2k views

rotating 2D coordinates

I've tried googling this, but I always end up somewhere that just says it's easy. Anyhow, I have a coordinate system, where I need to rotate a bunch of points. It's all 2D. Coordinates varies and so ...
2
votes
1answer
134 views

How to get new orientation on a sphere?

This is my first question here, hopefully it fits. Imagine all people on the northern hemisphere are looking North to the Pole. Now I want them to look towards a new location given by latitude, ...
0
votes
1answer
453 views

Tracking a point on an object during rotation

I've been trying to solve for this a while now. What I am trying to do is to find the coordinates of a point on an object while it rotates. After digging around I have found the following equation ...
0
votes
1answer
127 views

How to “transform” $(f(x), g(x))$ to $(x, y(x))$?

I'm currently trying to solve the following problem: Let $L$ be the set of points of $\mathbb{R}^2$ that satisfy the condition $f(x,y) = 7x^2-6 \sqrt{3} xy + 13y^2 = 16$. It is possible to ...
3
votes
2answers
488 views

Plane and Matrix Question

I have this questions and it's really tough for me. Flat on a plane (with normal N through point P) sits a tank at point Q. The tank's local coordinate system is described by the 3x3 rotation ...
0
votes
1answer
881 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 ...