0
votes
1answer
18 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 ...
2
votes
3answers
39 views

What kind of transformation an upper triangular matrix represents

Every matrix represents a linear transformation, but depending on characteristics of the matrix, the linear transformation it represents can be limited to a specific type. For example, an orthogonal ...
1
vote
1answer
105 views

Analytic geometry - rotation + translation

In $K=O\vec{e_1}\vec{e_2}\vec{e_3}$ I have to find the analytical representation of the screw motion( rotation + translation) $\psi$ with a rotation axis $g$ given by the points $A(5,-4,3)$ and ...
0
votes
1answer
52 views

Describing Cartesian transformations in Cylindrical Polar Coordinates

I have a question about converting functions defined in Cartesian coordinates to a cylindrical polar system. The particular coordinate transformation that I'm reading about is: \begin{equation} ...
1
vote
1answer
78 views

Rotation formalisms in three dimensions

I'm little bit confused. The Rotations are described by various means Direction Cosines Matrix (DCM); Euler Angles; Euler Axis/Angle; Quaternion. What is the difference between them. How I can ...
1
vote
2answers
152 views

Combine a rotation matrix with transformation matrix in 3D (column-major style)

I'm trying to concatenate a rotation matrix with a 4x4 homogeneous transformation matrix with column-major convention. I want this rotation matrix to perform a rotation about the X axis (or YZ plane) ...
1
vote
0answers
121 views

How to determine yaw-pitch-roll orientation by specifying a plane via 3 points?

[Note, this question is an attempt at rephrasing the one posted here, as it has not garnered any attention, unfortunately] Hello, Let's say you have three points in 3D space: A, B and C. Together, ...
0
votes
1answer
190 views

Givens rotation of the following vector of 3 elements.

I have to find the givens rotation matrix that will transform the following vector $[1, 1, -1]^T$ to $[y, 1, 0]^T$ (basically to insert a $0$ on the third position without altering the second one). I ...
0
votes
1answer
56 views

Find rotation angle of given image

At first: our aim is to find the total transformation of left house to the right house. What I did it first is translating the house with the center to the origin. I already found out that the ...
0
votes
0answers
81 views

How does orthonormal basis rotating work?

When you insert an orthonormal set into the column vectors of a matrix, you create a rotation matrix. I can't understand how this works, by simply placing the the vectors in there you have a rotation ...
0
votes
2answers
80 views

Matrix of transform rotation [solved]

Im trying to create matrix which rotates vector. I have $\vec{g}=(g_1,g_2,g_3);\:g_1\in\mathbb{R},g_2\in\mathbb{R},g_3\in\mathbb{R}$ - it represents gravitation. And $\vec{o}=(o_1,o_2,o_3)$ is vector ...
1
vote
1answer
286 views

Complex Numbers and Transformations

If a transformation t acts by rotating every point of the plane around the origin by $\pi/5$ clockwise and then proceeds to translate it by vector $v$ = $(1,2)$. How do I describe this ...
1
vote
1answer
120 views

Rotation of 2D polar graph in a 3D space along some fixed axis?

Does there exist some systematic way of rotating a 2-D polar graph $r=f(\theta)$ around some axis in a 3D space? For example: $f(\theta)=cos(\theta)$ in 2-D looks like: If we want to rotate the ...
1
vote
1answer
149 views

Geometry of Complex Numbers

Write down in the form ${Z}\rightarrow{AZ+B}$ the following transformations of the complex plane: (a) translation in the direction $(2,-3)$ (b) rotation about (0,1) through $\pi/4$ I know from my ...
2
votes
1answer
55 views

What does “transform among themselves” mean?

I'm reading a script on atomic physics, and there's a chapter on irreducible tensors. I can't understand the meaning of "transform among themselves" in this context: An arbitrary rotation of the ...
0
votes
1answer
195 views

Step in Euler's rotation theorem

I have been examining the matrix proof for Euler's rotation theorem on Wikipedia. I have deduced every step up to proving that $\det (R - I) = 0$ for any rotation matrix R. However, I'm having ...
1
vote
0answers
70 views

Determining pose of an object in 3d space

Given a 3D model of an object centred at the origin, if I place a camera at position (x,y,z) and make it face the origin, from the image rendered the object appears ...
0
votes
0answers
76 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 ...
0
votes
0answers
89 views

Update rotation matrix

Imagine you have a two noded beam in space, defined by extreme nodes 1 and 2. Image is owned by Jean-Marc Battini. To ...
1
vote
1answer
35 views

Calculating transformation from origin to point

I have an icosahedron of radius $x$ with 12 vertices at known coordinates. If I have a point at $(0,0,x)$ where $x > 0$ and a vertex of this icosahedron at $(a,b,c)$ how can I find the rotation ...
0
votes
2answers
129 views

Transformation between the same rotation expressed in different coordinate systems

EDIT Lets assume my transformation does the following mapping: x = -y y = -x z = -z Which produces this transformation matrix $R_t$: $ \begin{array}{lll} 0 & -1 & 0 \\ -1 & 0 & 0 \\ ...
0
votes
1answer
223 views

my plane is not vertical, How to update 3D coordinate of point cloud to lie on a 3D vertical plane

I have a bunch of points lying on a vertical plane. In reality this plane should be exactly vertical. But, when I visualize the point cloud, there is a slight inclination (nearly 2 degrees) ...
2
votes
1answer
103 views

Find rotation that maps a point to its target

I have a 3D point that is rotated about the $x$-axis and after that about the $y$-axis. I know the result of this transformation. Is there an analytical way to compute the rotation angles? $$ ...
4
votes
2answers
357 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 ...
0
votes
2answers
201 views

3D transformation between two polylines problem

Say I have 2 separate objects. One is a line defined by two points, the other is a polyline defined by three points. Line 1 consists of the set of two points: $a=(0,0,0)$ and b=$(0,0,1)$ Line 2 ...
0
votes
1answer
259 views

Rotation matrix for a set of points

I've got a set of $N$ points $p_1,\dots,p_N$ that all belong to a real object. Consequently, there are $N-1$ vectors $\vec{v}_i$ when $\vec{v}_i$ points from $p_1$ to $p_i$. Now, the object is ...
3
votes
2answers
115 views

Put a transformation under the form of a rotation in the complex plane

On the complex plane, I have a transformation "T" such that : $z' = (m+i)z + m - 1 - i$ ($z'$ is the image and $z$ the preimage, $z$ and $z'$ are both complex number) and $m$ is a real number. ...
3
votes
2answers
5k views

How do I rotate a matrix transformation with a centered origin?

This is actually something I'm doing in Objective-C programming, but since it's very math-oriented I thought I'd post it here. I was reading up on linear transformations: ...
0
votes
1answer
98 views

2D transformation without rotation

Is there a name for 2D transformation with the least squares adjustment having the following parameters: shift_x, shift_y, scale. Transformation does not use any rotation... Thanks for your help.
1
vote
1answer
305 views

correct rotation and translation matrices

I wrote a C++ program that can calculate the magnetic field $\bar{B}$ generated by a circular coil that is placed in the origin, for a given point $\bar{P}$ in 3D ...
0
votes
1answer
516 views

how to perform a rotation around a point which itself is rotating?

I'm working on rotating human limbs in a 3d game. I use Linear Algebra matrix rotations and translations to achieve moving the human and limbs. I currently can rotate around a pivot point by first ...