1
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1answer
86 views

Quaternion and Matrix

I have a quaternion for rotation and a matrix for changing axis(change coordinate from camera to my rendering scene ). I have tested two method and i except to have equal resuls but results are ...
0
votes
1answer
62 views

Quaternion isn't normal!

I use the following scheme: Quaternion: [ w, x, y, z ] Then I use Euler Angles and convert it to a quaternion, as following: ...
1
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0answers
65 views

Indefinite quaternion algebra over Q

Let $D$ be an indefinite quaternion algebra over $\Bbb Q$. We have a chosen isomorphism $\iota \colon D \otimes_{\Bbb Q} {\Bbb R} \cong {\mathrm{M}}_2({\Bbb R})$. Q: If we choose another isomorphism ...
1
vote
2answers
51 views

Show by Example that $\mathbb{H}^n$ to $\mathbb{H}^n$ is not necessarily $\mathbb{H}$-linear

Show by example that for$ A \in M_n \mathbb{H}, L_A : \mathbb{H}^n \rightarrow\mathbb{H}^n $ is not necessarily $\mathbb{H}$-linear So I thought it would be linear by definition. Because if we have $ ...
0
votes
0answers
17 views

Polar form of Bi-Quatenrion

I have a complex Quaternion(Bi-quaternion) and i want to convert that to Polar form (Euler). Let say we have Fourier transform of a ( bi-quaternion ) like, then how can we get a polar form ...
0
votes
1answer
127 views

3D Positioning Vectors to Matrix & Quaternions

This is also programming related, but I think it's more about math than anything else. I have an Object which I want to represent it's 3d position, rotation and scale with vectors, and then I need to ...
0
votes
0answers
79 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 ...
2
votes
1answer
171 views

Quaternions vs Axis angle

Whats the use of representing rotation with quaternions compared to normal axis angle representation? I've been trying to learn quaternions and they make enough sense but as far as I can tell ...
2
votes
0answers
28 views

Computing a particular finite set of quaternion matrices.

Let $B = \left(\frac{-1,-11}{\mathbb{Q}}\right)$ be a choice of quaternion algebra ramifying at $11$ and consider the maximal order ...
0
votes
1answer
76 views

Quaternion Matrix Multiply

My question is about applying rules of quaternions to quaternion matrices. I know that for some rotation quaternion q = [w, x, y, z], I can find the rotation of ...
3
votes
3answers
158 views

Are there different conventions for representing rotations as quaternions?

I am trying to understand how quaternions are represented as rotations, in particular how to convert from a quaternion representation to a rotation matrix. The following paper by Diebel gives an ...
5
votes
2answers
317 views

Does anyone know any resources for Quaternions for truly understanding them?

I've been studying Quaternions for a week, on my own. I've learned various facts about them but I still don't understand them. My goal is to understand rotation quaternions specifically. I don't want ...
0
votes
1answer
34 views

Need help interpreting an equation from an article (related to quaternions).

At this link, about half way down the page, there is an equation I don't understand http://physicsforgames.blogspot.com/2010/02/quaternions-why.html This is the equation. $$VV† = -x^2I^2 - y^2J^2 - ...
4
votes
3answers
254 views

How do you construct the quaternion and the multiplication rules, like Hamilton did?

So, I understand complex number multiplication, and how it represents $2D$ rotations. What I don't understand is, how you add two more imaginary numbers $j$ and $k$, and get $3D$ rotations. I believe ...
3
votes
1answer
157 views

The multiplication of 2D vectors produces what?

I am trying to learn about rotation quaternions, and in the process I am currently looking at 2D vector multiplication. To avoid confusion with other types of multiplication, this is the basic form I ...
3
votes
2answers
57 views

What type of division is possible in 1, 2, 4, and 8 but not the 3rd dimension?

In this article that talks about some history of hamilton http://plus.maths.org/content/curious-quaternions There is a snippet that says this: Multiplication is very sneaky. You can only set up ...
1
vote
1answer
39 views

How does one derive this rotation quaternion formula?

given an angle and an axis, the corresponding quaternion can be computed like this. $w = \cos( Angle/2)$ $x = \text{axis}.x * \sin( Angle/2 )$ $y = \text{axis}.y * \sin( Angle/2 )$ $z = ...
1
vote
0answers
132 views

How is the Quaternion multiplication derived?

Quaternion multiplication seems suspiciously similar to the cross product. How is it derived? Here is a description of the multiplication: Let $Q_1$ and $Q_2$ be two quaternions, which are defined, ...
2
votes
1answer
191 views

Matrix representation of the Quaternions?

Can anyone explain how why the matrix representation of the quaternions using real matrices is constructed as such?
16
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9answers
2k views

Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$ [duplicate]

Possible Duplicate: Relation of this antisymmetric matrix $r = \left(\begin{smallmatrix}0 &1\\-1&0\end{smallmatrix}\right)$ to $i$ On Wikipedia, it says that: Matrix ...
0
votes
1answer
130 views

strange matrix -> quaternion conversion problem

I find two different rotation matrices are mapped to a single quaternion. $$ \begin{pmatrix} -1 & 0 & 0 \\ 0 & \frac{\sqrt{2}}{2} & -\frac{\sqrt{2}}{2} \\ 0 & ...
2
votes
2answers
287 views

Matrix Representation of Octonions

Since quaternions $\mathbb{H}$ have a matrix representation as elements of $\text{SU}(2,\mathbb{C})$ as the following $$ 1 \mapsto \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix},\quad \mathrm ...
5
votes
1answer
734 views

Using quaternions instead of 4x4 matrices for transformations

I'm interested in implementing a clean solution providing an alternative to 4x4 matrices for 3D transformation. Quaternions provide the equivalent of rotation, but no translation. Therefore, in ...
0
votes
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 ...
0
votes
2answers
1k views

How would I create a rotation matrix that rotates X by a, Y by b, and Z by c?

How would I create a rotation matrix that rotates X by a, Y by b, and Z by c? I need to formulas, unless you're using the ardor3d api's functions/methods. Matrix is set up like this ...
5
votes
3answers
742 views

On multiplying quaternion matrices

Both matrix multiplication and quaternion multiplication are non-commutative; hence the use of terms like "premultiplication" and "postmultiplication". After encountering the concept of "quaternion ...