For questions about the quaternions: a noncommutative four dimensional division algebra over the real numbers.

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Axis Angle to quaternion and quaternion to Axis angle question

Axis Angle to quaternion and quaternion to Axis angle question Greetings All (matlab / octave code) Link to text file in case formatting gets messed up http://db.tt/nVv8Ivj I created two functions ...
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2answers
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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 ...
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Question regarding practical SLERP

We are suppose to compute the quaternion which performs 1/5 of the rotation of this quaternion: [ 0.965 (0.149 -0.149 0.149)] The answer provided is shown as ...
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3answers
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Euler angles and gimbal lock

Can someone show mathematically how gimbal lock happens when doing matrix rotation with Euler angles for yaw, pitch, roll? I'm having a hard time understanding what is going on even after reading ...
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4answers
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Quaternion Division

If $q$ and $r$ are quaternions, and $p$ is a point, applying $q$ then $r$ to $p$ is: $$ (qr)p\dfrac{1}{qr} $$ What if I want to go the other way? Instead of concatenating rotations, I want to remove ...
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How can one intuitively think about quaternions?

Quaternions came up while I was interning not too long ago and it seemed like no one really know how they worked. While eventually certain people were tracked down and were able to help with the ...
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1answer
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Differences in Quaternion properties?

In Quaternion mathematics, normally $$i ^ {2} = j ^ {2} = k ^ {2} = i*j*k = {-1}$$ But I am looking at a different type of Formula where $$i ^ {j ^ k} = {-1} $$ (edit again, since somehow this ...
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Using Padé approximants for the quaternion exponential

On a lark, I wanted to know if one can use Padé approximants to compute the exponential $\exp(z)$ of a quaternion $z=a+b\mathbf{i}+c\mathbf{j}+d\mathbf{k}$. Since Mathematica has a package meant for ...
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2answers
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the logarithm of quaternion

I'm reading 3D math primer for graphics and game development by Fletcher Dunn and Ian Parberry. On page 170, the logarithm of quaternion is defined as \begin{align} \log \mathbf q &= \log \left( ...
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3answers
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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 ...
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2answers
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Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?

Why are the only (associative) division algebras over the real numbers the real numbers, the complex numbers, and the quaternions? Here a division algebra is an associative algebra where every ...
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Real world uses of Quaternions?

I've recently started reading about Quaternions, and I keep reading that for example they're used in computer graphics and mechanics calculations to calculate movement and rotation, but without real ...