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Point rotation in Quaternion?

Posted 3 years ago

I am a newbie investigating the migration from python(sympy) to Mathematica.

I have looked through the quaternion documentation and cannot find any functionality equivalent to inverse or point rotation (rotate_point in sympy).

I can't find any information on the web, what are you guys doing?

POSTED BY: A Kim
11 Replies
Posted 3 years ago
POSTED BY: Hans Milton
Posted 3 years ago
POSTED BY: A Kim
Posted 3 years ago

Is there any way to explicitly handle the unit quaternion for the rotation?

Not clear to me what you mean. Please explain a bit more.

Also how can I get the components of the inverse quaternion?

Use Conjugate[q] if the quaternion is symbolic, otherwise you can also use q^-1

Note also that the standard package does not handle symbolic quaternions

POSTED BY: Hans Milton
Posted 3 years ago

Not clear to me what you mean. Please explain a bit more.

Sorry. My understanding and explanation was not clear enough.

For example, Julia's library rotation.jl has a QuatRotation that represents a unit quaternion. Since your package is 3D rotation oriented, I was wondering if you have such a mechanism.

Use Conjugate[q] if the quaternion is symbolic, otherwise you can also use q^-1

I got it!

Note also that the standard package does not handle symbolic quaternions

Oh,really? I had not considered that some mathematica packages do not support symbolic processing.

There is a description of quaternion on this page, but does it not support symbolic processing?

POSTED BY: A Kim
Posted 3 years ago

For example, Julia's library rotation.jl has a QuatRotation that represents a unit quaternion. Since your package is 3D rotation oriented, I was wondering if you have such a mechanism.

The function that converts a quaternion to explicit rotation parameters is quatToFromθV[quat]. Numeric input will be normalized, while symbolic input is assumed to be normalized.

POSTED BY: Hans Milton
Posted 3 years ago

As an alternative to the Wolfram standard quaternions package, you could check this one on GitHub.

A pdf overview is attached

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POSTED BY: Hans Milton
Posted 3 years ago
POSTED BY: A Kim

Time permitting, please consider packaging this and contributing to the Wolfram Function Repository.

POSTED BY: Daniel Lichtblau
Posted 3 years ago
POSTED BY: Hans Milton
Posted 3 years ago

Daniel, I replied too quickly. This is a package with about 1000 lines of code distributed over 94 separate functions. So I think it is beyond the scope of the Function Repository.

POSTED BY: Hans Milton

It could still be a good item in the newer paclet repository. Alternatively, have a look at EisensteinIntegers in the Wolfram Function Repository for a way to bundle functionality that might be applicable here as well.

POSTED BY: Daniel Lichtblau
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