# tf::Quaternion getAngle() eqivalent for rospy [closed]

Is there an equivalent to the getAngle() method of C++ interface of tf in Python version too?

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### Closed for the following reason the question is answered, right answer was accepted by allenh1 close date 2018-09-13 11:14:45.625950

Sort by » oldest newest most voted I don't know if there's a built in function to do this. But the relationship between the w element of a quaternion and the angle it's rotating by is fairly simple.

w = cos(angle / 2)


therefore:

angle = 2 x arccos(w)


So you can calculate this yourself using this equation from the w element.

Update:

This is mathematically equivalent to the more complex form shown on the Wikipedia page here. See their curves here:

Note: I've replaced sqrt(qi^2 + qj^2 + qk^2) with sqrt(1-qr^2) since this expression can more easily be calculated using just the w value.

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Are there any preconditions to be met to use this formula? Wikipedia uses atan2 ( https://en.wikipedia.org/wiki/Quatern... )

The two equations are mathematically equivalent, for some reason they've put the more complex form on Wikipedia! I've added the graphs of them both to my answer, as you can see they give the same results.

Ok thanks, I thought that the Wikipedia was maybe better because essentially it enforces normalization on the vector part or something into this direction.

No worries, rotation quaternions are 4D unit vectors so they should always be normalized. The tf.transformations library has a lot of useful conversion methods for rotations.

You can get Euler angles from your quaternion. If you are trying to get the axis-angle representation you could get a rotation matrix from your quaternion and convert that to axis-angle.

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