Source code needed for calculating quaternions

Question

I have gyroscope + accelerometer data at each time period T. I want to calculate the rotation of the object at each time - it can rotate on its axises. So I've read that it is convenient to represent the rotation of the system in terms of quaternions (not in Euler angles).

Is there any source code that can transform from angular velocity (from gyroscope) to the quaternions representation? Because in order to do it I need to solve the differential equation using numerical methods, what I don't want to do.

EDIT: Sorry forgot to say, the C++ source needed, thank you!

Answer 1

Would you be talking about a Slerp? (Spherical Linear Interpolation)

See Jonathan Blow's article "Understanding Slerp, Then Not Using It" which has example source in C++...

http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/

Answer 2

What language? E.g. for Python cgkit has a nifty quat module (quaternions initialized from a rotation matrix, not "an angular velocity", but presumably you can build the former from the latter?) and euclid.py has Python source code for a Quaternion class including class methods to build it from rotation matrix and in other ways.

Answer 3

Each sample from your gyroscopes represents a small rotation:

rot_x = angV_x * timestep
rot_y = angV_y * timestep
rot_z = angV_z * timestep

If the resulting rotations are small, you can convert this directly into a quaternion by taking half the rotation angle:

// for small rotations, quick & dirty quaternion is sufficient
// (note: all angles *must* be in radians!)
float k = timestep * 0.5;
quaternion raw_delta_Q(1.0, angV_x*k, angV_y*k, angV_z*k);  // unnormalized!

// combine rotation for current timestep with orientation state
estimated_orient_Q *= raw_delta_Q;  // multiply by unnormalized delta
estimated_orient_Q *= 1 / norm(estimated_orient_Q);  // then renormalize it!

If your rotations are larger than a few degrees, or if you need maximum accuracy, you will need to pay closer attention to how you get your quaternion.

EDIT: Note that the above code assumes *= is defined to do quaternion multiplication by both quaternions and real scalars. Some form of these functions (as well as the obvious constructor) will be present in any reasonable quaternion library.