Fix method 'difference'

When switching to the double covered quaternion pair, the corresponding distance was not computed correctly

assigned to @osander

How do you know this is correct? I tested this code quite thoroughly back in the days. I'm afraid you'll have to provide a unit test to convince me that the formula is really incorrect.

I found the bug when using the interpolate method to create initial configurations. There, the prescribed end values were not the same anymore (in the recomputed values resulting from interpolate). One can see that it is a bug as follows:

1. The double coverage pair of a given quaternion q is given by -q, which is changed in the code if the two input parameters of difference are not in the same half of the coverage.
2. In this case the parameter dist = 2*acos(q[3]) needs to be adjusted accordingly. So newDist = 2*acos(-q[3]). Using the symmetry of acos which is given by acos(x) = PI - acos(-x) one can derive that dist = 2*acos(q[3]) = 2*PI - 2*acos(-q[3]) and hence newDist = 2*PI - 2*acos(q[3]) = 2*PI - dist

Is this sufficient?

Sorry, but I really do want a unit test. You may be able to convince me that your patch is correct, but I don't trust my own judgement well enough here. And in this particular part of the code I'd rather be super-conservative.

Here is a small test that is interpolating between two rotations to illustrate the failure.

differencetest.cc

Okay. Now can you turn this into a proper unit test and include it in the merge request?

Thanks.

added 2 commits

• 9a9a53e1 - Add two more test points
• ddc2a701 - test interpolation between two rotations

Compare with previous version

mentioned in issue #1 (closed)

Okay! With this test I trust the change. The offending code path seems to be triggered quite rarely!

Thanks!

merged

mentioned in commit acd17b13