(beginner) calculating orientation change with eulers

[farshizzo]

I'm not sure what the problem is. The solution you are getting for those sets of euler angles is correct. The problem with getting non-unique solutions is when extracting euler angles from a matrix. In this example we are creating a matrix from euler angles, so there should be no problem.

[astull]

Is the non-unique solution due to the selection of 90 degrees as the pitch angle? Ultimately, I need a unique solution. Is it reasonable to assume that this might be addressed by calculating the difference for a 3rd vector? I don't know the math so I'm only assuming the following modified script would retrieve the necessary values from the matrix to calculate a 3rd vector:

#Extract forward/up vector from euler1
m.setRot( vizmat.EulerToAxisAngle(euler1) )
d = m.get()
forward1 = d[8:11]
up1 = d[4:7]
side1 = d[12:3]

#Extract forward/up vector from euler2
m.setRot( vizmat.EulerToAxisAngle(euler2) )
d = m.get()
forward2 = d[8:11]
up2 = d[4:7]
side2 = d[12:3]

Am I wondering in the dark?

Alternatively, wouldn't a unique solution also result if I calculated the displacement from the facing direction AND the angle of rotation about that axis (the facing direction)?

[farshizzo]

Yes, you could also compute the angle difference between the side vectors as well. Here is a modified version of the sample code that also returns the difference between the side vectors:

import viz
viz.go()

euler1 = [0,0,0]
euler2 = [0,90,30]

def ComputeAngleDifference(euler1, euler2):
	m = viz.Transform()
	
	#Extract forward/up/side vector from euler1
	m.setRot( vizmat.EulerToAxisAngle(euler1) )
	d = m.get()
	forward1 = d[8:11]
	up1 = d[4:7]
	side1 = d[:3]
	
	#Extract forward/up/side vector from euler2
	m.setRot( vizmat.EulerToAxisAngle(euler2) )
	d = m.get()
	forward2 = d[8:11]
	up2 = d[4:7]
	side2 = d[:3]

	#Compute angle difference between forward/up/side vectors
	forward_diff = vizmat.AngleBetweenVector(forward1,forward2)
	up_diff = vizmat.AngleBetweenVector(up1,up2)
	side_diff = vizmat.AngleBetweenVector(side1,side2)

	return forward_diff,up_diff,side_diff
	
print ComputeAngleDifference(euler1,euler2)

Alternatively, wouldn't a unique solution also result if I calculated the displacement from the facing direction AND the angle of rotation about that axis (the facing direction)?

Yes, this should provide a unique solution as well. I'll write up a sample script that does this and post it shortly.

[astull]

I don't mean to be a bother but the modified script still yields a non-unique solution. For example, both of the following sets of eulers yield the same solution:

euler1 = [30,90,0]
euler2 = [0,0,0]

euler1 = [0,90,30]
euler2 = [0,0,0]

solution: (90, 90, 30)

I don't understand why this happens. Maybe the vector/rotation alternative may be a more practical solution.

Thank you again for your help!

[farshizzo]

Those values are correct. I'm not sure what you are expecting. There is always going to be multiple euler sets that will yield the same angle difference. The vector/rotation alternative will also yield the same value for multiple sets. For example, the vector/rotation difference between the following sets will be the same:

euler1 = [0,0,0]
euler2 = [90,0,0]

#Vector difference will be 90
#Rotation difference will be 0

euler1 = [90,0,0]
euler2 = [180,0,0]

#Vector difference will be 90
#Rotation difference will be 0

From your first post it seems you are interested in the relative error between the two orientations. I don't see how having non-unique solutions affects this. Maybe I'm misunderstanding your original request.

[astull]

Yes, indeed! There are likely to be multiple euler sets that yield the same displacement errors. Sorry for being so bone-headed.

[farshizzo]

No worries. I know how confusing all this 3d math can get.

Would you still like me to provide you with the vector/rotation alternative?