(beginner) calculating orientation change with eulers

[farshizzo]

Using the euler angles, you can find the look vector of each orientation, then compute the angle difference between these vectors. However, this method will not take roll into account. For example, if both orientations are looking straight ahead, but one has the head rolled 90 degrees, the difference will still be 0 degrees. If you are interested in the roll, then you can also extract the up vector of each orientation and compute the angle difference between these. It would then be up to you to figure out how to convert these two angle differences into some orientation error metric.

Let me know if you are interested in this method and I will supply you with some sample code.

[astull]

Yes, this method makes sense and sample code would be welcomed.

[farshizzo]

Here you go

import viz
viz.go()

euler1 = [90,0,0]
euler2 = [91,0,5]

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

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

	return forward_diff,up_diff
	
print ComputeAngleDifference(euler1,euler2)

[astull]

Jerry pointed out that the script doesn't always give a unique solution. For example, both of the following sets of eulers give the same forward_diff and up_diff solution, which is (90, 90).

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

and

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

Is there a way to address this?

[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.