(beginner) calculating orientation change with eulers

[astull]

I'm capturing Euler angles before and after a user manipulation. The object is fixed in location and only changes in orientation. What I want to measure is the error between a target orientation and the user's response orientation for the object. I've calculated the difference for each of the 3 axis but, if I understand correctly, this doesn't give a measure of the orientation change in 3D space. What is the proper method/strategy to attack this question? I'd like one measure of orientation error but I'm not sure how to get it.

[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]

I met with Andy B. today and he pointed me to the quatdiff function as a potential single metric solution to the error calculation. I know the function is available through Vizard but I'd like to verify it on paper. He said that you might be able to send me the C code.

Thanks again!

[farshizzo]

The QuatDiff function simply uses the above method of computing the angle difference between the forward and up vectors, and returns the maximum of those two values.

You can modify the sample code I gave you to replicate this behavior.

[farshizzo]

Here is some code that calculates the difference between two angles based on the method steve described:

import viz
import math
viz.go()

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

def ComputeAngleDifference(euler1, euler2):
       q1 = viz.Quat( vizmat.EulerToQuat(euler1) )
       q2 = viz.Quat( vizmat.EulerToQuat(euler2) )

       delta = q1 * q2.inverse()

       return viz.degrees( math.acos( delta.w ) ) * 2.0

print ComputeAngleDifference(euler1,euler2)

I'll updated Vizard's QuatDiff function to use this method in the next release.