Perhaps bugs when converting axisangle to rotation matrix

[kyang-06]

Very impressive and elegant theory to push this field forward!

But I notice there may exist a bug.

RotationContinuity/sanity_test/code/tools.py

Lines 172 to 180 in aee1e34

	axis, theta = normalize_vector(rod, return_mag=True)
	sin = torch.sin(theta)
	qw = torch.cos(theta)
	qx = axis[:,0]*sin
	qy = axis[:,1]*sin
	qz = axis[:,2]*sin

RotationContinuity/sanity_test/code/tools.py

Lines 141 to 147 in aee1e34

	theta = torch.tanh(axisAngle[:,0])*np.pi #[-180, 180]
	sin = torch.sin(theta)
	axis = normalize_vector(axisAngle[:,1:4]) #batch*3
	qw = torch.cos(theta)
	qx = axis[:,0]*sin
	qy = axis[:,1]*sin
	qz = axis[:,2]*sin

Code above are the function converting axisangle/rodrigues to rotation matrix.
The θ passed to torch.sin and torch.cos is the identity but should be θ/2 instead, referring to Maths - AxisAngle to Quaternion
I've hand-written a toy case (rotate y axis by 90 degrees around x axis) and only θ/2 is correct.

I wonder if it is a bug, and if so, does it influence other conversion functions and further influence result of experiments?

[papagina]

Hi, thank you for examining our code! You are right, the function should be θ/2, but since the scaling can be accommodated by the neural network, it wouldn't influence the approximation capability of the network for the representations. To justify it, I also ran the training with the scaled θ and the result remains similar.

[meaten]

Thanks for the great work!
I also noticed that compute_rotation_matrix_from_Rodriguez has the same mistakes on halving theta.
Could you kindly update tools.py for anyone using your codes?