# vtk.vtkTransform.GetOrientation giving wrong results for large scale differences

vtk.vtkTransform.GetOrientation produces the incorrect orientation if the difference in scales is more than 100.

Running on
Elements:

``````40 0 0 0
0 0 -10 0
0 0.04 0 0
0 0 0 1
``````

gives the correct: [90.0, -0.0, 0.0]

But changing the scale slightly

``````41 0 0 0
0 0 -10 0
0 0.04 0 0
0 0 0 1
``````

results in [0.0, -0.0, 0.0] which is incorrect

The reason why I need this in the first place is because I need to set the transform matrix of an actor. And the only way to do that is using SetScale, SetPosition and SetOrientation separately.

``````    m0 = mat1.GetElement(0, 0)
m1 = mat1.GetElement(0, 1)
m2 = mat1.GetElement(0, 2)
m4 = mat1.GetElement(1, 0)
m5 = mat1.GetElement(1, 1)
m6 = mat1.GetElement(1, 2)
m8 = mat1.GetElement(2, 0)
m9 = mat1.GetElement(2, 1)
m10 = mat1.GetElement(2, 2)

scale1 = (m0 * m0 + m4 * m4 + m8 * m8) ** 0.5
scale2 = (m1 * m1 + m5 * m5 + m9 * m9) ** 0.5
scale3 = (m2 * m2 + m6 * m6 + m10 * m10) ** 0.5

actor.SetScale(scale1, scale2, scale3)

x = mat1.GetElement(0, 3)
y = mat1.GetElement(1, 3)
z = mat1.GetElement(2, 3)

actor.SetOrigin(0, 0, 0)
actor.SetPosition(x, y, z)

out = [0, 0, 0]
vtk.vtkTransform.GetOrientation(out, mat1)

print("=======================================================")

print(mat1)
print(out)

actor.SetOrientation(*out)
``````

A possible work-around is to remove the scaling from the matrix before calculating the orientation:

``````    mat1.SetElement(0,0, m0 / scale1)
mat1.SetElement(0,1, m1 / scale2)
mat1.SetElement(0,2, m2 / scale3)

mat1.SetElement(1, 0, m4 / scale1)
mat1.SetElement(1, 1, m5 / scale2)
mat1.SetElement(1, 2, m6 / scale3)

mat1.SetElement(2, 0, m8 / scale1)
mat1.SetElement(2, 1, m9 / scale2)
mat1.SetElement(2, 2, m10 / scale3)
``````

Hi Ruben,

I looked at the vtkTransform source code, and apparently this behavior was intentional. The code defines this constant:

``````VTK_AXIS_EPSILON = 0.001
``````

If the ratio of the smallest scale to the largest scale is less than `VTK_AXIS_EPSILON`, then the angle is set to zero. For 0.04 and 41, the ratio is 0.00097561.

When the code was first written, this epsilon check was needed to avoid numerical issues with single-precision floats. But with double-precision, the epsilon should be something like 1e-12.

I can check to see if the VTK test suite succeeds with `VTK_AXIS_EPSILON = 1e-12`. If it does, then we can permanently change it.

Yes, but your method of computing the scale does not work if the scaling occurs along oblique axes. The general method of removing the scaling is to orthogonalize the matrix.

So perhaps `GetOrientation()` should be changed so that it automatically orthogonalizes the matrix before computing the angles. At the very least, it could check the condition number of the matrix and orthogonalize if the matrix is ill-conditioned like yours. This is also something that I can look into.

Euler angles are really bad for representing angles due to singularities and ambiguities when converting to/from axis directions (3x3 matrix). By adjusting tolerances or using more bits we cannot solve the problems, just reduce the frequency of failures.

I would recommend to use `SetUserMatrix` to position, scale, and orient actors and never use Euler angles (`Get/SetOrientation`) for representing orientation.

@dgobbi , thanks for looking into the code. Changing the epsilon to 1e-12 would be more than sufficient for my purpose. The epsilon of 1e-3 is already on the edge of occuring cases.

@lassoan , about the UserMatrix, Iâ€™ve been trying to avoid UserTransforms due to Are UserTransforms going to be deprecated?.

For me the ultimate solution would be to set the Matrix of the actors transform directly. Would a PR for that be appreciated or is there a reason to disallow setting it directly?

I would love to be able to directly set the actorâ€™s transform. Ever since I first started using VTK, the way VTK handled transformations seemed very clumsy. For me, it doesnâ€™t even make sense to have methods like â€śSetOrientationâ€ť or â€śSetPositionâ€ť for actors. The vtkTransform already has all the methods necessary to build a 4x4 matrix, so just passing the 4x4 matrix (or the transform itself) to an actor would be much more flexible. The current API is very limiting.

However, as you can see from Ken Martinâ€™s comment in the issue that you linked, you probably wouldnâ€™t get very far with a PR.

1 Like

We need to be able to set user transform/matrix directly. Requiring setting the orientation using Euler angles would be very complicated and fragile when you already have the position+orientation+scaling as a matrix.

I asked for the exact requirements on discourse and submitted the issue in gitlab to sort out this issue proactively, instead of having to push back on a pull request that breaks/removes the essential direct matrix setting API.

@ken-martin could you describe what are the user transform/matrix requirements that must be fulfilled for correct behavior?

For example we could require the user matrix to be a homogeneous transformation matrix composed of rigid transformation + scaling with positive factors, resulting in a:

• 4x4 matrix with bottom row equal to (0, 0, 0, 1)
• topeft 3x3 submatrix is orthogonal and has positive determinant

We may also define some soft requirements for accuracy and numerical stability. For example, maximum ratio between smallest and largest absolute value of scaling factor is recommended to be below 1e3 (or 1e6 or 1e12?). It might be also useful to specify a tolerance for the orthogonality of the orientation submatrix and for the (0,0,0,1) values in the last row.

Fully agree. We have been always using `SetUserMatrix` in 3D Slicer. Require using Euler angles for setting the actor orientation would be completely unacceptable. Setting the orientation using a quaternion would be sufficient and make sense in theory, but it would be impractical.

@ken-martin could you describe what are the user transform/matrix requirements that must be fulfilled for correct behavior?

FYI Ken has retired, I doubt youâ€™ll get a response.

Thanks a lot for the information. This is very important news. Iâ€™ve just checked and his profile no longer shows up on Kitwareâ€™s website (at least searching by his name did not bring up anything for me). Was there an announcement on the forum that I missed?

Could you recommend people to bring into this discussion who have the experience and authority to make the necessary changes in VTK? It may be just documentation change in the end, but whatever is described in the end should be aligned with long-term plans for THIS API.

No external announcement that I am aware of, Ken wanted to go quietly. But donâ€™t feel bad for him, I understand heâ€™s having a lot of fun adventures

As far as moving ahead with this discussion, David G knows more about VTK transforms than probably anyone else. @Sankhesh Jhaveri is moving towards a rendering leadership position, and should be involved in discussions. I know the folks in Kitwareâ€™s French office are very talented with lots of great rendering experience, Iâ€™ll make sure that they (as well as any others I can think of) are aware of the discussion. And of course thereâ€™s a lot of smart people across the VTK community - hopefully they will speak up.

BTW, Iâ€™ve never been completely happy with the transformation/matrix implementation and design, I personally would like to see something cleaner. Itâ€™s going to be a challenge though with all the code out there. And FYI, much of the API was initially designed in the mid-1980s in an object-oriented system called LYMB (a precursor to VTK). Graphics have changed a little bit since then

Thank you @will.schroeder.

This is amazing. Huge enterprises, frameworks, libraries emerged and disappeared during this time but VTK stayed around. I guess it is due to VTK developers being very smart to make many good decisions and being humble to admit and fix the few mistakes.

You hit the nail on the head: the community is amazing. A great mix of talent, but maybe more importantly very little drama and people trying to do the right thing (even when it means humbly admitting a mistake or less than stellar design :-)).

@ken-martin will be missed to be sure. He has always been the go-to resource once other people got over their heads.

Ideally we turn this into an opportunity for more people to get active in the rendering pipeline and re-think from todayâ€™s graphics perspective. It would be nice to have althernate rendering paths so that the legacy features donâ€™t break but new, cleaner, more flexible code can be developed. Ideally multiple ways of rendering could be composited at the framebuffer/zbuffer level efficiently.

If weâ€™re going to rethink rendering, we need to address the eventual EOL of OpenGL. The last I heard is that Dawn was still a path forward, but whatever, this is a good opportunity.

Agreed, Dawn is a good option. Iâ€™ve also experimented with WGPU which is similar to Dawn but uses Rust instead of C++. WGPU also has some nice python bindings. Having more than one WebGPU compatible implementation option is a nice strength I think, and sharing code/expertise between C++, JavaScript, and Python development environments would be awesome.

Also, just as an aside before people get too concerned, itâ€™s true that OpenGL is deprecated on MacOS and being replaced by Vulkan in many places but there are several ways to continue using the OpenGL API with a compatibility layer. So rethinking the rendering pipeline is more of an opportunity than a crisis.