Hello, this is some continuation of my previous posted topic on transformation. I have attached two pictures of rotation of different axes, i.e. X, Y and Z. Z rotation is the projection on XY plane for two different Z rotation. It shows how the length of the axis varies depending on Z rotation. Now my question is, from this information is it possible to figure out rotation of Z axis. Here as rotation is on XY plane, the length of X and Y axis does not vary, but that of Z-axis varies.

Thanks in advance.

Hello, this is some continuation of my previous posted topic on transformation. I have attached two pictures of rotation of different axes, i.e. X, Y and Z. Z rotation is the projection on XY plane for two different Z rotation.

I don't know what "Z rotation" means, and the sentence above makes no sense, so it doesn't help me. Mathematics requires precise language.

It shows how the length of the axis varies depending on Z rotation. Now my question is, from this information is it possible to figure out rotation of Z axis. Here as rotation is on XY plane, the length of X and Y axis does not vary, but that of Z-axis varies.

What is "it" at the beginning of what I just quoted? Is it supposed to match "two pictures"?

Axes doesn't have lengths: Vectors do, but rotations don't change the length of any vectors.

In short, I don't understand anything in your question.

If you know the projection, and can guaranty unit length axii, you should be able to reverse engineer a transformation. How ever, I'm not 100% sure that the result is a unique transformation, without having the depth to go along with the projected image. If it is possible, the resulting transformation would be an axis angle rotation, which you would have to further decompose into euler angles.