Can a Rigid Body's Rotation Be Described with Only Two Successive Rotations?

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SUMMARY

The discussion centers on the limitations of describing a rigid body's rotation using only two successive rotations, specifically yaw and pitch, as opposed to the full three rotations including roll. It is established that while two rotations allow for pointing a camera in any direction, they restrict the ability to achieve certain orientations, such as taking an upside-down picture. The inability to perform a roll limits the generality of the rotation representation, particularly in scenarios where a complete 3D orientation is required.

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  • Knowledge of camera mechanics and positioning
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This discussion is beneficial for computer graphics developers, robotics engineers, and anyone involved in 3D modeling or camera systems who seeks to understand the constraints of rotation representations in three-dimensional space.

Barkan
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I try to clearify it as much as I can, and I greatly appreciate the given answers.

Suppose that we have a rigid body. We attach a movable coodinate frame on this body.

Normally, if I perform 3 successive rotations such as Z-Y-X or Z-Y-Z (or any other 24) I can describe its rotation in the most general case.

If I perform only two rotations what will happen then? Let's suppose I only perform a Z-Y rotations (first rotate about yaw then rotate about the current pitch) what would be the loss in terms of generality? Let's say, without the 3rd successive rotation, I cannot describe the half of the ... plane and/or sphere?

Thank you very much in advance.
 
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So you only have yaw and pitch, but no roll. Camera tripods rotate this way. You can point the camera in ANY direction, so you're not limited there. However, you cannot point the camera at an object and then roll the camera to take an upside-down picture for example. That's what you lose by only having two rotations.

If this doesn't help any, do you think you can clarify the question? What is the motivation (what exactly are you trying to do?)
 
I made a small mistake in my previous post. You could actually take a picture in any direction upside-down. You would do this by yawing so that you're pointing in the opposite direction, then pitching the camera so that it's inverted to look at the object.

So 0 degrees and 180 degrees are special cases. In general, you cannot take a rotated picture of an object.
 

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