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If you have one point and the quaternion, that's about as compact a data representation as you can get for free space position. The second vector is redundant with the quaternion, you don't need to keep both.

On modern computers storing thousands of poses is not particularly large enough to worry about most of the time.

If you have one point and the quaternion, that's about as compact a data representation as you can get for free space position. The second vector is redundant with the quaternion, you don't need to keep both.

On modern computers storing thousands of poses is not particularly large enough to worry about most of the time.

Edit:

If the cylinder is of known size, yes the lowest point and orientation is enough to compute any position on the cylinder. Otherwise no.