For a vessel that has a single half-wave, along the ship, you will have to locations with 0 translation, but pure rotation, and 1 location at center with pure translation but no rotation. Depending on the size of the facility, however, you can have whole waves or multiple waves.
Everywhere else will have a combination of rotation and translation.
In the real world, you also have piping acting as a catenary and everything attempting to slide towards the lowest point, but CAESAR and we tend to ignore this. We also tend to simplify all rotations as translations. We rationalize this because the pipe is allowed to pivot around supports freely and naturally rotate.
In a static analysis, as far as piping stresses are concerned, it doesn't really matter which point on the pipe you say stays still, so long as the deflected shape meets reality. As far as restraints are concerned, however, the more accurate the model, the more accurate the restraint report.