Is there a name for this operation of collecting the translation of a point in several directions?

Question

I am writing some code that deals with a 2-dimensional grid and have an operation I am calling project which takes a point and translates it by the grid unit in each direction. Is there a more descriptive name for this sort of operation -- collecting the results of translating a point and applying n rotations? Or perhaps a name for applying the process once (translate + rotate)?

Answer 1

When a group $G$ acts on a set $X$, the set of all possible images of a selected point $x\in X$ after being acted on by elements of $G$ is called the orbit of $x$.

I'm not totally sure this is also applied to a set of transformations acting on a set, but you could call it "the orbit of $x$ under this set of transformations" and that would be pretty natural.