I'm trying to wrap my head around what I think is 50% a definitions problem and 50% me not understanding affine/vector spaces and subspaces well enough.
I have an operation that I can apply to any set of surfaces (in this case in 3D Euclidean space), with the constraint being that each surface has to be the result of an affine transform of any other surface in the set. For instance, in 2D this operation will work taking a set consiting of a square, a rectangle, and a Rhombus, but it would not work if I tried to give it a set consisting of a square and a triangle, or a set consisting of a square and a square that had been projected from the surface of a sphere.
I am trying to describe this operation, and the best I can do is to explicitly describe it as I have, saying "it only works when each input is an affine transformation of another". Is there a better way of saying this? From my limited understanding of affine space, I am tempted to believe that I could say "This operation works when all inputs are members of the same affine space" but I am not confident in my knowledge of affine space definitions to say this for sure (I wonder if the correct definition would be that they are of the same affine subspace? Or perhaps that an affine map exists between each item within the set?).
Thanks,
Blayzeing
It seems the word I was looking for was "Affinely Equivalent", as in all items passed to the operator are affinely equivalent to one another.
Slide 5 of this presentation directly defines this phrase, and this worksheet from the university of Manchester seems to imply it is also the correct word
Thanks to Blue and bob in the comments for that :)