> This seems counter-intuitive... I understand your reasoning, and I can't
> find a mistake in your logic, but it seems to me that the size shouldn't be
> constant (from an intuitive standpoint)...
you are probably thinking about the usual texture mapping setup, where
a projective mapping (from screen space to texture space) is performed.
In this canonical case, the texture footprint is position dependent (you
describe the mapping of projective planes by a homography, which is
linear in homogenous coordinates, but non-linear in texture/screen coordinates due to the perspective division).
Your setup is just a linear transform of a 2D subspace (you want to transform
the UV plane into the world space triangle plane), i.e. you seek a mapping of the UV-basis vectors to their respective world-space counterparts.