Hmm, is this "car(ing) about distance between specific points" something that would matter if we were going to operate in reverse and splat something at each point to render the triangle?

I think that sort of splatting is how I intuitively think about this problem, and likely where I went wrong in thinking there would be a distortion of the density function. I'm not confident whether this actually matters though. Would it still approximate the same distribution regardless of what splat shape is used...?