That's true, but typically, quad-based models are not decomposed directly into triangles, but, rather, subdivision surfaces that do have a predictable resolutio

That's true, but typically, quad-based models are not decomposed directly into triangles, but, rather, subdivision surfaces that do have a predictable resolution. In other words, a direct triangulation of a non-planar quad can be resolved in two contradictory ways -- but smoothing it out produces a hyperbolic paraboloid with just one consistent resolution.