The main rationale is removing redundant degrees of freedom -- since the page is allowed to rotate freely, the edges of the page can still move around plenty.
I see, so basically assume the two end points are at zero and there is some rotation accounting for the endpoint offset in real space.
It still doesn't seem fully accurate as I can imagine a non-rotated cubic curve with endpoints at an offset, but I assume your simplification works well enough.
It still doesn't seem fully accurate as I can imagine a non-rotated cubic curve with endpoints at an offset, but I assume your simplification works well enough.