Planar trimmed surface not accurate to curves

[ogould]

I'm trying to mess around with the idea of tessellated shapes that fit together. I have a basic shape done, and am trying to turn the curves into a surface. Seems easy enough, but when I use the planar surface option it's not quite accurate to the curve I made. As you can see in the picture, it doesn't reach as far as the curve does. I've tried adding more vertices to the curve, but that didn't work, as well as trying all the different options in the planar trimmed surface settings and that didn't work either. Also deleted the history of the curve, didn't change anything. None of the other surface options get the kind of shape I'm looking for, so I'm at a loss for how to make the surface accurate to the curve. Anyone know the reason it's not quite right? 

[hamsterHamster]

Planar tessellation edges has never been precise.

What you can possibly do is to Edit Mesh > Project Curve onto a pPlane and then perform splitting, Separating, deleting History.

Since you have several stacking shapes, you might wish to delete those parts of the next shape, that are already cut, because it will make a mess for the edges that are already split.