deforming curves based on other deformations

Hey, I'm wondering how to deform some geometry on the basis of a specified deformation. I don't even know how to do the specific deformation, so the referential deformation's actually the second issue. Here's the details:

I have a curve with two curves offset from it at arbitrary distances. I want to flatten the curve, then apply the exact process of that flattening to the offset curves.

So A maps to B with f, and I want to get what f would map C and D to.

(A = initial curve, B = flattened curve, C and D = offset curves)

I hope there's nothing fundamentally difficult with this. I have to admit, I'm probably least familiar with the transformation tab's elements...