Parametric modulation of the components.

Hello everyone.

Probably it's a simple issue to solve, but as I'm not very good in grasshopper yet I really need help.

I need to model a group of components that can behave parametricaly and so that it will be possible to control them. (File Components)

Basically they are plates that can bend either into convex or concave shape. They should maintain the same size even if the bend (same edge lenght, same surface area) as they are made of not elastic material. I modeled components in each shape it can be to obtain the curves along which the corners can move.. (File Bending)

Anyone has any suggestions at least how i can start modelling it? 

Thank you

Olga