How to divide/control surface according to non-perpendicular lines.

Hi,
I have a problem which suppose to be easy but I can`t find a solution.
Surface which I created contain a lines in both direction (not perpendicural) created by "contour" function from Rhino.
The question is how to divide a surface according to those lines and control the output sub-surfaces (be able to deffine specyfic one and add something only for it)?

Probably the solution is very simple but by using isotrim surface or divide surface I couldn`t get the sub-surfaces with the proper edges (outline curves are not a straight lines) 

Thanks