Surfaces & Trimming

Would you help me to solve next task:
Let’s have surface of revolution (it is created by means of rotating the arbitrary
curve around the axis). It’s simple to visualisate such body. Problem is, that
this body can be trimmed in a same way
like the nurbs surfaces are.
I’d like make it as simple as possible (I’d like to avoid mathematics and intersections computing). Has OpenGL tools for solving this? To define a surface by means of grid of 3d points and then to use trimming?

Thanks for your opinions.
Adrian Helcman.