Bird's nest on a surface

Hello all,

This may be a ridiculously long and convoluted definition (and question), but what I'm trying to create is a bird's nest structure similar to the one in Beijing. I'm aware there has been similar discussions, but those definitions create piped intersection lines. What I need is an open surface, split by these strips, to be imported into solidworks for further development.

I am using Hoopsnake to iterate the rotation of a planar surface around 3 different axis. I then extrude the surfaces and try to perform a boolean union.  After the union I can split my base surface by the solid union to achieve my desired effect.

The problem I am having is the boolean union seems to fail with too many items.  I'm not sure if it is because of geometric problems or what.  

My next approach was to skip the union and solve for the intersection of my base surface and the extruded surfaces, then shatter those curves and try to eliminate the curves inside the intersection by sorting lengths. The problem I am having there is, I can't figure out how to sort the data  between the curves and intersection points.

If anyone can help, or come up with a better solution, it would be greatly appreciated.

Thanks