algorithmic modeling for Rhino
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P.S. You could, and probably should, automatically remove sub-surfaces that are not triangles (have more than three edges or vertices). Sometimes only a tiny bit is clipped so area is nearly the same, but with four or more edges/vertices, it would be filtered out in any case as a partial.
Amusing enhancements to the test bench; ability to rotate the clipping polygon and change its radius, with a two second delay ('Data Dam') before the slow clipping and surface splitting operations, which get VERY LONG as the radius goes up! But that's data prep in this case, yours are already clipped (and split?), so you'll want only the blue and green groups from this to test surface sections.
It worked, Thanks a lot!!
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