Hi Charles, it is possible to show points for a booleaned object, but when you do so you'll probably see that the points are not as you are expecting.

To show points on your booleaned sphere, use Edit > Separate on it first to break it apart into individual surfaces, then show points will work on those individual surfaces.

When you do that, you'll see that the surfaces involved there are actually larger than the edges - that's due to the structure of how NURBS solids work, where when things are trimmed or intersected, the underlying surface stays the same and only new trim curves are created. Trim curves are kind of like markers that live on a surface and mark different portions of the surface as being active or inactive, making holes in it.

But the shape of the surface (and therefore what you would alter by pulling points around) comes from the underlying untrimmed surface and not the trim curves directly, except in the special case where the trim curves are the same as the full outer boundary of the surface.

MoI will not turn on control points when you've got joined pieces that do not have surface control points that touch each other because it would be too easy to create gaps and holes in the model since pulling the points around would just pull one part of a surface around and not pull the edges more directly.

This all is another big difference between NURBS and polygon modeling - in poly modeling the edges that you see are always the exact same thing as the edges of the surfaces involved, so pulling edges and pulling the surface are equivalent. With NURBS where you have a trim edge, that's a kind of separate thing from the surface and there is not the same concept of pulling around the edge directly.

However, this entire structure is also the reason why boolean operations work better with NURBS surfaces than they do with polys - with polygons when you do booleans the boolean code has to create a lot of little slivered polygons, and the more booleans you do the more dicing and chaotic little fragmented pieces are generated.

With NURBS surfaces on the other hand, when you do booleans and trimming the underlying surface itself stays the same and only new trim curves are calculated that mark areas of that surface as being holes. No matter how many cuts you do on a surface it does not fragment into a bazillion little shards like poly booleans do. And you can also do stuff like erase the trim curves to get back to the underlying surface.

See this FAQ answer here: Why does show points work for some objects but not others? for some more information and some illustrations about this.

- Michael