Hi Klingbeil, could you maybe describe a bit more about kind of end result goal you're trying to achieve, like why is it that you are trying to turn on control points?

Control points can be turned on for an individual surface, but if you have multiple trimmed surfaces joined together, control points for something like that will not turn on, since it would be kind of easy to pull the surfaces apart so that there is a gap at a place where there used to be a shared joined edge.

Are you possibly thinking from a polygon modeling viewpoint? NURBS modeling with trimmed surfaces is a really different kind of structure than polygon modeling - often times with NURBS models the edges that you see in the model are "trim curves" which are not actually defining the surface but are instead marking areas of the surface as being holes or trimmed away areas. The trim curves live on the surface but they don't actually define the shape of the surface, there is an "underlying surface" that does that. So when you turn on control points you are turning on control points of the underlying surface. This is very different than a polygon modeler - in a polygon modeler all the edges that you see are what actually defines the polygon surface, they aren't a separate thing from the surface as with trimmed NURBS.

So with trimmed NURBS you aren't free to just grab any edge you see and pull it around, but on the other hand the benefit that is gained from trim edges is much better cutting and boolean operations, because when you do a boolean between 2 objects the surfaces themselves stay the same and only new trim curves are created on them. When a polygon modeler tries to do booleans it has to actually dice up surfaces into smaller and smaller little fragments, it's one of the reasons why there are problems with booleans in polygon modelers.

Also see this FAQ answer for some more details on why show points is not working for your joined object:

FAQ: Why does show points work for some objects but not others?

- Michael