Control Points dissappear?

 From:  Michael Gibson
2073.2 In reply to 2073.1 
Hi slayer - at some point you got a boolean or a join in there.

When you have 2 joined surfaces that are joined at a trim edge that is not a "natural" edge of the underlying surfaces, then control points are not able to be turned on for that object. That is to prevent the problem of pulling apart a gap in what is supposed to be a shared joined edge.

You can use Edit/Separate to break such objects into individual surfaces, and then control points should always be available for an individual surface.

Check out here for some more detailed information with some illustrations:

- Michael