Rhino SubD objects are standard Catmull Clark subdivision surfaces with support for creases, darts and corners. Away from exceptional points, these surfaces are nonrational bicubics.
One drawback of this choice is that Rhino SubD objects cannot have exact spherical regions, so you either have to approximate the spherical region with a subd or have a separate spherical NURBS object adjacent to your subd. The SubDSphere command is a way to explore a variety of ways to get good approximations to a spherical region.
You conclusion is correct. It is mathematically impossible for a non-rational polynomial to have the shape of an exact circle. More generally, any type of ellipse or hyperbola requires a rational polynomial. Parabolic regions can be exactly represented by non-rational quadratics, and hence by non-rational cubics.
So, a standard Catmull Clark subd surface cannot have exact spherical and cylindrical regions. However, typically cubic approximations get pretty close without adding too many control points. If you need exact spherical / cylindrical regions in your model, those regions need to be modeled with Rhino polysurfaces.
Yes, the purpose is having a simple flexible manipulator for NURBS. But a precise one.
having 4 elements (with example 4 points of control of 0.707)
Staregy @John_Brock extending SubD flexibility and improving precision:
For controlling good meshes, NURBS is the best approach (Rhino strategy). For controlling NURBS surfaces, the SubD user interface approach is a good choice. And can be the main UI component of a new tool that control NURBs as a manipulator. So that the user is comfortable.
Yes, but is not possible to maintain that deviation across the model.
Until now, SubD is nice for making potatoes faster
It is more for undemaining bio-design. The Lotus Elise was done using this technology. But we know that is not appropriate for hard surfaces modelling.
That’s why video game car meshes look melted compare to a real car surface converted to mesh.
Instead of Catmull Clark, use NURBS directlly and start with second degree.
I put a car as example but let talk about a Propeller Blade
SubD: You can’t build a real propeller blade. I try that. You can’t maintain the airfoil profile and correct twist. Good for video game but not for a realone.
Surface: You can do it using the surface but is a long process, complex to maintain. Produce target. across all the surfaces when you are modifying the profile is impossible. Grasshopper helps a lot for the transitions. But maintaining the smoothness with the root, cone, or tip can be a nightmare. Grasshopper is the key but can be much better.
SubD second degree using NURBS, will let you be fast and precise at the same time. And Grasshopper over it will be very attractive to the industrial design sector.
"SubD as a manipulator of second degree NURBS can be a new tool (with a new name) using a dynamic polysurface of second degree under the hood. But the same UI of SubD.
It will be more difficult to manipulate than a normal SubD, but much precision and faster than actual polysurface. We all know that.