Can you render NURBS on the GPU with DirectX 11? I've been reading up on current trends to rendering surfaces like these, but I don't see anything on NURBS.
I found some related references, but nothing solid... like "Approximating Catmull-Clark Subdivision Surfaces with Bicubic Patches" by Charles Loop and Scott Schaefer.
The quick answer is no. NURBS are pretty complex, and it would be difficult to write an efficient shader that can render them on the GPU. I think it's possible, but it isn't usually done because there's a better way.
The better way is to render Bézier patches directly on the GPU, since any NURBS can be converted into a connected set of Bézier patches. To generate the patches, you perform knot insertion at every knot until it hits the same multiplicity as the degree; e.g. on a cubic NURBS, you would perform knot insertion at every knot until every knot is a triple knot. The control points of the NURBS can then be treated as a connected Bézier mesh.
There is a problem with this, specific to shaders: When you triangulate your Bézier patches, it's critical that patches which share a boundary also share the exact same tessellation settings, or there will be cracks in your NURBS surface due to tessellation mismatch. If you use fixed tessellation settings, this isn't a problem, but if you use view-dependent tessellation, then you need to make sure that each patch boundary has its "view dependent" tessellation calculated independently, so that adjacent patches will match.
There are 2 demos in the DirectX SDK; SubD10, SubD11 for DirectX 10/11 implemenations respectively of the techniques described in this article.
