There is no standard definition for what an “organic shape” is. Probably the best definition, in the context of CAD, is that it’s a shape that’s a real pain in the neck to model using traditional methods with NURBS surfaces.
Here’s an example. While you could certainly find a way to model this shape with NURBS, and even get the nice G2 continuity shown here, it would definitely fall into the “pain in the neck” category:
There are a number of interesting tools available for doing organic shape modeling. Most, however, don’t use NURBS—they use subdivision (SubD) surfaces. SubD surfaces, though based on the same mathematical underpinnings as NURBS, are quite a bit different. And the process of creating and editing SubD surfaces is quite a bit different too.
The Freestyle extension in PTC’s Creo Parametric 2.0 program is one of the most interesting SubD surface modelers. It’s not only included at no extra charge with the base program, it’s well-integrated with Creo’s parametric modeling capabilities, allowing you to create aesthetic surfaces with SubDs, and precise surfaces (for interfaces) with NURBS.
PTC has recently posted a video that compares using Freestyle SubD surfaces in Creo Parametric 2.0 with NURBS surfaces in Pro/E Wildfire 5.0:
While it’s likely that PTC is trying to encourage their Pro/E users to upgrade to Creo, the video really highlights the difference in modeling methodology using SubD surfaces versus NURBS surfaces. It’s worth a watch, even if you’re not a Pro/E or Creo user, because it shows what can be done with SubD surfaces. If you do any kind of aesthetic surface design, you want SubDs.