Increasing computer power together with new developments in 3D hardware and fast algorithms for geometry optimization have opened the door to extremely complex virtual environments that can now be displayed at interactive speed. But still, with traditional modeling technology, industrial 3D construction is typically very expensive. As every object is basically unique, the created models suffer from two main problems, poor changeability and poor reusability of 3D models. Detailed models are typically designed on a part-by-part basis to reduce the modeling complexity. But then, many dependency relations between geometric entities within the 3D scene get lost. As these relations cannot be expressed explicitly, it is not possible to alter them directly. This conceptual limitation abates both changeablity and reusability, as even a slightly different object may require many construction steps to be repeated in a different fashion.
Many steps in the modeling process are repeated several times with different parameters on different objects. Consequently, it is desirable to automate 3D modeling using some form of geometric programming language. When a user can specify variables and functions in a geometric program to let object parameters be computed automatically, even dynamic models become possible. Programmed models have a different space-time tradeoff: When low-level primitives are generated only on demand from higher-level descriptions, space is traded for model evaluation complexity. With a geometric modeling language that permits compact and comprehensive descriptions of very detailed models, this model description has to be quickly translated to OpenGL primitives at runtime _ . This leads to the following research directions:
Subdivision surfaces can be used to define freeform surfaces over irregular control point meshes and introduce discontinuities like spikes or creases in a controlled way. Moreover, they help to reduce freeform modeling to polygonal modeling, as any polygonal mesh can be used as control polygon. Thereby, they drastically reduce the degrees of freedom (DOFs) in freeform modeling and consequently fit very well to a generative modeling framework. The advantage of using subdivision surfaces in this context is twofold: