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> Research > Projects > GenerativeModeling

Generative Modeling

Prof. Dr. D.W. Fellner, Dr. Sven Havemann
Computer Graphics and Knowledge Visualization, Graz University of Technology, Austria, www.cgv.tugraz.at

Motivation

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.

Gothic window: basic ’style’ in left image is augmented with a rosette and then applied recursively once and twice to the window geometry in the center image and right image, respectively.

Generative Modeling

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:

• language-based 3D-modeling
• efficient model evaluation and visualization

In fact, this approach initiates a paradigm change from traditional objectbased modeling to function-based, i.e. generative, modeling. Objects are not described in terms of triangles anymore, but merely in terms of the function sequence which was used to generate it. _

Subdivision Surfaces

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:

• Reduction of the degrees of freedom
• Adaptive tesselation during an interactive session

In contrast to polygonal models, subdivision surfaces do not suffer from an approximation quality that is a priori limited. Instead, they can be tesselated on demand to any resolution needed, which is essential for high-fidelity close-ups.

Separating basic geometry from ’presentation’: the styles ’arcade ’ and ’building ’ are applied to a basic u-shape and then the basic shape is changed independently from the applied style in the lower row.

References

_ _

• D. W. Fellner, S. Havemann, G. Müller, Modeling of and Navigation in Complex 3D Documents:Computers & Graphics, Vol. 22, No. 6, Dec 1998
• K. Müller, S. Havemann: Subdivision Surface Tesselation on the fly using a versatile Mesh Data Structure, Computer Graphics Forum, Vol. 19, No. 3, Aug. 2000
• D. W. Fellner et al.: Beiträge der Computergraphik zur Realisierung eines verallgemeinerten Dokumentenbegriffs, it+ti 6/2000