Generative Mesh Modeling

Generative Modeling is an alternative approach for the description of three-dimensional shape. The basic idea is to represent a model not as usual by an agglomeration of geometric primitives (triangles, point clouds, NURBS patches), but by functions. The paradigm change from objects to operations allows for a procedural representation of procedural shapes, such as most man-made objects. Instead of storing only the result of a 3D construction, the construction process itself is stored in a model file. The generative approach opens truly new perspectives in many ways, among others also for 3D knowledge management. It permits for instance to resort to a repository of already solved modeling problems, in order to re-use this knowledge also in different, slightly varied situations. The construction knowledge can be collected in digital libraries containing domain-specific parametric modeling tools. A concrete realization of this approach is a new general description language for 3D models, the "Generative Modeling Language" GML. As a Turing-complete "shape programming language" it is a basis of existing, primitv based 3D model formats. Together with its Runtime engine the GML permits - to store highly complex 3D models in a compact form, - to evaluate the description within fractions of a second, - to adaptively tesselate and to interactively display the model, - and even to change the models high-level parameters at runtime.Die generative Modellierung ist ein alternativer Ansatz zur Beschreibung von dreidimensionaler Form. Zugrunde liegt die Idee, ein Modell nicht wie üblich durch eine Ansammlung geometrischer Primitive (Dreiecke, Punkte, NURBS-Patches) zu beschreiben, sondern durch Funktionen. Der Paradigmenwechsel von Objekten zu Geometrie-erzeugenden Operationen ermöglicht es, prozedurale Modelle auch prozedural zu repräsentieren. Statt das Resultat eines 3D-Konstruktionsprozesses zu speichern, kann so der Konstruktionsprozess selber repräsentiert werden. Der generative Ansatz eröffnet unter anderem gänzlich neue Perspektiven für das Wissensmanagement im 3D-Bereich. Er ermöglicht etwa, auf einen Fundus bereits gelöster Konstruktions-Aufgaben zurückzugreifen, um sie in ähnlichen, aber leicht variierten Situationen wiederverwenden zu können. Das Konstruktions-Wissen kann dazu in Form von Bibliotheken parametrisierter, Domänen-spezifischer Modellier-Werkzeuge gesammelt werden. Konkret wird dazu eine neue allgemeine Modell-Beschreibungs-Sprache vorgeschlagen, die "Generative Modeling Language" GML. Als Turing-mächtige "Programmiersprache für Form" stellt sie eine echte Verallgemeinerung existierender Primitiv-basierter 3D-Modellformate dar. Zusammen mit ihrer Runtime-Engine erlaubt die GML, - hochkomplexe 3D-Objekte extrem kompakt zu beschreiben, - die Beschreibung innerhalb von Sekundenbruchteilen auszuwerten, - das Modell adaptiv darzustellen und interaktiv zu betrachten, - und die Modell-Parameter interaktiv zu verändern

Efficient ordinary differential equation-based modelling and skin deformations for character animation.

In the area of character animation, skin surface modelling, rigging and skin deforamtion are three essential aspects. Due to the different complexity of the characters, the time cost on creating corresponding skin surface model, animation skeleton in order to achieve diverse skin de- formations, fluctuates from several hours to several weeks. More importantly, the data size of skin deformations could sharply influence the efficiency of generating animation. Smaller data size can also speed up character animation and transmission over computer networks. Over years, researchers have developed a variety of skin deformation techniques. Geometric skin deformation approaches have high efficiency but low realism. Example-based skin deformation approaches interpolate a set of given example poses to improve realism and effects that cannot be easily produced by geometric approaches. Physics-based skin deformation methods can greatly improve the realism of character animation, but require non-trivial training, intensive manual intervention, and heavy numerical calculations. Due to these limitations, many recent activities have initiated the research of integrating geometric, example-based, and physics-based skin deformation approaches. The current research is to develop techniques based on Ordinary Differentical Equations (ODE) to efficiently create C2 continuous skin surfaces through two boundary curves, automatically generate skeleton to make the rigging process fast enough for highly efficient computer animation applications, and achieve physically realistic skin deformations for character animation by integrating geometric, physical and data-driven methods. Meanwhile, it is the first attempt to obtain an analytical solution to realistic physics-based skin deformations for highly efficient computation, to avoid the solving of a large set of linear equations, which largely reduces data size and computing time. The basic idea is to build ODE mechanics model, involve isoparametric curves and Fourier Series representation, develop accurate and efficient solutions to calculate physical skin deformations through interpolating input realistic reconstructed 3D models. The proposed techniques will greatly avoid tedious manual work, reduce data size, improve skin deformation realism, and raise efficiency of producing character animation