Generative Modelling Language
The Generative Modeling Language GML is a language for describing three-dimensional form. It follows the paradigm of generative modeling, in which no object lists, but ( object- generating ) operations are used for data representation.
Generative modeling
The generative modeling is an alternative approach to the description of three-dimensional form. The basic idea is a model not as usual by a collection of geometric primitives (triangles, points, NURBS patches ) to describe, but by functions. The paradigm shift from objects to geometry - generating operations makes it possible to represent procedurally structured models ( chair, car rim ) also procedural. Instead of storing only the result of a 3D design process, so can the design process itself will be represented. The generative approach allows to draw on a pool already dissolved design tasks to be reused in similar, slightly varied situations. The design knowledge can be collected this in the form of libraries of parameterized, domain - specific modeling tools.
The Generative modeling language
The " Generative Modeling Language (GML )" is a concrete realization of a generative model description language. It is a stack -based, interpreted programming language, which is similar in structure to Adobe Postscript, but without operators for 2D layouts. Instead, it contains a full set of operators for the construction of 3D models ( inter alia, for polygons, b- Reps, subdivision surfaces ). As a " programming language for the form " it provides, among other things a real generalization of existing primitive - based 3D model formats such as OBJ, DXF or VRML dar.
Along with their OpenGL -based runtime engine allows GML,
- A compact description of parameterized 3D objects
- Which can be evaluated at run-time on-the -fly,
- The representation with adaptive level of detail ( LOD),
- And the interactive change of the model parameters.
GML example
Applications
In procedural models, the model size does not depend directly (ie linear) on the file size. The " Procedural Cathedral ", a coarse model of the Cologne Cathedral, contains 70 tracery windows, in the highest resolution contains a single window around 7 million triangles. This " unfold " from only 126 kB GML code ( 18 kB zipped).
Gothic architecture is an example of the richness of the procedural form design: In all the Gothic constructions were carried out only with a compass and ruler. Variations were obtained by very simple parametric basic operations were combined procedurally in ever new ways basically. Therefore, it is practically impossible to find two tracery windows in different buildings where the parametric design is identical.
The interactive CAVE Designer helps fit a CAVE in a small room. Because of the joists, it is difficult to solve the problem only with 2D plans (floor plan, elevation ). Degrees of freedom ( blue arrows) are the position and orientation of the screens and the opening angle of the projectors.
Based on 30 given CAD models of car rims was here trying to find a common parameterization, so that each of the given rim can be generated from it ( " generative reverse engineering "). Now, go into the design space, which is spanned by the individual wheels, easily create new, similar models.
The generative model specifies a differentiation between " structure" and the "appearance" (eg, style) of a 3D model close. A surprising number of objects have established the same structure as a chair, that is, are structurally similar. In principle, this separation then allows to transmit the "appearance" of an object within this class to each other.
Didactic applet to illustrate Voronoi diagrams. It is about the question whether it is possible the centers of the Voronoi cells derived from the boundaries of the regions. The applet conveys the idea behind the formal proof is based.