Space Partitionning with G-Maps A new n-dimensionnal "Model" object

@inproceedings{ConreauxRM1997b,
 abstract = { A Mode! is defined in aOcAD as a partition of space. The inner space of a Modelis subdivided into Regions, bounded by a set of Boundary frames. This structure allows to represent for instance geological layers. As the definition of a model is independant from its dimension, this also applies to 2D cross-sections, that can be subdivided into 2D regions. The relationships involved in the representation of a model are known as the connectivities of the objets, as the decomposition of the objects into vertiees, edges and polygons is known as their subdivision. In the current topological model of aOcAD , known as the model of Weiler, the representation of the connectivities and the subdivision are tightly linked, and involve many kind of different objects. This has several drawbacks, such as making the algorithms quite complex and difficult to maintain. Moreover, the data structures are not general enough to represent objects different from triangulated surfaces. The new topological model, based on the notions of G-Map and Dari, gives a consistant answer to this problem. In this model, only one type of elements and one type of relationship between these elements is required for representing a subdivision of spaee. This applies to both the subdivision and connectivities of an object. Moreover, the subdivisions and connectivities are represented by two separated structures, thus enabling to construct models where the boundary frames are splines, for instance. But the most important advantage of this new structure is that al! algorithms can be proven, as the structure of G-Map is not only a computer program data structure, but also a wel! defined mathematical structure, on which mathematical proofs can act. },
 author = { Conreaux, Stéphane AND Levy, Bruno },
 booktitle = { 16th gOcad Meeting (Dallas) },
 month = { "november" },
 publisher = { ASGA },
 title = { Space Partitionning with G-Maps A new n-dimensionnal "Model" object },
 year = { 1997 }
}