Cellular Graphs: an introduction to G-Maps, Weiler and other topological Models

@inproceedings{Levy99GMGM,
 abstract = { Combinatorial topology is a recent field of mathematics which promises to be of great benefit
to geometric modeling and CAD. As such, this article shows how the notion of Generalized
Map (G-Map) can be used to implement a dimension-independent topological kernel for industrial
scale modelers and partial derivative equation (PDE) solvers. Classic approaches to
this issue either require a large number of entities and relations between them to be defined, or
are limited to objects made of simplices. The G-Map representation relies on no more than a
single type of element together with a single type of relation to define the topology of arbitrary
dimensional objects (surfaces, solids, hyper-solids ... ) containing primitives with an arbitrary
number of edges and faces. The mathematical origin of G-Maps facilitates the characterization
and the definition of validity checks for the objects, which can be important for industrial scale
applications. The method might also have important implications for topology-intensive computations
such as mesh compression, mesh optimization or multi-resolution editing. Teaching
abstract mathematics, such as the notion of orientability and cellular partition, is another
possible application of the method, since it provides a way to intuitively visualize some of
these notions. },
 author = { Levy, Bruno AND Conreaux, Stéphane AND Mallet, Jean-Laurent AND Lienhardt, Pascal },
 booktitle = { Proc. $19^{th}$ Gocad Meeting, Nancy },
 title = { Cellular Graphs: an introduction to G-Maps, Weiler and other topological Models },
 year = { 1999 }
}