## Subdivisions de surfaces et cartes généralisées de dimension 2. (Subidivisions of surfaces and generalized maps of dimension 2).(French)Zbl 0734.68095

Summary: This paper deals with modeling subdivisions of orientable surfaces, with or without boundaries. Modeling this kind of subdivisions is of great interest in Boundary Representation.
Following H. G. Griffiths [Surfaces, Cambridge etc.: Cambridge University Press (1981; Zbl 0457.57001)] for instance, we present a constructive definition of subdivisions of surfaces, and a classification of these subdirections into topological surfaces. We also present the notion of topological 2-map, which allows to model the topology of any subdivision of any orientable surface without boundaries, and the notion of 2-G-map, introduced by W. T. Tutte, which allows to model the topology of any subdivsion of any surface (orientable or not, with or without boundaries). Any 2-map can be deduced from a 2-G-map, which defines the topology of a subdivision of an orientable surface without boundaries. Characteristics are associated to any 2-map and to any 2-G-map. These characteristics make it possible to classify 2-maps and 2-G-maps, according to the classification of the subdivisions which are defined by these 2-maps and 2-G-maps. Finally, we present basic operations, which allow to construct any 2-G-map (and consequently, of any 2-map).

### MSC:

 68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

### Keywords:

subdivisions; orientable surfaces; Boundary Representation

Zbl 0457.57001
Full Text:

### References:

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