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Extension of the notion of map and subdivisions of a three-dimensional space

  • Pascal Lienhardt
Contributed Papers Geometrical Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)

Abstract

We define here the notion of V-map, inspired by the notion of topological map. As a map enables the modeling of a subdivision of a two-dimensional space, so the notion of V-map enables the modeling of subdivisions of the usual three-dimensional space, giving a global definition of these subdivisions, and is, to our knowledge, the first model of this kind.

After a recall of the combinatorial definitions of maps and hypermaps, and a brief recall of their interest in solid modeling (Boundary Representation), we give a combinatorial definition of the notion of V-map. Moreover, we define some operations, enabling the construction of certain kinds of V-maps, which enable the modeling of subdivisions of the usual three-dimensional space.

Keywords

Graphs maps hypermaps V-maps representation of polyhedra computational topology 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Pascal Lienhardt
    • 1
  1. 1.Département d'informatiqueUniversité Louis PasteurStrasbourg Cedex

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