Discrete & Computational Geometry

, Volume 9, Issue 4, pp 387–426 | Cite as

Representing geometric structures ind dimensions: Topology and order

  • Erik Brisson


This work investigates data structures for representing and manipulatingd-dimensional geometric objects for arbitraryd ≥ 1. A class of geometric objects is defined, the “subdividedd-manifolds,” which is large enough to encompass many applications. A new representation is given for such objects, the “cell-tuple structure,” which provides direct access to topological structure, ordering information among cells, the topological dual, and boundaries.

The cell-tuple structure gives a simple, uniform representation of subdivided manifolds which unifies the existing work in the field and provides intuitive clarity in all dimensions. The dual subdivision, and boundaries, are represented consistently.

This work has direct applications in solid modeling, computer graphics, and computational geometry.


Geometric Structure Simplicial Complex Voronoi Diagram Computational Geometry Klein Bottle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • Erik Brisson
    • 1
  1. 1.University of WashingtonSeattleUSA

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