Discrete & Computational Geometry

, Volume 47, Issue 2, pp 393–414 | Cite as

Dual Complexes of Cubical Subdivisions of ℝn

Article

Abstract

We use a distortion to define the dual complex of a cubical subdivision of ℝn as an n-dimensional subcomplex of the nerve of the set of n-cubes. Motivated by the topological analysis of high-dimensional digital image data, we consider such subdivisions defined by generalizations of quad- and oct-trees to n dimensions. Assuming the subdivision is balanced, we show that mapping each vertex to the center of the corresponding n-cube gives a geometric realization of the dual complex in ℝn.

Keywords

Simplicial complexes (Hierarchical) cubical subdivisions Counting Distortion Freudenthal triangulation Geometric realization 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.IST Austria (Institute of Science and Technology Austria)KlosterneuburgAustria
  2. 2.Departments of Computer Science and of MathematicsDuke UniversityDurhamUSA
  3. 3.GeomagicResearch Triangle ParkUSA

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