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Abstract

Given two simplicial complexes \({\mathcal C}_{\rm 1}\) and \({\mathcal C}_{\rm 2}\) embedded in Euclidean space \({\mathbb R}^{d}\), \({\mathcal C}_{\rm 1}\) subdivides \({\mathcal C}_{\rm 2}\) if (i) \({\mathcal C}_{\rm 1}\) and \({\mathcal C}_{\rm 2}\) have the same underlying space, and (ii) every simplex in \({\mathcal C}_{\rm 1}\) is contained in a simplex in \({\mathcal C}_{\rm 2}\). In this paper we present a method to compute a set of weighted points whose alpha complex subdivides a given simplicial complex.

Following this, we also show a simple method to approximate a given polygonal object with a set of balls via computing the subdividing alpha complex of the boundary of the object. The approximation is robust and is able to achieve a union of balls whose Hausdorff distance to the object is less than a given positive real number ε.

Keywords

Convex Hull Simplicial Complex Voronoi Cell Weighted Point Underlying Space 
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 Berlin Heidelberg 2004

Authors and Affiliations

  • Ho-lun Cheng
    • 1
  • Tony Tan
    • 1
  1. 1.School of ComputingNational University of Singapore 

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