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Gift-Wrapping Based Preimage Computation Algorithm

  • Yan Gerard
  • Fabien Feschet
  • David Coeurjolly
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4992)

Abstract

The aim of the paper is to define an algorithm for computing preimages - roughly the sets of naive digital planes containing a finite subset S of ℤ3. The method is based on theoretical results: the preimage is a polytope that vertices can be decomposed in three subsets, the upper vertices, the lower vertices and the intermediary ones (equatorial). We provide a geometrical understanding (as facets on S or S ⊝ S) of each kind of vertices. These properties are used to compute the preimage by gift-wrapping some regions of the convex hull of S or of S ⊝ S ∪ {(0,0,1)}.

Keywords

Convex Hull Double Inequality Discrete Apply Mathematic Visibility Cone Digital Plane 
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 2008

Authors and Affiliations

  • Yan Gerard
    • 1
  • Fabien Feschet
    • 1
  • David Coeurjolly
    • 2
  1. 1.LAICUniv. Clermont 1AubièreFrance
  2. 2.LIRISUniv. Lyon 1, Bât NautibusVilleurbanne CedexFrance

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