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Meshes Preserving Minimum Feature Size

  • Greg Aloupis
  • Erik D. Demaine
  • Martin L. Demaine
  • Vida Dujmović
  • John Iacono
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7579)

Abstract

The minimum feature size of a planar straight-line graph is the minimum distance between a vertex and a nonincident edge. When such a graph is partitioned into a mesh, the degradation is the ratio of original to final minimum feature size. For an n-vertex input, we give a triangulation (meshing) algorithm that limits degradation to only a constant factor, as long as Steiner points are allowed on the sides of triangles. If such Steiner points are not allowed, our algorithm realizes \(\ensuremath{O}(\lg n)\) degradation. This addresses a 14-year-old open problem by Bern, Dobkin, and Eppstein.

Keywords

Feature Size Steiner Point Linear Number Interior Face Minimum Feature Size 
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 2012

Authors and Affiliations

  • Greg Aloupis
    • 1
  • Erik D. Demaine
    • 2
  • Martin L. Demaine
    • 2
  • Vida Dujmović
    • 3
  • John Iacono
    • 4
  1. 1.Université Libre de BruxellesBelgium
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.Carleton UniversityOttawaCanada
  4. 4.Polytechnic Institute of New York UniversityBrooklynUSA

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