Discrete & Computational Geometry

, Volume 50, Issue 2, pp 474–490 | Cite as

Polygons with Parallel Opposite Sides

  • Marcos Craizer
  • Ralph C. Teixeira
  • Moacyr A. H. B. da Silva


In this paper we consider convex planar polygons with parallel opposite sides. These polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For such polygons, we define discrete versions of the area evolute, central symmetry set, equidistants, and area parallels and show that they behave quite similarly to their smooth counterparts.


Discrete area evolute Discrete central symmetry set  Discrete area parallels Discrete equidistants 

Mathematics Subject Classification (2010)




The first and second authors wish to thank CNPq for financial support during the preparation of this manuscript.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Marcos Craizer
    • 1
  • Ralph C. Teixeira
    • 2
  • Moacyr A. H. B. da Silva
    • 3
  1. 1.Departamento de MatemáticaPUC-RioRio de JaneiroBrazil
  2. 2.Departamento de Matemática AplicadaUFFNiteróiBrazil
  3. 3.Centro de Matemática AplicadaFGVRio de JaneiroBrazil

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