Polygons with Parallel Opposite Sides
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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.
KeywordsDiscrete area evolute Discrete central symmetry set Discrete area parallels Discrete equidistants
Mathematics Subject Classification (2010)53A15
The first and second authors wish to thank CNPq for financial support during the preparation of this manuscript.
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