Polygons with Parallel Opposite Sides
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
- 4.Giblin, P.J.: Affinely Invariant Symmetry Sets. Geometry and Topology of Caustics, vol. 82. Banach Center Publications, Warsaw (2008)Google Scholar
- 5.Giblin, P.J., Holtom, P.: The Centre Symmetry Set, vol. 50. Banach Center Publications, Warsaw (1999)Google Scholar
- 6.Holtom, P.A.: Affine-invariant symmetry sets. Ph.D. Thesis, University of Liverpool (2001)Google Scholar
- 10.Domitrz, W., Rios, P.M.: Singularities of equidistants and global symmetry sets of Lagrangian submanifolds. Geom. Dedic. (2013, to appear)Google Scholar