2011/03/14 by Marcos Craizer, Craizer, Marcos, Ralph Teixeira +4
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #53A15 #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A15
paper · pdf · doi:10.48550/arxiv.1103.2722
16 pages, 10 figures
openalex publication_date 2011/03/14 · arxiv created 2012/08/02 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate closed convex smooth curves almost uniformly with respect to affine length, convex equal-area polygons admit natural definitions of the usual affine differential geometry concepts, like affine normal and affine curvature. These definitions lead to discrete analogous of the six vertices theorem and an affine isoperimetric inequality. One can also define discrete counterparts of the affine evolute, parallels and the affine distance symmetry set preserving many of the properties valid for smooth curves.