2016/09/28 by Marcos Craizer, Craizer, Marcos, Sinesio Pesco +1
Mathematics · #53A15 #53A20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53A15 #msc:53A20
paper · pdf · doi:10.48550/arxiv.1609.08906
18 pages, 11 figures
arxiv created 2016/09/28 · arxiv updated 2016/09/29
Equal-volume polygons are obtained from adequate discretizations of curves in 3-space, contained or not in surfaces. In this paper we explore the similarities of these polygons with the affine arc-length parameterized smooth curves to develop a theory of discrete affine invariants. Besides obtaining discrete affine invariants, equal-volume polygons can also be used to estimate projective invariants of a planar curve. This theory has many potential applications, among them evaluation of the quality and computation of affine invariants of silhouette curves.