  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.
