Affine arc length polylines and curvature continuous uniform B-splines

We study the recently introduced notion of polylines that form a discrete version of planar curves in affine arc length parametrization, showing that they match the control polylines of curvature continuous uniform quadratic B-splines (with analogous results in Rn). It is demonstrated how inflection-free planar curves may be approximated by such affine arc length polylines in a way that the polyline is close to an affinely equidistant discretization of the curve and allows good approximations of the smooth affine curvature.