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 ...

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 ...

In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators ...

It is hereby established that, in Euclidean spaces of finite dimension, bounded self-contracted curves have finite length. This extends the main result of Daniilidis et al. (J. Math. Pures Appl. 94:183–199, 2010) concerning ...

The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. Based on this link, we propose an extremely ...

This paper develops a new scheme of four points for interpolating curve subdivision based on the discrete fi rst derivative (DFDS), which reduces the apparition of undesirable oscillations that can be formed on the limit ...

The discrete Fréchet distance is a measure of similarity between point sequences which permits to abstract differences of resolution between the two curves, approximating the original Fréchet distance between curves. ...

A discrete element method is designed to evaluate the relative wear on hoppers caused by friction during operation in an open-pit mine. The results of the model show good agreement with measurements on real industrial ...