Simple polygons can be made convex by a finite number of flips, or of flipturns. These results are extended to very general polygons.

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

Here we study the kth symmetric trigonometric moment curve and its convex hull, the Barvinok–Novik orbitope. In 2008, Barvinok and Novik introduced these objects and showed that there is some threshold so that for two points on S1 with arclength below this threshold the line segment between their lifts to the curve forms an edge on the Barvinok–Novik orbitope, and for points with arclength abov...

At the morphism level, exponentiability implies the existence of certain injective hulls. We prove a converse statement, thus showing an intimate link between the concepts given by the title.

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm comp...

The construction of a planar convex hull is an essential operation in computational geometry. It has been proven that the time complexity of an exact solution is Ω(NlogN). In this paper, we describe an algorithm with time complexity O(N + k), where k is parameter controlling the approximation quality. This is beneficial for applications processing a large number of points without necessity of a...

Given k finite point sets A1, . . . , Ak in R, we are interested in finding one translation for each point set such that the union of the translated point sets is in convex position. We show that if k is part of the input, then it is NP-hard to determine if such translations exist, even when each point set has at most three points. The original motivation of this problem comes from the question...