Single point incremental sheet metal forming is a sheet metal forming process that forms products without the complex dies and tools with low cost. In this study, the incremental sheet metal forming process has been experimentally investigated on the explosively-welded Al/Cu bimetal sheets. Also, the effects of process parameters, such as arrangement of layer`s bimetal, tool diameter and tool p...

We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of n pseudolines has no member incident to more than 4n/9 points of intersection. (This shows the “Strong Dirac” conjecture to be false for pseudolines.) We also prove non-trivial lower bounds on the maximum number of intersection points on any curve in an arrangement of curves in the plane, for various classe...

Among the many ways to view oriented matroids as geometrical objects, we consider two that have special properties: • Bland’s analysis of complementary subspaces in IRn [2] has the special feature that it simultaneously and symmetrically represents a realizable oriented matroid and its dual; • Lawrence’s topological representation of oriented matroids by arrangements of pseudospheres [4] has th...

We study two kinds of segment orders, using definitions first proposed by Farhad Shahrokhi. Although the two kinds of segment orders appear to be quite different, we prove several results suggesting that the are very much the same. For example, we show that the following classes belong to both kinds of segment orders: (1) all posets having dimension at most 3; (2) interval orders; and for n ≥ 3...

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.

Let GH(S; H) be the bipartite graph with partition sets S and H , the set of simplices and hyperplanes of H, where simplex s∈ S is adjacent to hyperplane h∈H if one facet of s lies on h. In this paper, we give a complete characterization of GH(S; H) when H is a -arrangement. We also study GH(S; H) when H is a pseudoline arrangement. c © 2001 Elsevier Science B.V. All rights reserved.

Any finite set of lines in the real projective plane determines a cell complex; these complexes and their combinatorial properties have been a subject of study at least since 1826 [9]. More recently, Levi [6] considered a topological generalization of this notion, defined as follows: Consider a simple closed curve in RP2 which does not separate RP2; this is called a pseudoline. (It is clear tha...

Let G = (V0; V1 ; V2; E) be a 3-layer graph. The 3-layer drawings of G in which V0 , V1 , and V2 are placed on 3 parallel lines and each edge in E is drawn using one straight line segment, are studied. A generalization of the linear arrangement problem which we call the 3-layer pseudo linear arrangement problem is introduced, and it is shown to be closely related to the 3-layer crossing number....

We introduce a new combinatorial object, the double-permutation sequence, and use it to encode a family of mutually disjoint compact convex sets in the plane in a way that captures many of its combinatorial properties. We use this encoding to give a new proof of the Edelsbrunner-Sharir theorem that a collection of n compact convex sets in the plane cannot be met by straight lines in more than 2...