Edge-intersection graphs of paths in grids are graphs that can be represented with vertices as paths in grids and edges between the vertices of the graph exist whenever two grid paths share a grid edge. This type of graphs is motivated by applications in conflict resolution of paths in grid networks. In this paper, we continue the study of edge-intersection graphs of paths in a grid, which was ...

In this paper, we present a new heuristic for orthogonal graph drawings, which creates drawings by performing a depth-first search and placing the nodes in the order they are encountered. This DFS-heuristic works for graphs with arbitrarily high degrees, and particularly well for graphs with maximum degree 3. It yields drawings with at most one bend per edge, and a total number of m−n+1 bends f...

This paper shows that any planar graph with n vertices can be point-set embedded with at most one bend per edge on a universal set of n points in the plane. An implication of this result is that any number of planar graphs admit a simultaneous embedding without mapping with at most one bend per edge.

The synchrotron integrals used to compute emittances, the energy spread, etc., have been analyzed assuming no coupling between the horizontal and vertical planes[1, 2]. With Mobius, these assumptions are not valid and so this paper presents the appropriate generalizations. To simplify matters it will be still be assumed that the bends are in the horizonal plane. In this case I1, I2, I3, and I5 ...

In this paper, we explore the problem of producing process diagrams and introduce a linear time technique for creating them. Each edge has at most 3 bends and portions of the edge routing have optimal height. While developing a solution, we explore the subproblems of determining the order of the layers in the diagram, assigning x and y coordinates to nodes, and routing the edges.

Spur dike is one of the hydraulic structures used in rivers to protect river banks. In this paper, flow pattern around a T-shaped spur dike which is located in a 90◦ bend and different amounts of submersion has been studied using Flow-3D. Numerical results have been compared with experimental results and have been analysed.

We consider orthogonal drawings in the general position model, i.e., no two points share a coordinate. The drawings are also required to be bend minimal, i.e., each edge of a drawing in k dimensions has exactly one segment parallel to each coodinate direction that are glued together at k − 1 bends. We provide a precise description of the class of graphs that admit an orthogonal drawing in the g...

We use basic results from graph theory to design algorithms for constructing three-dimensional, intersection-free orthogonal grid drawings of n vertex graphs of maximum degree 6. The best previous result generated a drawing bounded by an O( √ n) × O( √ n) × O( √ n) box, with each edge route containing up to 16 bends. Our algorithms initiate the study of bend=bounding box trade-o issues for thre...

We investigate the problem of constructing planar drawings with few bends for two related problems, the partially embedded graph problem—to extend a straight-line planar drawing of a subgraph to a planar drawing of the whole graph—and the simultaneous planarity problem—to find planar drawings of two graphs that coincide on shared vertices and edges. In both cases we show that if the required pl...

The aim of the present study is to investigate the stability of crack propagation in cementitious materials. Tests were conducted on bend specimens in three-point and four-point loading conditions.Three-point bend specimens showed stable crack growth for mortar, normal strength and high strength concrete specimens. Alternatively, four-point bend specimens showed catastrophic failure for mortar ...