An EPG-representation of a graph G is a collection of paths in a plane square grid, each corresponding to a single vertex of G, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In this paper we focus on graphs admitting EPG-representations by paths with at most 2 bends. We show hardness of the recognition problem for this class of graphs, ...

We report on some extensions of the Kandinsky model: A new and highly nontrivial technique to incorporate nonplanar drawings into the Kandinsky model in the same way as in the GIOTTO approach is presented. This means a major step towards the practical usability of our approach. The used technique even gives new insights for the solvability of network ow problems. Another variant of Kandinsky en...

We study bend loss in chalcogenide negative curvature fibers with different polarizations, different tube wall thicknesses, and different bend directions relative to the mode polarization. The coupling between the core mode and tube modes induces bend loss peaks in the two non-degenerate modes at the same bend radius. There is as much as a factor of 28 difference between the losses of the two p...

spur dike is an important element for protection of river banks. spur dike causes variations in flow field, sediment transport and bed topography. the mechanism of flow and sediment transport in a channel bend is very complex, especially when a spur dike is constructed in a bend. in this paper the time variations of dimension of the scour hole and the bed’s topography were considered around a t...

Recently, a new layout style to avoid edge crossings in straight-line drawings of non-planar graphs received attention. In a Partial Edge Drawing (PED), the middle part of each segment representing an edge is dropped and the two remaining parts, called stubs, are not crossed. To help the user inferring the position of the two end-vertices of each edge, additional properties like symmetry and ho...

bendway weirs are an important tool in multi-purpose erosion control and are implemented to control erosion, restore streams, and improve habitat. these structures create a hydraulic effect that reduces erosion on the outer bank of a bend by reducing flow velocities near the outer bank and reduce the concentration of currents on the outer bank creating better current alignment through the bend....

Resonance Raman spectra were obtained for 2-nitrophenol in cyclohexane solution with excitation wavelengths in resonance with the charge-transfer (CT) proton transfer band absorption. These spectra indicate that the Franck-Condon region photodissociation dynamics have multidimensional character with motion along more than 15 normal modes: the nominal CCH bend+CC stretch nu(12) (1326 cm(-1)), th...

We consider embeddings of planar graphs in R where vertices map to points and edges map to polylines. We refer to such an embedding as a polyline drawing, and ask how few bends are required to form such a drawing for an arbitrary planar graph. It has long been known that even when the vertex locations are completely fixed, a planar graph admits a polyline drawing where edges bend a total of O(n...

We study drawings of graphs of maximum degree six on the hexagonal (triangular) grid, with the main focus of keeping the number of bends small. We give algorithms that achieve 3.5n + 3.5 bends for all simple graphs. We also prove optimal lower bounds on the number of bends for K7, and give asymptotic lower bounds for graph classes of varying connectivity.