This paper discusses the calculation of bend minimal shapes for non-planar graphs with given topology. Based on the Simple-Kandinsky drawing standard – a simplification of the more complex Kandinsky standard – we show the disadvantage of using standard models for this task: We show that the minimal bend count is suboptimal, when these models are applied to non-planar graphs; it is therefore ben...

In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal (45◦) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A k-planar graph is a planar graph in which each vertex has degree less or equal to k. In particular, we prove that every 4-planar graph admits a planar...

A rigorous classical analytic model of confined optical wave propagation along 2-D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise frequency domain ansatz for bend mode profiles in terms of Bessel and Hankel functions. This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of...

In this study, the effects of heat treatment of aluminum alloy on the tube bending process were investigated in the rotary draw bending process. As two experimental and numerical simulation methods were used to determine the wall-thinning, ovality, and spring back for extruded, annealed, and aged AA6063 aluminum alloy tubes in different bending angles and bend radii. Numerical simulations were ...

Polarization dependence of bend loss caused by the polymer coating layer for a standard singlemode fiber (SMF28) is investigated theoretically and experimentally. Bend loss for SMF28 for both the TE and TM mode is calculated separately. Normalized polarization dependent loss is proposed for the characterization of the polarization sensitivity of bend loss for different bend radii. Corresponding...

We modified a 2-bend cystotome for continuous curvilinear capsulorhexis (CCC) in manual or phacoemulsification cataract surgery to improve the safety and ease of performance. A 26G needle was converted into a cystotome with 3 bends. In this retrospective study, the performance of modified 3-bend cystotome was compared with conventional 2-bend cystotome. During cataract surgery, in the 3-bend cy...