We investigate weighted straight skeletons from a geometric, graph-theoretical, and combinatorial point of view. We start with a thorough definition and shed light on some ambiguity issues in the procedural definition. We investigate the geometry, combinatorics, and topology of faces and the roof model, and we discuss in which cases a weighted straight skeleton is connected. Finally, we show th...

In this paper, a three dimensional analysis of arbitrary straight-sided quadrilateral nanocomposite plates are investigated. The governing equations are based on three-dimensional elasticity theory which can be used for both thin and thick nanocomposite plates. Although the equations can support all the arbitrary straight-sided quadrilateral plates but as a special case, the numerical results f...

Sexual orientation can be accurately identified from photos of faces, but previous work has focused exclusively on straight versus gay and lesbian individuals. Across three studies, the current work investigated the facial perception of bisexual men and women, a less socially salient category. Although participants could identify straight and gay men at above-chance levels in a trichotomous cat...

By means of He's homotopy perturbation method (HPM) an approximate solution of velocity eld is derived for the ow in straight pipes of non-Newtonian uid obeying the Sisko model. The nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to He. Furthermore, the obtained solutions for velocity eld is graphically sketched...

We give an algorithm that reduces the straight skeleton to the motorcycle graph in O(n log n) time for (weakly) simple polygons and O(n(log n) logm) time for a planar straight line graph with m connected components. The current fastest algorithms for computing motorcycle graphs are an O(n ) time algorithm for non-degenerate cases and O(n ) for degenerate cases. Together with our algorithm this ...

The classical Fáry’s theorem from the 1930s states that every planar graph can be drawn as a straight-line drawing. In this paper, we extend Fáry’s theorem to non-planar graphs. More specifically, we study the problem of drawing 1-planar graphs with straight-line edges. A 1-planar graph is a sparse non-planar graph with at most one crossing per edge. We give a characterisation of those 1planar ...

We prove that any PSLG has a conforming quadrilateral mesh with O(n) elements, all angles ≤ 120◦ and all new angles ≥ 60◦ (the complexity and the angle bounds are both sharp). Moreover, all but O(n) of the angles may be taken in a smaller interval, say [89◦, 91◦]. Date: January 2011. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary: